Hi, during these trying times of the pandemic, the City of Columbia Parks and Recreation Department realizes that choices can be limited in enhancing one's physical, social and mental well-being. The Parks and Recreation staff have been involved in developing a number of videos in which citizens can participate in and enjoy in the privacy of their own home. These videos consist of arts and crafts, gardening, physical activity and sports instruction with many more to come as we work through this pandemic. The videos will be available to you on a number of our social media outlets. We hope you enjoy and thank you very much. Hi, my name is Bohumila Augustinova with Columbia Earth Center with Parks and Recreations for City of Columbia and today we will be making a puppet out of recycled materials. So I made a little sample here, a little simple dog, but you can make any kind of animals and what are we using today is toilet paper rolls. We're going to use some craft paper, but you can also use scrap of fabrics or magazines and newspapers and a piece of string. I am going to use a yarn, but any kind of string will do, ribbons, twine, whatever you have at home could be used. We also have, I'm using a popsicle stick, but you can use a twig or any kind of piece of wood. The first thing is to decide what kind of animal we're going to make and I have a little dog so I'm going to make a little dog again and I believe that dogs can be any color. So I'm going to use my craft paper first and measure the width of the paper and cut it out. I'm just going to glue this piece of paper on. So you want to glue the whole surface and like with every glue you want to give it a few seconds to start working. If you put the glue on a surface and put the paper on it right away it is not going to stick. So you want to have maybe 15 seconds before you actually start gluing. Put this around the roll and try to make it nice and neat, but you don't have to use paper if you don't have a craft paper at home. You can use fabric scraps, you can use magazine paper or you can just use your crayons and pastels and draw designs. You do not have to use craft paper.  Now the head of the piece doesn't have to be as big so we're going to cut it I would say maybe to half. Okay so now that we have the base of the body and head done we're kind of going to figure out where we're going to make the holes for legs and the neck for when we're putting the strings through. So we are going to need four holes on the bottom of the body and two holes on the top. I kind of want to make sure that they are in the same area so you don't have a crooked legs or anything like that. And I do love this tool, you can buy it in any craft store. If your mom sows or your grandmother sows she probably has one of these at home and they're super safe to use. So we're going to make four holes right here and two holes on the top. And this would be the part to do any kind of decorations. I like to use scrap paper every bits and piece of it and so this is perfect. If you already have pieces like this just use them. So I have a couple stripes or three stripes I'm going to attach them here. I hope my dog won't look too much like a zebra. I do like using glue sticks for projects like these because it's just not as messy. If you're using regular glue it's a little messier but it can be done just when you do so. Maybe use a brush to keep things little neater.  We actually have a little set of googly eyes but you don't have to use those. You can use markers or buttons or scraps of paper.  I actually really like to use the leftover of my roll and kind of do that as a support for my ears.  You cut it out and use it to make sure your ears are matching. Glue this on to our toilet paper roll cutouts. So we can attach them to the dog and just make sure when you're gluing them on the actual head you don't cover the hole that we already punched through and you're going to have to hold this just for a few seconds again for the glue to attach. Okay so now we have a head and the body kind of done and let's put it all together. So I have a yarn together today with me but as I said you can use any kind of string anything you have at home could be done. I'm going to pull this string through one of the legs, through the inside of the tube and down inside of the leg. So we want to make sure our legs are about same length but for right now we kind of want to keep them a little longer so we have enough room to make a knot on the bottom. So I have some beads here today. If you don't have beads you can use a lid from your soda bottle and these are really great. They have a big holes in them so they're really easy to string through. So the best way to kind of ensure that the bottom bead stays on that kind of holds everything I'm actually going to loop it around and tie the knot above the bead. Move this out of the way so you actually see what I'm doing. Tie a knot, let's make a double just for safety or you can put a little bit of glue there, piece off and now the beads are not going anywhere they're just there. Okay let's do the other side and great thing about doing the legs this way is that you don't have to measure and worry about how you make your legs symmetrical because then you can just adjust the length like this. Alright now we have a front legs let's give it a back legs.  You can start with the knot and pull it through the bottom hole and again I'm making a double knot just to make sure that everything's secure. We want to attach it to our popsicle stick we're going to get our yarn again and we're going to cut two slightly longer pieces they're not going to have to be the same length but we can adjust that. So the longer piece will go on the back of the dog's body and the shorter piece is going to go on the head and we're going to I'm actually not going to attach this just yet to the popsicle stick I'm going to wait when I have the front done as well. Okay now we kind of want to make sure that our dog is even when we're attaching it. So I'm going to give it a little bit of a trim over here kind of make sure that this part and this part are about the same. And now we're going to attach them to our stick. We just wrap it around give it a nice tight knot over there. As I said before if you don't have popsicle sticks at home you can use any piece of wood you can use twigs of course you can play with this and add tail which we can do right away or tongue or anything you really want to do with your dog right because he's yours you can get creative you can decorate your stick as well. If you're using if you're doing a tail best thing to use is a little pipe cleaner. You can cut those very easily and I am actually going to tape it on the inside of the dog's body. When pipe cleaners are super fun you can actually do the legs with pipe cleaners as well and we can give a happy tail to the dog. Let's give him a little bit of a pink one. I have a little bit of pink paper here.  All right now we're going to tape it in. We made a dog.


Okay, la registrazione si esa. Thank you. All right. So for this second half of today's class, we are gonna derive the optimality equation for the discounted setting, okay? So the good news is that if you are not impressed about all the heuristics we've been giving in the last part, doesn't really matter because we start, basically from scratch and derive the Bellman's equation from its bare assumptions, okay? So this where the first part was meant as a motivation. Maybe after the fact you will want to go back and understand where it comes from, okay? So let's recap what the problem is. We want to find out the policy, you know, a single actually policy by AS which maximizes, so this will be our optimal policy, which maximizes our expectation going from zero to infinity of the discounted rewards which we can write as usual in this form. And just as we did for the time-dependent Bellman equation, we introduce value functions for a certain policy pi, okay? So specify the policy. We have the expectation of the same discounted sum. Now it's conditioned on the fact that we start at the initial time at a state S, okay? So nothing has changed except for these minor changes about the presence of the horizon and the presence of discount factor in this definition. All right, so and then in a sense we want to find that what is the optimal value function, this object, which is the one which maximizes overall positive policies to value function. So once we have obtained this, we know what the best policy is in a way that we will figure out in a second. So this is just to recap what the task is. So the first step in this derivation, so the step one is to find a recursion relation, okay? So this will be very similar to what we did for the time-dependent Bellman equation. So I'm gonna go quite quickly on this. If we start from the value, what we do here, as usually we split this sum here into two terms. So this is gonna be the expectation of the reward for the first step, that is for state S which is the initial state, action one, state two, okay? Which I can say S note as if you wish, same clear, plus gamma, and then I have the sum from T going to from one to infinity. I pulled out a gamma here explicitly so that this becomes the T minus one and then I have R ST, AT, ST plus one okay, all this is conditioned on S mode equals S. And so very easy step, separate what is happening now from what is happening from the next step until infinity. And then just going by the same steps that we had last time, we see that this first average can be written as sum over all possible S primes and A, or again, S note is S, so I have to pick an action from S, then I have to pick a new state from S and A and then I have my average reward for the triplet SAS prime. So this is this first expectation value. And the second expectation value is plus gamma and it's absolutely similar in the sense that I pick an action. I'm sorry. Yep. S is S naught. Yeah, they are the same. Yeah. Okay, and in the first equation, it's S R of S zero, A one, and S one. No, no, you're right. You're right. So thank you. Thanks for pointing that out. Okay, so the same happens here. We are going to move one step forward. And then in that step, then we get, we see the new value function in the new state S prime. And that one, we put everything together here. We went up with our recursion relation, which is sum over S prime, A of I S, A of, okay. And we're writing this here, this object. Now, this is a recursion relation, which is recurrent, strongly recurrent, because there's no more this feedback structure that there were for times. So you don't have a vector at a certain time and then you can derive the vector the previous time. Now, every state talks to every other state with the same object, okay. But nevertheless, you can solve this equation. It's a linear equation. So you can solve it very simply. It requires just one sweep to be solved explicitly. And this is our starting point. Then the second step is to look, step two, look for optimal P. Okay, V star, which is the vector of optimal values. That is what you get on average if you follow the optimal policy yet to be discovered. Now the proof of the optimality equation is extremely straightforward. So it's a mathematical proof. So it's very elegant and concise. It doesn't shed a lot of light on what