{"action":"created","comment":{"url":"https://api.github.com/repos/EPDnM-TQM/web-tutorial/pulls/comments/27306335","id":27306335,"diff_hunk":"@@ -0,0 +1,341 @@\n+<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01 Transitional//EN\">\n+<html><head>\n+<!-- Copyright: Daemon Pty Limited 2006, http://www.daemon.com.au\n+\n+     This program is free software: you can redistribute it and/or modify\n+\n+     it under the terms of the GNU General Public License as published by\n+\n+     the Free Software Foundation, either version 2 of the License, or\n+\n+     (at your option) any later version.\n+\n+\n+\n+     This program is distributed in the hope that it will be useful,\n+\n+     but WITHOUT ANY WARRANTY; without even the implied warranty of\n+\n+     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n+\n+     GNU General Public License for more details.\n+\n+\n+\n+     You should have received a copy of the GNU General Public License\n+\n+     along with this program.  If not, see <http://www.gnu.org/licenses/>.\n+\n+-->\n+  \n+  <meta http-equiv=\"Content-Type\" content=\"text/html; charset=UTF-8\">\n+  <title>Total Quality Management</title>\n+\n+  \n+  \n+  <link rel=\"stylesheet\" type=\"text/css\" href=\"css/main.css\" media=\"screen\">\n+\n+  \n+  <link rel=\"stylesheet\" type=\"text/css\" href=\"css/print.css\" media=\"print\">\n+\n+<!--[if lte IE 6]>\n+\n+    <link rel=\"stylesheet\" type=\"text/css\" href=\"css/ie6_or_less.css\" />\n+\n+<![endif]-->\n+  \n+  <script type=\"text/javascript\" src=\"js/common.js\"></script>\n+</head><body id=\"type-b\">\n+<div id=\"wrap\">\n+<div id=\"header\">\n+<div id=\"site-name\">Total Quality Management</div>\n+</div>\n+<div id=\"content-wrap\"><!-- TODO: add sidebar navigation. -->\n+<div id=\"content\">\n+<div id=\"breadcrumb\"> <a href=\"homepage.cfm\">Home</a> / <a href=\"devtodo\">Section Name</a> / <strong>Page Name</strong> </div>\n+<h1>SCREENING</h1>\n+<h2>Introduction </h2>\n+<p>Screening designs are useful as they are a practical compromise\n+between cost and information. Their main contribution is in suggesting\n+which of many factors that may impact a result are actually the most\n+important. Because screening designs require fewer runs, they are far\n+less costly than the more informative full-factorial designs where the\n+practitioner uses all combinations of factor levels. Screening runs are\n+usually a prelude to further\n+experimentation, namely the response surface and confirmatory runs,\n+where specific information is gained around target (desired) outcomes. </p>\n+<hr>\n+<h2>Key Assumption For Screening Studies </h2>\n+<p>In screening designs, we make the assumption that our real-world\n+processes are driven by only a few factors, the others being relatively\n+unimportant. This usually works quite well but it is a crucial\n+assumption that requires careful consideration by subject matter\n+experts. Also keep in mind that the fractional factorial designs may be\n+upgraded to full factorial designs (main effects plus all interactions)\n+if there are only a few main effects. This allows us to observe\n+interactions at a reasonable cost. </p>\n+<h2>Number Of Runs </h2>\n+<p> With screening designs, responses are taken only for a small\n+fraction of the total possible combinations to reduce the number of\n+runs and thus cost. The total number of runs is calculated by raising\n+the number of levels to the power of the number of factors (e.g., for\n+three factors at two levels each we have runs = 2^3 = 2x2x2 = 8). This\n+is actually a full factorial design as we are testing all combinations\n+of factor levels. Full factorial designs allow us to build predictive\n+models that include the main effects of each factor as well as\n+interactions. This brings us to three important concepts of these\n+models: interaction (the effects of one factor on another),\n+orthogonality (all factors are independent of one another), and\n+aliasing (when the effects due to multiple factors cannot be\n+distinguished). </p>\n+<h2>Interactions</h2>\n+<p> One of the more important things that practitioners need to know\n+about is that main factors may affect each other in ways known and\n+unknown (i.e., interaction among effects). For example, the interaction\n+of two reagents in a chemical process may be a significant driver of\n+the overall process(think enzyme and substrate). In deciding which are\n+important, statistically and physically, it is necessary to consult\n+with the bench scientists and technicians to get a handle on what is\n+already known and suspected to be important