is happening, but we will derive the Balmain's equation in other ways tomorrow in order to see more from the different angles what is happening. But now this proof will just require basically four lines of computation. And it starts out as it should in the sense that the definition of the optimal value is just the maximum over all possible policies of the value of any given policy, okay. So, and then the next step is nothing but replacing this quantity by the explicit expression that is in the red box above, okay. So quite not particularly demanding from the intellectual viewpoint, I just copy. Okay, now in taking the maximum, there are here of course a couple of problems because you cannot take the maximum inside simply because there's a sum. So you cannot just make it go through. It's a non-linear operation, okay. So in order to manipulate these things we have to do something. So the first thing we do is quite obvious in the sense that by definition V star is optimal, okay. So for any pi by definition, let me write here, by definition of V star we have that P star S is larger equal than V pi S for any state S just because it's a maximum. So using this I can say that this quantity here since it has a V pi in here is a smaller equal than the same thing where I replace V pi with V star. So you see what has happened here? This thing here, I replaced with this one because of the property of the maximum. Okay, quite easy so far. Next step is again, relatively simple. We have to look now, what have we gained here from going from here to here? Is that pi has disappeared here? So there's no pi any longer inside. The only pi is here. So second step of this second step second step, we realize that term in square bracket is linear in pi. So the dependence on the policy of the term over which we maximize now is linear. And therefore, as you remember, we discussed this last time. When you optimize a linear function over a convex set the maximum takes place on the boundaries. If you remember, we had this very simple example. So let me go back to that for a second. So maybe it refreshes your memory. We've been discussing this at the end of last lectures. So the linearity and the example was this one in the very simple case in which you have a policy of two actions. This means that it's a linear function so it can only take values at the boundaries which in this case are zeros and ones. And the value that it takes is just the maximum between the two coefficients that are in front of this. So the equivalent multidimensional argument here leads us to say that this object here is equal to the maximum over a and we drop the pi in there. So once again in interest of clarity. So we've been using the property of optimality of V star to simplify the dependence on the policy of the right hand side. What is under the maximum operator? The first line on the top has become the third line and the third line has become the fifth line because of linearity in the policy. This is very nice, but we have an inequality yet here. So we wish to find an equality. So we have to do a little bit of steps yet. So now next step that we do is that we define, we define arbitrarily a new policy. Let's call it pi bar, which is defined as the arc max over a of this last square bracket. Sorry, this sum here was over as far in. Of course, S prime of B of S prime S a. This is not going to end well. So let me take some more space here. This defined as the arc max over a sum over. And then again, I'm coping the last line. Okay, so I am defining a new policy which was not present at the beginning. Now, what is important, if I choose this, this means that this last line that I have here is also equal to the value of my policy pi bar by definition, because if my policy is to pick the argument of this, then the maximum is just the value of my policy, okay? Because I use the recursive relation, okay? So this is just an autology, it's just by definition. But then if this is true, well, this is one possible policy among many. So again, this has to be suboptimal by definition. So this has to be smaller than B star. And therefore, if you look at this in full, well, you have this here and you have this here at the beginning, this is where we started from. So I don't know if you probably it's not possible to see it in all, but we started from here. And then we put series of less than, less than something which is the same thing which we added at the start. So this chain of inequalities basically is our starting thing is less equal than our final thing which means that they must be equal and everything that is in between must be the same, right? So as a result of this chain of inequalities, also this object must be equal to B star. So that putting all things together, we can conclude that B star of S is equal to the maximum over A sum over S prime, which is the Bellman's optimal equation. And which is nothing but exactly the same thing that we derived heuristically in the first half of today's class. So the intuitive solution of the problem which could have been demonstrated to be true otherwise is also shown to be valid by this mathematical reasoning.   We will give, like I said, tomorrow, more concrete proofs about how this optimal equation emerges, okay? A more sort of little bit more constructive way of deriving it. But that's the bottom line. This is the Bellman's optimal equation. Now that we have an equation, again, this is a no linear equation. We cannot use dynamic programming, okay? Because we have the same thing on the left and on the right. So we have to find out some other way of solving this equation. But first of all, if we approach this problem mathematically, the first question is, are there solutions to this equation? Are they unique? So now what I'm gonna do in the next minutes that are left is to derive one result which answers to these three questions altogether. That is, it will tell us that the solutions exist, that they are unique and will give us a method to solve them, okay? So the following step that we take now is step three, solving Bellman. Okay, so the first thing to notice is that if we reason at a very abstract level, we can write down the Bellman's equation in the following form. So V star, you can see it as a vector, okay? V star is a vector in R to the cardinality of the state space. Oh, you're frozen again. Hello, hello. I can hear you, but the screen is frozen. Now I can open it. No, it's like the freezing came with a little bit of lagging. Hello, you were totally frozen for a while. Yeah, we saw you freezing after that you say that you are frozen, but no, it's okay. Okay, so V star is, you can think of it as a vector in a space which has the dimension of the number of states. And before we can write down the Bellman equation in the following formal way, which is some operator B acting on V star gives back V star. So what this operator is while you read it from here, you have to take your vector V star here. You multiply it by gamma, you make a linear combination with the transition probabilities and you add on top of this other thing, okay? So it's a combination, and then you take the maximum. So it's a combination of linear and non-linear operations that returns you another vector. And we call this non-linear operator without much of a imagination, it's Bellman operator. Now what we're gonna show here is that this operator B is contracting. What does it mean to be contracting? It means that it takes pieces of the space of this space where the value functions leave. And if you take any pair of points in this space, this operator brings them closer. So it creates, if you apply this operator to a cloud of points, this cloud of points will get closer. And then intuitively, this means that if you repeat many times this operation of applying the Bellman operator, this will get you closer and closer and closer, which is the important intuition. Because this will tell you that there exists a solution which is the center of this contraction. And this solution is unique. This is what is one example of a broader concept in mathematics, which is called the fixed point theorem. Okay? So, excuse me. Let's move on and try to prove the contractivity of the Bellman's operator. So again, it's quite compact as a proof. It works as follows. Take two vectors, W1 and W2 in this space where the value functions leave. A vector which has as many entries as states. Then you ask yourself, so if I apply B to W1 and B to W2, and then I take the norm according to some norm, what is it? So my goal is to show that this distance is smaller than the distance between W1 and W2. So if I take two vectors and I apply the Bellman operators, after one iteration, they will be closer, okay? That's my goal. How do I go about it? Questions, any questions? If I go about it, I will go about it. So let's first replace my definition of the Bellman's operator. This is just copying and pasting the definition. So this is max A of sum over X prime. Sorry, not to restart, but minus. So this just follows from the definition and there is an absolute value outside, okay? No manipulation here so far. Now, remember, we want to show that this is smaller than the initial one. So we want to bound this expression with something that is larger than that. And the basic idea here is let me take a short break by using a different color. So what I'm going to want to show here is realize that this is the difference of two maxima, okay? So it's a maximum of a vector minus the maximum of another vector. So I'm gonna use, so let's draw a little box here. I'm gonna use a very simple inequality. So this is very simple inequality and I'm just gonna play around with that a little bit. So let's suppose we have the maximum over A of the difference of two functions, F and GA. Then if I take this as the, I sum the maximum over GA. This is smaller equal than the maximum over A of the sum of these two, which is F, A. So this is very straightforward to show, okay? Because the maximum of a sum is less than the sum of the maximum, okay? So recall that the maximum of the sum of two functions which are different from this, let's say H1A plus H2A, okay? So since every one of this is a smaller equal than the maximum over A of the maximum of each, and then this maximum here doesn't matter any longer, the one outside, this is equal to maximum over A of HA prime plus maximum over A of HA2, okay? So the same inequality here, if you use it by changing the names of H1 and H2, you get this. And therefore this tells you that the maximum of, yeah, the difference of the maxima is smaller than the difference of this two taken in the proper order, okay? So you can use this to bound the absolute value of this, okay? So basically this tells you that maximum A of FA minus maximum A of GA is smaller equal than the maximum A of FA, okay? So we're gonna use this here. The difference of maxima, we can sum inside, so algebraic sum of the things that are inside. So take this minus that, this minus that, and therefore be able to write that this object is smaller equal than the maximum over A of the difference. But when we take the difference, you realize that the first term here is the same.  And therefore what you get is that this is smaller equal than gamma times sum over S prime E of S prime S A E of S prime S A W one S prime minus W two S prime. This is close and then there is an absolute value outside. Okay, now next step. Excuse me, but according to the last orange equation, if I'm solving it, I'm obtaining that the sum of the maximum over A of F A minus GA plus the maximum of GA is greater than... Oh, sorry, yeah, I don't know what I'm writing here. They're perfectly right, sorry. So that's not what I'm writing here. Sorry about that. Yeah, so let me just go quickly through it, see what was wrong with this last step. Oh yeah, because I was wrong in the first, sorry, sorry. I copied this thing wrong in the very beginning. Apologies, apologies. This is the statement which derives from this, okay? So if you recombine, then it's the first line as they are in the opposite dimension. Thank you for pointing that out. I see you're wide and awake much more than me. Very good. So you can directly check this separately. It's just a straightforward calculation, but I was wrong in writing down the answer at the top. Very good. All right, so if you use this, then we go to the next step. And then, of course, there are a few things, few easy things to do. The first one is to pull out the gamma, which is the number. It's just a prefactor. And then the second thing we can do is that, so this is every one of this term here is actually smaller equal than the modulus, okay? So this is, again, very quite obvious. If it's positive, it's the same. If it's negative, it's less than the absolute value. So we can bound this with the modulus. And of course, if this is positive, then all these, the things which are inside the square bracket are also positive. So I can drop out to the modulus outside because everything will be positive. And this becomes the sum over S prime P of S prime S A times the modulus of one, S prime W two. Very good. Next step. So next step, we are going to introduce the infinity norm, okay? Which is a mathematical concept. It's a distance in vector space, which is defined as, or it's also called the total variation distance. It's just the maximum overall S, which are in the S of the modulus of the vectors, of the components of the vectors, okay? So it's a norm.  It's not the Euclidean norm, but it's a proper norm. If you're thinking of it geometrically, the Euclidean norm has a level lines which are spheres. In this case, the infinity norm has a level lines which are squares, okay? Cubes, hypercubes. Okay. So if you define this, then you realize that you can bound each of those, each of these terms. These are components of a difference of two vectors. So you can go one step further and say that this is the infinity norm of W1 minus W2 is bounded by this. Because every component must be smaller than the norm in absolute value, okay? Then now we're almost done because now the sum over S prime is acting only on this. But this is a probability. So this object gives one. And now the next nice thing is that the maximum over A now is totally vacuous because the dependence on the action has disappeared. So this object is actually equal to gamma, the infinity norm of W1. So let's look at where we started from, okay? So this was basically, if I have to write it properly here, so I'm sort of making it even more transparent. This was taken for two different S, okay? Because there was still an S around. So this was component by component, okay? You see that there was this dependence on S heading over. So recap, we have shown that the Bellman operator applied to the vector W1 component S minus the Bellman operator applied to vector W2 component S the modulus is smaller equal that gamma, the infinity norm of W1 minus W2. This is valid for all components. So I can take on both sides, I can take max over S on both sides and the max over S of what is here is just the same thing because there's no dependence on the component. But what this object here is for by definition the maximum of the modulus of this is just the infinity norm. And then we're done. We're done because now we conclude that if gamma is smaller than one, the Bellman operator is contracting. And then by the fixing point theorem, we conclude that B V star equals V star has one unique solution which is again intuitively given by this property of contracting points. Okay, so first take home message. This apparently nasty nonlinear equation in fact has rather nice mathematical properties at least when we use the infinity norm. Okay, so we will discuss a little bit if this is really crucial or this is a mathematical artifact. I can anticipate that it's mostly for demonstration purposes that you can sort of make it more sensible even with other norms. It's not a necessity, okay? Why do we care about this? Well, I mean, it's a good and interesting mathematical property which we have to cherish because this means that if we find, if we look for an optimal solution of our planning problem, we don't risk ending up in the spurious optimal results or local maximum, for instance, okay? This is not the case. This has a unique optimal solution which is not obvious from the outside. But it's even more interesting than that because this provides us step four. An algorithm for solution. And this algorithm is called value iteration. So what is the area? Well, the area is extremely straightforward. So the pseudo code for this algorithm is the following. Initialization, choose vnode. What is vnode? It's a guess. It's a guess for your value function, okay? Thanks to the fact that the Bellman operator is contracting, everywhere contracting, it doesn't matter where you start, okay? So your initial guess, did you miss any part of? The initial guess. The initial guess is arbitrary, okay? Because it doesn't matter where you start, you will always be converging to the optimal solution. But of course, if you start very far away, it will take a lot, okay? This is to be expected. So then you define your next, then there is a loop, which defines your next approximation to the value function as the Bellman operator applied to your previous approximation. So you start with a guess, you apply the Bellman operator. This produces another vector, and then you repeat this again and again and again until your distance from the new guess to the previous one is smaller than some tolerance, okay? Where you should define this in the infinity norm in order to be able to apply the theorem, okay? So when the two vectors, the previous one and the new one are close enough in this hyper-cubic distance, then you call it off. You say, okay, I'm happy. So you're close enough and then you define your optimal approximation to the policy. So you're after this step when you're exited. So this is return, the optimal policy, the approximation, which is, as usual, a function which is defined as the arc max over a of the Bellman operator. So it's S, S prime, C, R, S, K, S prime. Okay, so it's the usual thing that I'm rewriting thousands of times all over again. So even if you cannot read it well, it's the same object which has appeared many, many times. And that, this algorithm guarantees you that given the tolerance, you are within, you are close to the optimal policy as much as you want. If you decrease the tolerance, you will get even closer. So in a sense, this tends to be star and pi star. And pi star. So graphically speaking, just to give you the final intuition toward what is happening here. So you may think of this being the space of values, okay? So it's not a line, it's a possibly high-dimensional space. So this stands for something which should be R to the power number of states, real numbers to the power number of states. So this is the space of values. Now, then there is a function which sends values into values, which is the Bellman operator. So how the Bellman operator is to think about it as something like a function like this, which everywhere has a slope lesser than one, okay? So this is what the B of V is. Like the graph for B of V. Everything is, I mean, this is just a one-dimensional sketch. So be aware that these are maps of vectors into vectors, okay? So, and this axis would be the outcome. So again, here, I drew it really horribly. So please let me just try to do it better. Otherwise, this is gonna be messy. It's something like, all right. And it's no linear, okay? So I'm trying to draw something which is at the same time, no linear, but not too ugly. So it has to have the right properties, something like curve like this, okay? So what is the solution of the Bellman equation? Well, it is a solution when there's two lines. Oh my God, this is open. So this is the curve of V prime equals V. And this is V V prime equals V V, okay? So this object here, this point here, this is V star, which is the solution of V star equals V star. The contractivity property is equivalent to saying that this green curve here has a slope lesser than one. Why is that? Because if I take two points like W1 and W2, what will happen to them? Well, I look at here and then this will be my, the position of my W1 prime and W2 prime, which correspond to this. And you see that if the slope is lesser than one, two points which were far apart will become close. So this is the contractivity property. And what does the value iteration algorithm do? Well, you start from one guess, okay? Say you start from, let's use another color. Let's, you start with your guess V nodes, then you go up, you see, okay, this is sending me to a value which is larger than V nodes but because the green curve here is above the white one. So this will send me to V1 here. And then if I apply again the Belman operator, I will get here and so on and so forth. So you see that this sequence approaches V prime and the same thing happens V star. And the same thing happens from the other side. Of course, again, this is one dimensional, but you can take my word that this idea of contracting does the same job in an arbitrary number of dimensions. Okay, so I think that that was quite a lot for today. In the exercises session, you will see how this value iteration works, okay? But tomorrow for starters, I will go back to this idea of value iteration and show you a little bit, some intuition about what kind of approximation it produces in some simple example, like the green one, okay? But that's for tomorrow. Fine, any questions? I just wanted to ask you just a little bit above what you wrote, okay? Where there's the infinite norm of Vk plus one minus Vk, it needs to be lesser than you said, tolla. And I think also- This is some tolerance that you decide at the beginning. Okay, so you have to decide when to stop, okay? So you basically decide maybe I want to stop when the difference of my value functions is lesser than given number or you can use actually other things. So you can use also the percentage change, okay? So you might want to also to choose when these objects divided by the norm of Vk infinity becomes smaller than something, okay? So you have different choices depending on if you have an idea of the vertical value that it takes or if you haven't, you maybe want to use the percentage tolerance. It's the substance of the algorithm doesn't change. The performance might be different, of course. This requires a little bit of craftsmanship to be tuned. Thank you. So, any other question? Okay, so that's good. Thank you very much and see you tomorrow at nine, okay? Okay, thank you. Thank you, bye. Have a good day.