to the process. Too few\n+factors risk missing something important. Including too many factors\n+will render the screening more costly and lead to a lack of\n+orthogonality due to aliasing. Aliasing occurs when two columns in the\n+design (referred to by statisticians as a vector of the input space)\n+are identical or when one column is identical to another formed from\n+the interaction of two columns (i.e. the “vector” or “dot” product of\n+two columns). </p>\n+<img style=\"width: 218px; height: 218px;\" src=\"/Users/joonasrehand/GitHub/web-tutorial/Joonas/table1.png\">\n+<p>Figure 1 presents a design table for a full factorial design in\n+three factors </p>\n+<p>This design requires eight trials (rows) and has three factors (A,\n+B, C) for which we can estimate main effects. It is also possible to\n+estimate all possible two-way interactions with this design (AB,\n+AC,BC)as well as the single three-way interaction ABC that is shown in\n+the design table. If later, the design is augmented with a fourth\n+factor D (all runs not shown below), we have a problem. Now the\n+contribution to any measured outcome (effect) from ABC is\n+indistinguishable from D and, therefore, we do not know if the driver\n+was D or ABC. The A, B, and C columns give the levels (coded +/-) of\n+four experimental design factors. The ABC interaction column is formed\n+as the “dot” product of the A, B, and C columns. Notice how each row in\n+the ABC column is formed as a product of the corresponding levels of A,\n+B, and C. In the analysis of such a design, the ABC interaction column\n+would be used to estimate the corresponding ABC interaction effect. The\n+sums of the levels of the A, B, C, and ABC columns all equal zero. This\n+means that the design is balanced. Balanced designs give more precise\n+estimates of main and interaction effects than unbalanced designs. </p>\n+<h2>Orthogonality </h2>\n+<p> Further, the “dot” product of any two of the columns A, B, C, or\n+ABC will also sum to zero (try it and see). This more subtle design\n+characteristic is called “orthogonality” and is critical to good\n+experimental design. To understand why orthogonality is so important,\n+we return to our concept of aliasing. Aliasing is the extreme absence\n+of orthogonality. It is impossible to separately estimate the effects\n+corresponding to two design columns that are aliased. In a sense, such\n+estimates are 100% correlated (the statistical term is “confounded”).\n+In contrast, when two design columns are orthogonal, the corresponding\n+effect estimates have zero correlation. This means that errors in\n+estimating one effect do not, on average, bias our estimate of the\n+other effect. Orthogonal designs prevent us from accidentally confusing\n+the effects of two different factors. DOE software provides us with\n+orthogonal (or nearly orthogonal) screening designs in which the main\n+effect and interaction columns are not aliased. These allow us to\n+estimate the corresponding effects without worrying about possible\n+correlations. This lack of correlation usually implies that the\n+estimates are independent. </p>\n+<img style=\"width: 203px; height: 203px;\" src=\"/Users/joonasrehand/GitHub/web-tutorial/Joonas/orthogonality.png\">\n+<p> Figure 2: Orthogonality.\n+</p>\n+<p> Figure 2 gives a good mental image of the value of orthogonality\n+and the independence it provides in our estimates. Let the three\n+mutually perpendicular (orthogonal) axes X, Y, and Z represent\n+dimensions along which three estimates from some experimental design\n+may lie. The results of an experiment may then be indicated as a point\n+in that three dimensional space. If we repeat the experiment many\n+times, the resulting estimates will form a cluster of points in space,\n+centered about the “true” effects being estimated. With orthogonal\n+designs, the cluster of points will be spherical in shape indicating a\n+lack of correlation (or independence) among the estimates. In designs\n+with aliasing, the points will fall along a one-dimensional line or\n+two-dimensional plane that indicate a complete correlation of three or\n+two effects, respectively. In between these extremes will be designs\n+that will produce ellipsoid-shaped clusters, whose axes are not\n+parallel to X, Y, and Z. Such designs are less efficient than fully\n+orthogonal designs and may result in misinterpretation of screening\n+results. Similarly, when the columns in our experimental design are\n+unaliased and when the vector products of any two columns sum to zero,\n+the corresponding effect estimates are mutually