We're here with MK Here are some of the things that have been announced here at IO today Who are you and why? Hi I'm Mariko You're terrified already I'm here because you DM'd me that I need to be here. That's actually correct. That's the first correct answer So how is it you got started in the web then right rather than native? I just kind of figure that out. So I well, so I grew up in kind of like very technologically inclined family like I was I always had access to a computer and Internet from I don't know grade four or five or something It was never like oh, this is amazing I'm gonna like code like assembly in like Commodore 64 and then I'm gonna be a programmer situation I just had there around and One computer that I had came with a like a web authoring tool that was made by IBM Came with Windows machine. What I wasn't dream of either. It wasn't dream we were dream we were was college for me What was the IBM one then so this is the one called IBM home page builder home page builder excellent I believe it is developed in IBM Japan Maybe Japan local, but that was my first authoring tool and it was amazing It had a GUI like very simple GUI because it was the back then when you know, you are designing page with Flames and tables. Yeah, so making with a wig was a little frame set simpler Right frame set. Yeah menu on the side and then it could resize it as a user Yeah And then I think it has a tab to open the HTML code but back then like it wasn't you know Complicated, right? So as a elementary schooler. I was just I kind of figure that out by just praying this this web authoring tool and then Somehow I already had access to internet. So I must have searched on the internet or whatever. I Do remember I didn't have Google. I did not use search engine. It was a delectree. Oh, yeah, like a Yahoo director Yeah, yeah, yeah, I was I was guided to the Yahoo kids because I was Yahoo kids, you know yeah somehow I found out what the FTP was and Signed up for free hosting with the ad banner that comes with it. Remember? And then I followed it and started making websites I think one of the things that really brought me to the web is that how quickly you can get something on screen when I tried to do I was gonna say real programming. Let's not say real programming But what actually definitely it felt to me at the time real programming versus whatever this new thing was and like You know, you felt like you're writing loads of code and this other thing and all you were doing is outputting some text Where it's on the web you're doing h1 and I've got big text and that font red now It's now got red text of marquee now. We're talking right. It's going everywhere And that's that is kind of is that sort of instant feeling of progress. Yeah back loose. Yeah Yeah, and back then Microsoft Word had amazing HTML rendering engine. Well, you say amazing. Yeah, let's let's I used it a lot But I also at some point alerted HTML and looked into what word was generating somehow the magic that flipped me into this was like I authored HTML file, right? Open it in Microsoft Word and still active like website. Yes, you can click on the link That's true. That's true. I think it was a different rendering engine to what Explorer did and I don't know it might even be different to the one front page used But they had a support for HTML Yeah, yeah, I mean you could also write a Word document with your normal buttons make it bold make it a heading Yeah, yeah, yeah, which is so so okay as a I don't know fourth sixth grader with with no friends None of us had friends coming coming home and then just turning on computer every day after school Yeah, and just you know that box was my little world Just just because my dad was teacher at like electrical like vocational high school like you know He was a technology teacher So I had access to internet like quite early on and I so I had internet friend And it wasn't like like those like a social media thing It was somehow randomly maybe from that like a delivery thing I found this one person's website that has a bbs the bulletin board Yeah, and it turns out it was like, you know, we're both girls in Tokyo in Same grade or whatever and you know Savvy enough to make web pages, right? So I would turn on the computer Do some coding or drawing or whatever, but then I go to that BBS and then I kind of like write a letter like today Now we have like a very slow Are you still in contact? No, no, I don't even remember what that site was I actually have a person when I was 12 and I was a member of a German Java programming Bulletin board kind of thing. Yeah, I'm so you're so Really Java programming But but but you're not supposed to meet people from the Internet dangerous almost the first messenger used was like a Japanese local You or I am or I think Must be a I am I wasn't into those like a real chat communication thing when I was in Japan It was always asynchronous written mode like in a posting I see thread kind of thing Which is kind of like how our chat apps are getting to be now. It's like yeah full circle back to Friday Right see it for me. It was Microsoft comic chat. What you know, this is the thing I'm assuming that's what it's called but you went on and you picked a room and You picked a character and you would type something and it would sort of be building this this comic book Like so your character there say something and someone reply and their characters appear Never seen or heard of that and it like people will start replying going you're being really annoying Like what what is all that garbage text mean? What's going on and it took someone else to figure out. Oh, they're using Microsoft comic chat, and I'm like Yes, like what what are you using or we are using IRC? And I figured this this Microsoft comic chat was just an IRC client But it would put loads of garbage text at the start of everything You wrote for encoded images or something along those lines What signal to say here's the character I am and here's the expression I'm pulling and and that was yeah, so that was my way into IRC You mentioned it didn't we have like a widget on the side of blog or side or something that's like mini Twitter. I Don't remember this. Well, I do I do that I decided to have a widget basically type chat messages chat messages But kind of like anonymous ish Maybe like it may be in the cookie that like you know your username that you said something It was certainly not like you create a counter anything But like I would go into certain like website that I was like following right And then like look at the top page on the side corner tiny box. I said, do somebody post it in there? Also, um, well it today is my birthday Thank you very much, and you and you got me a present. Yes We're giving it to her. It's your present. Well, I'm wanting I want to explain explain. What is this? What would we So you are explaining maybe two aisles ago that you got sunburned so hard Yes, yes, and there are videos of that have it on I don't know if I'm like supposed to tell you this But you have to put makeup on like yes makeup to counterbalance your redness I went on to YouTube and I typed in help. I'm sunburned. What do I do and there was this this Tiny woman who is like hey sometimes you get sunburned and here's what you do I was like tell me your secrets little child as I'm gonna put on the green makeup What the green maker of what planet are you from and I mean it's working kind of and yeah And so I went out and bought some green makeup. Yeah. Yeah. Well, we were you know watching the keynote You're like putting the your sunscreen and telling me that story. So I bought you some shield Sunshield Sun it's Foreface and so that it didn't feel left out. I got one as well I Feel I feel yours is a little bit more stylish mine. Oh, I don't even know how well that's up for debate. I think so This is this is like Handmaid's tail style, right? Yeah Yeah, is this how I'm supposed to wear it or do I go I go also I'm supposed to go down That's like a welding mask welding mask. It's definitely something I'm going to use. I'm a little bit worried that I mean It's gonna be difficult at the airport Well, it protects my face, but there's these two bits That these these are gonna fry and kind of peel off like bad Doritos I think it's it's just a look you should own as you know, well, thank you very much This is like having team meeting in real life, which never happens because we own a different office.


In the last class, we had talked about the different techniques of maintenance available to us namely the preventive maintenance, predictive maintenance and breakdown maintenance. But we must be always wondering now, well in a large plant which maintenance is to be used where and to answer this question we need to look into this lecture on failure modes, effects and criticality analysis. Well, failure mode effects and criticality analysis as you will see has many applications particularly in engineering design in the process design. But we will see how this FMECA or known as FEMICA can be used to decide on which maintenance strategies to be used in which kind of machine in the plant. Well, to define FEMICA it is a methodology to identify and analyze all potential failure modes or the various parts of the systems. You know, the system could fail in many different ways. Failure can be in many different ways. So we will see how this FEMICA is going to help us decide on which is a critical failure, which is a failure which is not critical in the sense it is not going to affect the downstream operations that much compared to critical failure. So deciding on that we can kind of rank I will say within quotes the failure. So once we have ranked the failure, we can use different maintenance strategies. Well, we will see that how this failures have different effects on the system and how we can avoid the failures to mitigate the effects of the failure on this system. So in a nutshell, FEMICA is going to answer, give us answer to all these different questions. We have in terms of the severity of the failure, in terms of the frequency of occurrence of the failure, in terms of whether a failure can be detected at all or not. Well, as I was telling you, FEMICA is just not used for maintenance strategy but also to decide on whether my design has an alternate, whether my design is robust, the design has a higher reliability and whether all the effects of failure have been considered while designing the system, try to establish the different potential failure modes and their severity. Sometimes we can also decide on planning schedule for the test equipment and the planning test procedure to detect this earlier failures and of course we need to have documentation for future references in the sense, if the planned system needs to be improved in terms of its operation, in terms of its maintenance, the FEMICA worksheets or FEMICA numbers will help us do that and of course, you know, provide a basis for maintenance planning. As we know, we have discussed that there are three types of maintenance, preventive, predictive and the breakdown. Other words for preventive was periodic, CBM and reactive. In the last class, I had told you that through that economic analysis that sometimes CBM is much economic in the long run than preventive but because of the high capital investments involved in CBM, we always cannot put high capital investments for all machines in CBM. So we have to decide by FEMICA which kind of maintenance or which machines need, which kind of maintenance in the scheduling. So this will give us a quantitative estimate or a ranking as to which machine needs to be done with what kind of maintenance, excuse me. Well the FEMICA should be initiated early in the design process, we are able to have the greatest impact on the equipment reliability, I mean, if a certain amount of maintenance has already been initiated in a process or in a plant or in a machine, we need not change its maintenance schedule but had we done a FEMICA analysis on such a plant, we would have known from before that such are the critical machines and we need to be careful about their maintenance.  For example, let us talk of a cement plant. You know in a cement plant, there is a large rotary kiln and this diameter could be about 2 meter okay and this could be about 20 meters long kiln and this kiln rotates at a very low rpm of the order of 2 to 3 rpm okay and then we have a motor which rotates at about 1440 rpm. So to bring about a slower reduction of speed of the skill, this requires for a large gearbox and then there is a pinion gear which measures with a ring gear or a bull gear is a ring gear and there is a pinion gear, pinion on this gearbox and then what happens, there is a feeding mechanism of the raw material which goes here and then they get ground here and there are very hard grinding media here and then finally we will have the cement powder which can be packed and sold off. This is in a nut cell, a cement plant or the mill. If you see the most important elements are of course the motor, gear box and the mill okay because you know as you know standard motors run at 1440 rpm the mechanical speed and then we have to bring about a large speed reduction from about 1440 rpm to 2 rpm. So imagine in such a plant if you are dependent on the daily production of cement powder or cement from the raw material of limestone, gypsum etc. Then if this gear box fails for some reason, if there is a failure in the gear box no matter what because this is a critical component in the plant, if this gear box fail this mill is not going to rotate and then we will not have any cement. So this is going to critically affect the flow or the process or the output or the productivity of the plant. So I have to be very careful in the gear boxes maintenance. So we need to evaluate this gear box around the clock, CBM has to be done on this gear box to evaluate it around the clock. Now the question is for this plant if I was to list down the critical component one is the motor other is the gear box and the third is the cement mill. I cannot afford to have any failures in this because they will affect the process or the process by which I have my final product as the cement. Now I need to have obviously a robust design, I am sure the designers would have done a Femica study to find out a robust design of the individual components but for the maintenance question is where should I put CBM in this motor gear box or cement mill. Now the question I will pose to you is suppose only one critical machine is to be selected for CBM which one should be that. Well many of you will come up with an answer of motor, many of you will come up with an answer of gear box and many of you would be of cement mill. Well you can have your own reasoning for that but you will see through the study of Femica that I can easily come up with a number and which will rank these two or three items motor gear box and the cement mill in terms of their severity or in terms of their criticality and importance. So had I done Femica study on the entire cement plan right from the beginning I could have planned on which equipment needed to do, needed to have a CBM and that is what we are going to look into in CBM and for a simple cement plant case it was very important, very easy for us in fact when we had a motor gear box and cement mill. But imagine if this was to be carried out in a large steel plant there could be many critical processes. So Femica must have to be carried out in all these different processes. Well what are the different types of Femica? One is the design Femica it is used to carry out to eliminate failures during equipment design taking into account all type of failures during the whole lifespan of the equipment. Well we are not concerned with design Femica right now because you know the designers would have already taken care of this Femica while doing their design of the equipment. But the next is the process Femica for example it is focused on how the problems are stemming and how the equipment is manufactured, maintained and operated. So once the equipment has been designed and put in place we need to understand what is the problems for different equipment in terms of its manufacturing, in terms of its maintenance and that is what sometimes something we are going to focus in through another example. And of course in a large system where there are many assembly lines people needs to see the system Femica as to find out bottlenecks in the assembly process and the entire production line. So there are different types of Femica people use according to their needs and to summarize one is the design Femica that is the process Femica and the system Femica. So how do we do the Femica? So there are certain system prerequisites and then one needs to know the entire structure of the system and then provide the failure analysis and prepare the Femica worksheets and the team review followed by corrective actions. The question is how do we do as I was telling you we have to assess the risk, risk or criticality of a process or an equipment and basically come up with a number or otherwise a rank for a particular process or an equipment so that we can decide on you know which machine needs to be having which kind of maintenance. So in the Femica prerequisites we need to define the system to be analysis again if you go back to the case of the steel plant should I do Femica on the entire steel plant or should I do the criticality analysis on the different process of the steel plant. Again let us through take you through an example say of a steel plant okay. The many critical process one could be the raw material handling system in raw material handling systems you know I will not go to the details of the raw material handling system you know basically the raw material handling system for the iron ore for the limestone for the cooking coal etc okay and then the next would be the blast furnace of course blast furnace requires its cooling system its air handling system is again its material handling both the raw material and the molten metal then we will have the iron removal and handling system once the pig iron has been made we have the steel melting shop sms sms once you have the steel we will have the depending on the products we could have rolling mill or we could have forging processes and then we will have the finished product. So if I was to have the different critical areas of the steel plant I have just listed them that these are about 6 different processes they all could be equal important in a steel plant but in the individual processes if I was to find out a criticality of an individual process I need to do Femica on each one of them okay. So if I say that I will only focus my attention in the blast furnace well that is good and that is what I meant by defining the system to be analyzed if I decided that I need to do Femica on the blast furnace only in a steel plant well good but then we now need to study all the system parameters of the individual blast furnace that could be the again the blast furnace you know the blast furnace material itself the blast furnace control the blast furnace operation the blast furnace maintenance all these are the individual components of the blast furnace same as to for the rolling mill the rolling mill the process the motors the material handling system etc. So if I was to focus on any one critical operation or critical path I could decide on any one of them so once I am clear about the system which is to be analyzed I will now go into the individual system kind of find out its drawing specification schematics etc and then so that we know its functional description as well and another is it is best if you do maintenance on an equipment to know its past history in terms of the in terms of its information from the operator from the design personnel from the component suppliers etc. So once such information in a nutshell all I need to do is if I was going to implement Femica on an individual critical component I need to know its entire specifications its entire operation from the right from the start to the end and know whether the functional description of each of the components and the also the past history of its performance its maintenance its feedback from the operator from the management on the same system once such a prerequisite is available to the person or persons who are doing Femica on such a system they will be well equipped or well informed to make a judgment about the criticality of that equipment and that is very essential and when I talk about this person or persons I do not limit it to only the technical analyst or the technicians or the professional on that equipment but it could be anybody who has some say you know right from the bottom most tire on the plant right from the workers to even the executives in that plant or the critical on the further critical process. So all of them can rank this process as for what they feel in terms of few numbers and we will see how this numbers can be taken into account to evaluate the performance of such a plant or an operation. So we will divide this system into manageable functional elements just like you saw the example of the steel plant where even we divided the steel plant about 5 or 6 different functional elements and so on and sometimes to give a clear picture to the Femica team it is good to have a Femica functional block diagram and the system analysis should be done on a very high level as possible because this gives us a view to look from the top down and so that we do not leave out any component by an ominant inner inadvertent error and so on. So this team review and risk ranking is very very important for doing Femica and they develop a risk matrix or what is known as a risk priority number or P n and this is the most important number out of Femica is I have to find out a number which relates to the critical path or process well it may not be critical till you find out its r p n number so I will tell you the important processes for which you have to find out the r p n numbers and question is how do we do or what do we do to find out this r p n numbers for different components. So this is perhaps the most important slide in this lecture that this r p n number actually depends on three parameters one is the O which is the rank of occurrence of the failure mode that means how frequently this system is going to fail is that kind of a number O and another is the severity of the failure if there is a failure in this component how severe is it is it going to affect the other components in my process so that is how we give a number of severity and another is the detectability it is the rank that the likelihood that the failure will be detected before the system reaches the end user or customer. If I am not able to because you know we always if I multiply this three numbers r p n is equal to O times S times D so the lower the r p n number the better it is the lower is the risk so if a fault is not being able to get detected then I will give it a number that it is very high see if your fault can be detected in a because we are we will focus this for maintenance only in our understanding right now if a fault has occurred and I cannot detect it it is dangerous so the detectability if I can detect it I should give it a lower number if fault can be easily detected otherwise if fault cannot be detected and then if I give it a lower number it will have a consequence in the sense that a fault has occurred in the system and I cannot detect it and that should not be my maintenance strategy well the occurrence of a fault is I mean I would not like that a fault to occur but if a fault is occurring how frequently it is occurring if it is occurring at a very high rate I need to give it a higher number but then if I was doing a robust design of the component this occurrence could be brought down if somebody says you know in a component I have repeated failures well there could be many reasons for that one could be a bad design design is not robust another is that I have to make a better design so that the occurrence of failure is a minimum so that is the most important parameter or rather one of the most important parameters while doing Femica on a system if the system is designed in such a manner that there are too many frequent failures either the design is bad or we are not doing something we have the functionality is not proper or we are not operating it within the specs and so on so if our occurrence of failure is high it is the over number of the this number for RPN will be high and severity is another failure mode where we rank the severity suppose a failure has occurred is it important that the this severity or this failure is not going to affect my system if it is not going to affect my other processes or system I can give it a lower severity number okay and I have just explained to you about the detectability the