independent. This means\n+that random errors in estimating one effect will not (on average) bias\n+the estimate of another effect. Designing for orthogonality is\n+excellent protection against aliasing. </p>","path":"Joonas/Screening.html","position":170,"original_position":170,"commit_id":"2ac30af06de7692461d1135f432fa441ef3412fd","original_commit_id":"2ac30af06de7692461d1135f432fa441ef3412fd","user":{"login":"bladerunner92","id":3470716,"avatar_url":"https://avatars.githubusercontent.com/u/3470716?v=3","gravatar_id":"","url":"https://api.github.com/users/bladerunner92","html_url":"https://github.com/bladerunner92","followers_url":"https://api.github.com/users/bladerunner92/followers","following_url":"https://api.github.com/users/bladerunner92/following{/other_user}","gists_url":"https://api.github.com/users/bladerunner92/gists{/gist_id}","starred_url":"https://api.github.com/users/bladerunner92/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/bladerunner92/subscriptions","organizations_url":"https://api.github.com/users/bladerunner92/orgs","repos_url":"https://api.github.com/users/bladerunner92/repos","events_url":"https://api.github.com/users/bladerunner92/events{/privacy}","received_events_url":"https://api.github.com/users/bladerunner92/received_events","type":"User","site_admin":false},"body":"ws","created_at":"2015-03-27T16:02:03Z","updated_at":"2015-03-27T16:02:03Z","html_url":"https://github.com/EPDnM-TQM/web-tutorial/pull/10#discussion_r27306335","pull_request_url":"https://api.github.com/repos/EPDnM-TQM/web-tutorial/pulls/10","_links":{"self":{"href":"https://api.github.com/repos/EPDnM-TQM/web-tutorial/pulls/comments/27306335"},"html":{"href":"https://github.com/EPDnM-TQM/web-tutorial/pull/10#discussion_r27306335"},"pull_request":{"href":"https://api.github.com/repos/EPDnM-TQM/web-tutorial/pulls/10"}}},"pull_request":{"url":"https://api.github.com/repos/EPDnM-TQM/web-tutorial/pulls/10","id":32116436,"html_url":"https://github.com/EPDnM-TQM/web-tutorial/pull/10","diff_url":"https://github.com/EPDnM-TQM/web-tutorial/pull/10.diff","patch_url":"https://github.com/EPDnM-TQM/web-tutorial/pull/10.patch","issue_url":"https://api.github.com/repos/EPDnM-TQM/web-tutorial/issues/10","number":10,"state":"open","locked":false,"title":"Taguchi, DoE and Screening","user":{"login":"jrehand","id":11387947,"avatar_url":"https://avatars.githubusercontent.com/u/11387947?v=3","gravatar_id":"","url":"https://api.github.com/users/jrehand","html_url":"https://github.com/jrehand","followers_url":"https://api.github.com/users/jrehand/followers","following_url":"https://api.github.com/users/jrehand/following{/other_user}","gists_url":"https://api.github.com/users/jrehand/gists{/gist_id}","starred_url":"https://api.github.com/users/jrehand/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/jrehand/subscriptions","organizations_url":"https://api.github.com/users/jrehand/orgs","repos_url":"https://api.github.com/users/jrehand/repos","events_url":"https://api.github.com/users/jrehand/events{/privacy}","received_events_url":"https://api.github.com/users/jrehand/received_events","type":"User","site_admin":false},"body":"Taguchi, DoE and Screening.","created_at":"2015-03-27T15:22:57Z","updated_at":"2015-03-27T16:02:03Z","closed_at":null,"merged_at":null,"merge_commit_sha":"bc19721407f9085f1ecd822a0bd63d0cac55f5ba","assignee":{"login":"josmil1","id":3432773,"avatar_url":"https://avatars.githubusercontent.com/u/3432773?v=3","gravatar_id":"","url":"https://api.github.com/users/josmil1","html_url":"https://github.com/josmil1","followers_url":"https://api.github.com/users/josmil1/followers","following_url":"https://api.github.com/users/josmil1/following{/other_user}","gists_url":"https://api.github.com/users/josmil1/gists{/gist_id}","starred_url":"https://api.github.com/users/josmil1/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/josmil1/subscriptions","organizations_url":"https://api.github.com/users/josmil1/orgs","repos_url":"https://api.github.com/users/josmil1/repos","events_url":"https://api.github.com/users/josmil1/events{/privacy}","received_events_url":"https://api.github.com/users/josmil1/received_events","type":"User","site_admin":false},"milestone":{"url":"https://api.github.com/repos/EPDnM-TQM/web-tutorial/milestones/2","html_url":"https://github.com/EPDnM-TQM/web-tutorial/milestones/Final%20submisison","labels_url":"https://api.github.com/repos/EPDnM-TQM/web-tutorial/milestones/2/labels","id":1012517,"number":2,"title":"Final submisison","description":"Ready for presenting. 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