if we give it a lower number if the fault can be easily detected so in a plant or a process if we can find out the critical parameters and specify their OSD numbers we can give them the RPN or calculate their RPN numbers and another thing which is to be done is all these numbers are given a rank 1 to 10 so the highest value of RPN could be 1 and sorry lowest value could be 1 in a highest RPN could be 1000 so any number which has an high RPN number is more critical and the maintenance efforts for that system or processes has to be the best and perhaps we can apply CBN for systems which have high RPN numbers so how do we calculate RPN numbers or risk priority numbers question is we can rank this O from 1 to 10 severity from 1 to 10 and detectability from 1 to 10 now there are many different processes and we have your FEMICA workforce which could consist of workers, engineers, designers, maintenance personnel and management so you can for a particular process you can pull out members from such different functionality group in your plant and ask them to evaluate the process a particular process where you have to establish a maintenance scheme ask them to give an individual RPN number or estimate an RPN number and you can come up with an overall RPN number and then rank them rank their processes. Now question is RPN has no units it is just a number RPN is just a number with no units so RPN has no clear meaning and how the ranks OS and D are defined depend on the application and the FEMICA standard that is used. For example the OSD in an RPN can have different meaning for different FEMICAs and it is since it has no basis of any it is very subjective it is a subjective evaluation reflected in numbers another definition another functionality subjective evaluation put in numbers okay. I will give you another example how people do FEMICA for example because this is a subjective evaluation it does not have units like 10 kg or 10 Newton so this RPN for a process for example I have two steel plants an RPN for one steel plant blast furnace is 780 the other steel plant blast furnace RPN is 500 I cannot say that the 500 RPN number means a better blast furnace I cannot say that because there is no clear meaning of this number from plant to plant because it is just to evaluate just to rank a process or a equipment in terms of its three parameters OS and D so there is no basis but in a plant or in a process where people have the familiarity with all the process and equipment they can decide on the ranking and then we can evaluate or put our efforts more efforts to the RPN where the RPN number is high and less maintenance efforts to the processes or equipment where the RPN number is low. I will give you another example just you will understand so let us take the case of a in fact this pen by which I am writing is a good example in fact if I take the case of this felt pen here felt pen if I had a manufacturer who is to manufacture felt pen he wants to do a FEMICA to evaluate the most critical component in his manufacturing processes do that let us assume the important components in a felt pen and this could be for example one could be the plastic cap with a short clip maybe number 2 is one is the felt with the writing nib writing tip the other is the body of the pen and of course there is a process of assembly of the pen. So in a manufacturing company where we have to produce a felt pen say for example if there are 4 different manufacturing operations one is the cap with the short clip other is the felt with the writing tip third is the body of the pen and fourth is an assembly line where we have to put all this different components together and make this pen the question is what which is the most critical component so that my maintenance efforts efforts could be put to the components which are the most critical. So I will list down this 4 components here in terms of OSD and calculate the RPN numbers so one is I will just list them briefly cap other is the felt tip and third is the body fourth is the assembly. Now let us try to give the ranks of OSD and RPN to this so cap if a cap you know how from a rank of 1 to 10 the failure of the cap you know caps are very robust at most the clip the clip may fail and it can occur out of the felt tip body and the assembly perhaps I will give it a rank of 2 felt tip it can become dry that would be an it can happen periodically for example you will have the pen for a lot of time and not use it the pell so this occurrence could be 3 or 4 body of the pen may not fail there could be an occasional crack and so I will give it a rank of 1 and then the assembly of the entire the pen once assembled make become loose and this occurrence is also very low and could be give it a rank 2. So the numbers I gave 2, 4, 1 and 2 this were very judgmental this were very subjective and I am sure if I ask each one of you to give your own rankings you may come up with a similar ranking as well. And next is severity of this failures now suppose this cap has failed how severe is it or how important is it to affect the failure of the pen as a writing media well this if the cap fails it will perhaps not influence or affect the performance of the pen that much so I will give a lower number felt tip yeah the felt tip fails it is very severe and it is going to affect the performance of the pen. So I should give it a very high number and the body fails in a felt pen the body fails it is not that severe because the ink is not going to leak out but suppose I had an you know the old days the fountain pen where we used to put ink inside the body and the body was used as a container of ink and if that failed it was severe in the sense that it would stain everybody but in the felt case of case of felt pen it is not that severe so I will give it a rank again of 2. Assembly of a felt tip is also very sorry the severity of the assembly yeah if the assembly was not proper the pen would not work so I will give it a high number now if you recall to my few slides earlier I told detectability is given a low number if fault can be easily detected obviously if there is a fault in the cap we all can see it from outside so I can give it a low number felt tip if there is a defect I cannot see it I cannot observe it unless I write it so I will give it a high number body if there is a crack I can see it while it can be easily detected so I will again give it a no number assembly if it has failed it can be easily detected so I will again give it a low number. Now let us calculate the RPN numbers of this so this is a 4 this is how much 49 36 times 7 7 3 21 plus 3 242 check my calculations and this is 4 and this is about 14. Now if you just do this calculations here you see the felt tip stands out among the cap the body and the assembly so in a pen manufacturing operation the according to the Femica analysis we just concluded the felt tip is most critical in its manufacturing so we can say that the machines which are used to manufacture in the felt tip have to have the best kind of all round maintenance and you see through this simple example we could very easily find out that how Femica is going to help us establish the maintenance schedule to be used on a different machine. So once we know the RPN numbers we can decide whether a CBM or condition based maintenance needs to be done to the most critical company so like in a steel plant now we can decide on the different processes and then try to establish RPNs and then find out in that in which process CBM has to be done in which process just a breakdown maintenance has to be done in which process a periodic maintenance is to be done. Now sometimes in the review of the Femica workshop once we have completed the Femica workshop whether we have to see whether what are the systems drawbacks whether it is acceptable not acceptable whether it is feasible to reduce the risk by reducing the likelihood of occurrence of the failure. So we have to work on the parameters which will reduce the occurrence of the failure so that will bring down the number O, reduce the effects of the failure that will bring out the number S and increase the likelihood that the failure is detected before the system reaches the end user because as a manufacturer if I am not careful that I cannot see or detect the fault easily then it is no good because you know if it goes to the hands of the person who is the end user and the faults cannot be detected but the faults keep on happening and that is not good design. So we have to ensure that the we have to make the D number the detectability low so that the low number is given in an RPN analysis the faults can be easily detected. Once such an analysis can be done we can then have established Femica as a tool to identify the different processes equipment so that more care or more efforts in maintenance can be taken in such equipment or plant. Well how do we reduce the risk? We can make design changes we can engineer certain safety features we can put safety devices warning devices and of course have the right procedure and training in place such that the RPN numbers criticalities can be reduced. But as a maintenance engineer we sometimes are called to maintain an equipment which has been already designed but like we did Femica for maintaining a plant or an equipment Femica could very well be done in the design stage as I was telling you right in the beginning by the designer itself to find out the different processes different factors by which the criticality of the equipment could be reduced so that there is enough robustness in the designs or the occurrence of failure is reduced. The process is laid out so that the severity of the failure is reduced and there are features in the system for example putting warning devices safety devices etcetera in the system so that the faults can be easily detected and that would constitute in a holistic manner a design which is very optimum a design which is maintenance friendly a design which is which brings down the number of failures and brings down eventually the loss of production. So to conclude in this design engineering the Femica worksheets are used to identify and correct potential design related problems in manufacturing the Femica worksheets may be used as an input to optimize production the processes the acceptance testing and so on but what we look today was in the maintenance planning in the maintenance planning the Femica worksheets are used as important input to maintenance planning for example as part of reliability centered maintenance maintenance related problems may be identified and corrected. So once we know that the maintenance is critical we will do CBM in such a maintenance once we know that it is less critical we may decide on whether to have a preventive sorry periodic maintenance or a breakdown maintenance. So we will talk about Femica in the future classes when we apply it to different systems and then we will see how Femica can be used how the RPN numbers can be estimated and how as a designer also we should have an insight how that RPN numbers could be reduced. Thank you.


60-Second Subjects from Newcastle University Civil Engineering Civil engineers design, build and maintain the infrastructure that underpins our lives. The course is design intensive, giving you the chance to study infrastructure, modelling and informatics, environmental systems, human management systems and surveying. You'll also get the chance to specialise in the aspects of civil engineering that interest you the most. An engineering degree will give you the skills for a career in a wide variety of areas such as management, administration, banking, insurance or teaching. Most of our graduates go on to work for industry leaders such as Arup, Atkins, Acom and Laying or Rock. You can even get involved with overseas meetings and conferences, field visits to live civil engineering sites and networking opportunities. You'll be assessed through written and computer exams, reports, presentations, portfolios and other coursework. The course is taught through a mixture of lectures, practical work, site visits, individual study and group work. Newcastle University are in the UK's top 10 for civil engineering and our courses are accredited by professional bodies giving you industry-wide recognition. And that's civil engineering at Newcastle University in 60 seconds. To find out more about this degree and others at Newcastle University, visit ncl.ac.uk forward slash undergraduate.


Welcome to Tick Mill Weekly Market Outlook for week commencing August 26th with me, Patrick Munley. Among the main economic readings in the US for the week ahead, Monday's durable goods release will be watched for signs of continuation in the week investment trends. Monday and Tuesday's Fed Manufacturing Surveys will likely remain pressured by tariffs and the ongoing dollar strength. Thursday sees second quarter GDP second estimate likely in line with the 2% target with little chance of material revisions. We wrap the week up on Friday with personal income, personal spending and core PCE inflation. Wage growth likely remains modest, spending growth should be robust but likely to slow and PCE most probably in line with expectations. Markets will also hire selection of Fed speakers on deck next week for further clues as to the Fed's next move at its September meeting. Now to the charts, from a technical perspective the dollar index has continued to consolidate above the 98th level. As we hold above the 98th level there is the potential that we challenge and test the prior highs up towards 98-92. However with momentum divergence developing I will be watching for reversal patterns in and around any test of these prior highs for an opportunity to set short positions. An early failure below 97-95 would suggest that we are likely to retest the 97 handle. Any pullbacks at that stage to test 98 from below I would be watching for reversal patterns to set short positions to ultimately target a test of the 96-50 level. Whilst we are talking about the dollar let's take a quick look at gold. Gold has continued to consolidate at highs and in a similar fashion to the triangle we saw develop in early July we seem to be replicating that price action currently. If that is the case we can expect a thrust hire to retest the prior highs at the 1534 level and then up to test trend line resistance in extension at the 1570-1575 handle. However a failure below the 1480 support will likely encourage a test of the prior highs at 1450. Once again I will be watching for the potential for reversal patterns to develop here and I will be looking to set longs to challenge the 1530 prior highs and then again up to the 1575 handle in extension. In Canada the only data note is Friday's second quarter GDP release with net exports likely boosting growth prospects. From a technical perspective the Canadian dollar has continued to consolidate just below the 13340 level. As this area contains we likely test trend line support back down to 13250. If by a step in here I'd be anticipating that we take out the 13340 level and actually have the potential then to trade higher and test up towards the descending trend line resistance at the 135 level. However a failure below the 3250 will likely see a retest of the prior base back down to 3150. In the Eurozone August economic and business confidence readings are due Thursday. Markets will watch for further softening after July's sub-zero reading for the business climate. Friday we'll see the release of Eurozone employment data and core inflation data which will likely remain sticky around the 1% level. From a technical perspective as anticipated from last week the dollar has grinded lower and we've tested into the 11050, 11030 support area. At the present the Euro is looking to try and reverse here. I could only really get constructive again on the Euro if we get a close above the 11115 handle. If we do then I'll be looking for a test of descending trend line resistance at the 11170 to 11180 handle. However a failure below 11050 likely sees us take out the 11030 year-to-date lows and test the much awaited 10950 major descending wedge trend line support area. Where once again I'll be watching from a mental divergence to develop and then looking for price confirmation with bullish reversal patterns to set long positions. Whilst we're talking about the Eurozone let's check in with the DAX. As discussed last week we've seen a recovery up to back towards the 11900 handle. I'd be anticipating we may see some resistance here and a pullback to test back towards the 11450, 11500 setting a potential inverse head and shoulders pattern which would set the base then for the next leg of recovery up towards the 12000 level. Where once again I'd be anticipating there would be potential for sellers to step in watching for bearish reversal patterns. But I'd look to set short positions targeting a retest back down of the prior lows at 11280. In the UK data is limited to Wednesday's nationwide house price index with Brexit uncertainties likely to continue to weigh. Friday sees GFK consumer confidence and mortgage lending readings which will likely remain soggy also driven by political uncertainties. From a technical perspective as anticipated last week Sterling is attempting a recovery. I'd look for this recovery to stall out at the 12350 to 124 area where again I'd be watching for bearish reversal patterns to develop. And I'd be looking set short to target a retest of the current lows at the 120 handle and down to the 11914 handle which is an equidistant swing target from this A point, this B point and this C point. If we see this test down here again I'll be watching from a momentum divergence where it could be possible to be picking up some cheap pounds and play for a bigger correction up back towards the 124 handle yet again. Data in Asia next week is pretty scant. Japan's key release is industrial production data delivered Friday which is expected to remain under pressure driven by the weak global manufacturing backdrop. The dollar again has spent most of the week in a consolidation pattern. Whilst we hold the 10570 as support there's the potential to move up to test 10750 as an ABCD corrective pattern. However a failure below 10550 would be a bearish development opening an early test of the 10470 flash crash lows that we saw at the beginning of the year. Down under in Australia data is confined to Thursday's Q2 private CAPEX readings with equipment spend expected to remain soft. Friday we'll see housing data with dwelling approvals expected to stabilize driven by approvals in house prices. From a technical perspective the Australian dollar has also spent much of the week consolidating as we come as we are trading in these end of summer quiet markets. However whilst we hold this 6730 area there's the potential that we complete a three wave corrective pattern testing up towards the 69 level reference in last week's review. This area will be interesting if we see sellers step in here we get some bearish reversal patterns I'd be looking to set short positions targeting a retest of the 6670 level. However if sellers don't step in at the 69 then we have another area of interest at the descending trend line resistance at the just shy of the 70 cents level where once again I'd be watching the price action for bearish reversal patterns to set short positions. In the interim a close above the 68 handle can be deemed bullish and that would be an opportunity to set along to target this move up to the 69 handle. And that concludes the weekly market outlook for we commencing August the 26th.


It's always an awkward situation at the front desk or the hotel the individual working at the desk will look at us perplexed You ordered a king-size bed. Is that really what you want? And it was certainly an awkward situation walking into the bank and asking saying my partner And I want to open a joint bank account and hearing you know a business account an LLC or an S corporation No, not my business partner my partner Being able to call him my husband is so definitive. It's something that everyone understands I'm a 45 year old woman and I have been in love with a woman for 10 years And I don't have a word to tell anybody about that the word marriage has a meaning if it wasn't so important We wouldn't be here today The civil union a Domestic partnership would relegate me to a level of second-class citizenship. Maybe even third-class citizenship It doesn't give due respect to the relationship that we've had for almost nine years Only marriage could do that I'd be able to stand alongside my parents and my brother and his wife To be able to stand together as one family who have all had the opportunity of being married and The pride that one feels when that happens


Just finished my run of 46 coins today. So today we're gonna talk strategy. I'm gonna show you guys exactly what it is that I'm doing with my shoes to earn $200 per day. I'm also going to share with you my strategy to get to four to $500 per day within the next month. So we're gonna talk about exactly what to look for when you're going to buy your first sneaker and exactly what you should be focusing on when it's time to level up your sneakers. You wanna make sure that your sneakers are optimized to perform the best to earn you the most tokens possible. All right, so I know a lot of you are probably still trying to get your hands on an activation code. I unfortunately do not have activations code to be able to give out to everybody. I get like one activation code every other day or something like that. And I have a long, long line of people waiting and asking me for these activations codes. So your best shot is on their discord still. You need to go on there and find someone else that already has the app and see if you can get an activation code from them. All right, so from here on out, I'm assuming that you've already got your activation code. You've already transferred over Solana to your step-in wallet and you're ready to buy your new shoes. If you're new to step-in and you didn't see the original video, then make sure to go to my YouTube channel and click right here where it says new step-in beginners guide. That will break down step-in for you and walk you through how to get started. So a few days ago, I started tracking exactly how much I'm earning every single day, including what it cost me to repair my sneaker and what it cost me to level up my sneakers. Unfortunately, I didn't start tracking this when I first started with the app back a month ago.  And I'm currently making between 200 to $215 per day jogging or walking. You can see that my earnings have been increasing as I've leveled up my shoe. So I've basically been earning in the range of 42 to 45, but it cost me about five to repair my shoe plus the cost of leveling up to the next level. You can see in the last four days alone, I've done over $800 in earnings minus the repairs and minus the level up cost. I've done a total of $438.66 in profit. So I'm basically making over $100 per day after taking out repair costs and level up costs. Eventually my level up costs will be gone in about 11 days or so. So then it'll just be pure profit. And I'm expecting my earnings to also grow in that time span. All right, so let's take a look at what's important when you're first buying your first sneaker. Before I show you guys the most optimal strategy for step in to earn the most amount of money possible, make sure to smash that subscribe button. If you wanna make money either trading through passive income or just wanna stay up to date on the latest crypto trends, I upload a video almost every single day about these topics. So please smash that subscribe button so that you never miss another opportunity to make money in crypto again. In addition to that, I answer every single DM that I get on Instagram and I also answer every single comment. So if you have any questions about anything that I'm covering in today's video, drop it in the comments below. All right, so let's open up our apps and go over to the marketplace. The first thing you need to look at when you're choosing a sneaker is what type of sneaker is it? The way that you can filter these sneakers is by going to where it says filter, hitting where it says sneaker and under class deciding which sneaker you want to purchase. So if you wanna walker, you just hit walker and confirm and you will see that all the sneakers will turn to walkers. I myself use a jogger and I will tell you guys why I think this is one of the best strategies if you're like me and can't run every day for 25 minutes. So the reason I prefer joggers over walkers and runners is because with joggers you can either jog or walk. Yes, that's right. With a jogger, you don't actually have to jog. You can walk at a fast pace and still earn tokens. And if you remember from my last video, joggers make more per energy than walkers. So even if you plan on walking, I 100% recommend you to get joggers because you can still walk at a fast pace and earn more per energy. So next you will notice the mint and the level. So what exactly does that mean and is it important? So mint simply means how many times that shoe has been used with another shoe to mint a brand new shoe. Basically the shoes breed a new shoe. You will notice that the more mints a shoe has, the cheaper they are, the less mints a shoe has, the more expensive they are. That's because if you look at this chart here, you will see that if you're minting with two shoes with zero or one mint on them, the cost is 200 regardless. But if one of your shoes has two mints and the other shoe has zero or one mint, the price goes up to 250. And if both of your shoes have two mints, the price goes up to 300. And you can see that the higher the mint count, the more expensive it costs to mint new shoes. That's why you will notice that shoes with higher mint counts are going to be cheaper. Starting off, I recommend just getting the shoe with the best base stats. And I'll cover what good base stats means, but I don't think you should be too focused on the amount of mints yet. However, if you already know that you wanna get to let's say nine shoes and you wanna do it fast, then maybe you might wanna consider the amount of mints that each shoe has. But the way that I did it, I bought a shoe with two or three mints that had good base stats and I worked my way up. Eventually I flipped that shoe for 15 sole and I bought two new shoes with zero or one mint on them. And that's part of how I got to four shoes. All right, so we've decided that we're going to start off with a jogger. We've decided that we're gonna go for a floor price. It's the most efficient way to enter into the market. So we're basically looking for a shoe with probably two or three mints on them. Now the next step is that we need to look at what the base stats of each shoe is. And we need to try to choose the shoe at the cheapest price with the best base stats. So how do you know what's considered good base stats? So these are the rules of thumb. The main thing is for efficiency and resilience to be over 10 together. And efficiency is the most important attribute on your shoe. That's basically what determines how much you're going to earn per energy. So ideally you want that one to be the highest out of both efficiency and resilience. Now don't get tricked by shoes like this one. When you open this up and you see 18.9 efficiency, you're like, wow, that's amazing. But you see how it has a green bar? That means that this shoe has already been upgraded a bit. So to see the actual real base stats, what you have to do is hit where it says base and you'll see that its actual base stats are 2.9 for efficiency and 1.4 for resilience. That equals 4.3. So that means that this shoe is no good. So looking at another one, you see this one has a base stats of 4.5 and 1.7 on efficiency and resilience. Again, that's no good is not enough. This one's a little bit better. You can see that it has 5.8 plus 1.8. So that's around 7.6. That's not bad, but we want a little bit better if we can find something better.  You will have to put some time in to find the right shoe. This one is 7.9, so even closer. So the idea is you wanna get as close to 10 as possible. If it gets out of your price range, then just find the cheapest one with the best efficiency on it. So this one's not bad. You can see that it's 4.1 and 5.4. That's 9.5. I obviously would like the efficiency to be a little bit higher, but this one's actually even upgraded a bit. So let's say that we decided to buy this one at 11.999 sole. Another thing that you will notice is these little locks with E, L, R and L on them. Now what that is, is that's where you place gems. As of right now, gems really are not that important and I don't think they become important until you max out your shoe. What each of those letters stand for is for one of your attributes. So E stands for efficiency, L for luck, C for comfort and R for resilience. So obviously the more E and R that it has, the better, but again, not too important when you're first starting out. So I would say don't worry too much about that. So now you got your first shoe, you're super excited and you wanna go for a run right at that moment. Unfortunately, when you first get your shoe, you start off with zero energy so you will have to wait about 24 hours to get your full two energy. At that point, remember that energy replenishes 25% every six hours until it reaches the energy cap. The only way to increase your energy cap is by getting more sneakers. So when you first get your initial sneaker, you will have two energy, each energy equals five minutes. If you wanna double that up, then you will need to get three sneakers.  Again, if you wanna raise that cap, then the next number is nine sneakers, then 15 and then 30 sneakers. So here are currently the optimal shoe combinations. If you're only gonna be using one shoe, I recommend just start off with a common, but if you have the capital, you can start with an uncommon shoe as well. A common shoe gives you 10 minutes. Uncommon shoe will give you 15 minutes of running and that's going to run you currently around 11 sole for a common and the floor right now on the uncommon sneakers are 58 sole. If you do decide to go to three shoes, the optimal strategy is to have one uncommon shoe that you use to actually run with or walk with and then two common shoes because you're not going to be using them anyways and they will be cheaper. This will get you 25 minutes per day to run or walk and it'll basically cost you about 58 sole plus 22 sole. So that's 80 sole, currently around $8,000. And then the final level is to get nine shoes. To do that, the optimal strategy will be to have one uncommon shoe plus eight common shoes. Now it says 35 minutes here, but that's incorrect. This actually will give you 10 energy and 50 minutes of walking or running. After that, I don't think it's really worth to continue onto 15 sneakers or 30 sneakers. The ROI is not as good, but if you have the capital, of course you can do it. I'm personally going to be staying at nine sneakers and 10 energy. Now after going on your first run, you will notice that the durability on your shoe has gone down. Now that will not affect your next run and you could technically not repair your shoe until you get under 51 energy because it really won't have an effect on you or your earnings. However, I recommend just repairing your shoe every single day before you level up because as you level up, the repairs get more and more expensive. So the optimized strategy to do after going for a run, repair your sneakers and then level them up.  Now, depending if you have a common or uncommon shoe is how many points you get. Common shoes get four points every new level. Uncommon shoes get six points every new level. If you currently look at my shoe, you will see that I have only upgraded to different attributes. That's efficiency, which is getting the majority of my upgrades in resilience, which I put a little bit of upgrades into it. So the way that the game is currently, the most important attribute by far is efficiency. That's what determines how much you're earning per energy that you're spending. The next most important attribute is going to be resilience because that's going to determine how much is going to cost you to repair your sneakers after every run. Then comes luck and comfort. The thing with luck right now, the gems are just not worth opening because they cost a lot more to open than what you can buy them for in the marketplace. So if you look at the marketplace right now, you can see that the floor price on gems are at 0.1. And I made the mistake of opening this efficiency gem for 40 GST. That's $190 for something that's worth about $10, $15 in the marketplace. Now to be fair, the efficiency gem that I opened is actually worth almost one entire soul. But again, it's still, I still spent $140 even if I could sell it for one soul, that would only be $105. So it's just not worth it. That's why I'm currently not even touching luck for upgrades right now. At least the way the game is set up currently. With future upgrades, I'm sure that they will put more utility into these and make it more viable. At that point, then we'll have to switch our strategy and optimize for the different changes and upgrades that they make to the game. And the final one right now is Comfort. So Comfort, there's not much utility for it right now, but Comfort, what it's supposed to do is earn you GMT, which is the other token that Stepping has available. However, you don't earn GMT, I believe till around level 29 or 30. So it's really not that important until you get to those levels. And at that point, you can probably just get a new shoe with your earnings. And if it becomes important, just max out Comfort all the way up to level 30 and then switch shoes. So for the moment, luck and Comfort are not important at all. The best strategy is to put all your upgrades into efficiency and resilience. Now the way that I split them up is for every 12 upgrade points that I have, I put 10 into efficiency and two into resilience. So every 12 points, 10 into efficiency, two into resilience over and over again. All right, here's a breakdown of your efficiency and how much GST you can earn per minute. These are just rough estimates from another user in the community. You can see at 34 efficiency, he was hitting one GST per minute. At 70, he was hitting about one and a half. At 100, he was hitting 1.79. That's more or less around where I'm at today. And if you add that up, that gives you pretty much what I've got the last two days on my walks. So if you look at their GST breakdown from the white paper, this is how it's broken down. It's based on players average speed, players sneaker efficiency, players sneaker efficiencies coefficient. So that means gem, socket, NFT badges, the system value. So this is the value set by the game developer, which is always subject to change. And parameter, a range of system values.  So that must have been what played a part on these two days.  I'm estimating that by the time I max out my sneaker, I will probably be around 160 efficiency. And you can see that this member here at 145 was earning 2.168 GST per minute at 145. So if I am to expect around, let's say 2.2 GST per minute, that would be 55 GST per day. At today's prices, that would mean $261 per day earned. Once I get my nine shoes and double up my energy cap by next month, if the GST prices stayed the same, that would mean that I'd be earning around $522 per day for walking or jogging for 50 minutes. Here you can see the level up table, how much it costs for each level. And you'll notice that the main ones to focus on is level five, which is going to cost basically what the first four levels cost together. To get to level 10, it's 30 GST, which is basically again the last four levels together. To upgrade to level 20 is 80 GST. And then to upgrade to level 30, it's 150 GST. But I believe that you also have to pay in GMT when upgrading to levels 29 and level 30. What I recommend you doing if you're not a runner is to just get a jogger. With a jogger, you can both walk or run. Look for a shoe with high efficiency and high resilience as close to 10 as possible when you add them up together. And don't worry too much about the mint count in the beginning. After running, always repair first before leveling up your shoe. And for every 12 points that you use for upgrades, put 10 towards efficiency and two towards resilience. Your goal should be to max out your shoe and build up to that at least three sneakers. With three sneakers, you'll be able to double your energy cap and make twice as much the amount of money per day. Ideally, you want one uncommon shoe to run with two commons, but you can also do three commons. And that's fine too. Make sure that you're running every 24 hours before the next replenish. Because remember that every six hours, it replenishes 25% until you're capped out.  You miss out on that 25%. You miss out on money. Now, with all that being said, if you want to know about these projects when I first get into them and they're still cheaper, you need to join my mentorship program where I post everything as soon as I get into it. No rug pulls, no Hail Marys, I do all the research, I do all the work, and then I post it in the Discord. In this group, I share every single trade that I take with my complete trading plan, entry, stop loss, take profit, all of it. I teach you guys how to trade using leverage to maximize your capital. I teach you how to use the correct position sizing and risk levels for your capital so that you guys never have to worry about blowing up your account again. In addition to that, I also post passive income opportunities. I post NFT projects, play to earn opportunities, and much, much more. Now, there are limited spots for this group because there's so many people that are trying to get in, but there's only so much time and so many people that I can work with at one time. So if you guys are interested, make sure to click the link in the description below.  I went from a broke failed artist to a regular nine to five working job to retiring in 2017 because of crypto. It changed my life and I know it can change yours as well, but these opportunities will not last forever. So please, if you're interested in joining the mentorship group, sign up in the link in the description below. If not, then I strongly suggest that you check out the next two videos that come up on the screen because those are the videos that YouTube thinks that you should watch next. Thank you so much for watching, guys. I will catch you on the next one. As always, peace and love.


These quotes from the CEO of Taglet Birthright will shock you. Welcome back to day five of our series, Boycott Birthright and Other Fruit Trips to Israel, where we've been following the birthright trip going on right now and exposing the propaganda behind each day. I can't believe it's day five and we're already halfway through this series, but I feel like we're kind of becoming pros at this now, and if we see Israeli propaganda, we'll at least know something is wrong. This is the article I'm going to be pulling these quotes from in case you want to check it out. I'm including all the full quotes here and I encourage you to read them in their entirety so that you can see how blatant the players in the occupation of Palestine are in their goal. In talking about the itinerary, he says, making an itinerary that provides a strategic long-term and effective response to the challenges of anti-Semitic and anti-Israel attacks. When talking about birthright tours, he says that they're one of the most significant tools for systemically confronting anti-Semitic organizations, BDS supporters, and others which work to slander Israel.