DFSS-BB310-Full-Factorial-DOE.ppt

《DFSS-BB310-Full-Factorial-DOE.ppt》由会员分享，可在线阅读，更多相关《DFSS-BB310-Full-Factorial-DOE.ppt（99页珍藏版）》请在淘文阁 - 分享文档赚钱的网站上搜索。

1、310-2 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedDemonstrate how to generate a full factorial designDemonstrate how to create & analyze designs in MINITABDemonstrate how to look for factor interactionsDemonstrate how to evaluate residualsDemonstrate how to set factors

2、for process optimization310-3 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedDetermine Customers & Ys:Quality, Price & Product DemandInitial Product Platform key Xs, product velocitiesMeasure the Xs and YsFind critical Y=f(x) relationshipsOptimize Ys & critical Xs, RMI, WI

3、P, FGI & Supply ChainSet critical Xs, kan-bansCheck Key YsFailure modes and analysesIdentify CTQC Metrics/MeasuresEstablish Business Needs & PriorityDevelop Project Charter & PlanIdentify Key Measurement Systems Identify Target Markets & SegmentsIdentify Customer Needs/WantsEstablish Critical to Qua

4、lity Characteristics (CTQCs)Establish Technical FeaturesDevelop Optimal Design Concept Develop Business Case & Schedule Design System, Subsystems & Components Design ProcessesModel & Assess Critical ParametersModel & Analyze Tolerances & SensitivitiesDevelop/Evaluate Measurement SystemsInitial Robus

5、t Product DesignMinimize Product ComplexityMaximize Product VelocityOptimize Critical Inputs - Final Robust Design Optimize, Simulate ProcessesFinal Robust Product DesignSet Initial Control Systems/PlansVerify Product PerformanceVerify Process PerformanceTest Plans & ReportsAnalyze/Minimize Product

6、& Process Risks310-4 Copyright 2001-2004Six Sigma Academy International LLC All Rights Reserved The selected design should align with the objectives of the experiment and resource commitment.OFAT (One Factor at a Time)Full Factorial (with or without replication)2k Full Factorial2k Full Factorial (ce

7、nter points)2k Full Factorial (blocking)2k-n Fractional Factorial DesignsRSM (Response Surface Method)310-5 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedHigher complexity designs offer greater knowledge at a higher priceExperiment TypesObjectiveRSM (Response Surface Meth

8、od)OptimizeModelResolution III Fractional Factorial DesignsFull Factorial DesignsResolution V Fractional Factorial Designs2k Full FactorialScreenFewManyPIVsLessMoreKNOWLEDGELessMoreCOST(6-15)(2-5) Review complexity vs value310-6 Copyright 2001-2004Six Sigma Academy International LLC All Rights Reser

9、vedA Full Factorial Design of Experiment will:- Provide the most response information aboutFactor main effectsFactor interactions-When validated, it will allow a process to be optimized310-7 Copyright 2001-2004Six Sigma Academy International LLC All Rights Reserved A full factorial DOE is a planned

10、set of tests on the response variable(s) (KPOVs) with one or more inputs (factors) (PIVs), each with all combinations of levels evaluated-ANOVA will show which factors are significant-Regression analysis will provide the coefficients for the prediction equations (for the case where all factors have

11、2 levels)-Mean-Standard deviation-Residual analysis will show the fit of the model310-8 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedLearning the most from as few runs as possible. Identifying which factors affect mean, variation, both, or have no effectOptimizing the fa

12、ctor levels for desired responseValidating the results through confirmation310-9 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedIs testing all combinations possible, reasonable and practical?A process whose output Y is suspected of being influenced by three inputs A, B and

13、 C. The SOP ranges on the inputs are:-A15 through 25, by increments of 1-B200 through 300, by increments of 2-C1 or 2A DOE is planned to test all combinations310-10 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedWe must make assumptions about the response in order to manag

14、e the experimentSetting up a matrix for the factors at all possible process setting levels will produce a really large number of tests.The possible levels for each factor are-A = 11-B = 51-C = 2How many combinations are there?2 x 51 x 11 = ?ABC15200116200117200118200119200120200121200122200123200124

15、2001252001152021162021172021.2230022330022430022530022 x 51 x 11 = ?310-11 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedThe design becomes much more manageable!The team decides, from process knowledge, that the test conditions of interest within the operating range of th

16、e factors (inference space) is as shown below:-A15, 20 and 25(3)-B200, 225, 250, 275 and 300(5)-C1 and 2(2)310-12 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedThis is a 3 x 5 x 2 full factorial design. (It consists of all combinations of the three factors) The revised ex

17、periment consists of all possible combinations of A, B and C at each of the chosen settings (levels):Total runs = 3 x 5 x 2 = 30ABC152001152002152251152252152501152502152751152752153001153002202001202002202251202252202501202502.252752253001253002310-13 Copyright 2001-2004Six Sigma Academy Internatio

18、nal LLC All Rights Reserved What is the total number of combinations for the following designs?2 x 3 x 43 x 3 x 33 x 2 x 2 x 4 x 3 x 5310-14 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedCreate a MINITAB design for:A pressure10, 12, 14, 16 psiB temperature65, 70, 75 degre

19、esC material vendorAcme, World-Wide4x3x2 Design310-15 Copyright 2001-2004Six Sigma Academy International LLC All Rights Reserved310-16 Copyright 2001-2004Six Sigma Academy International LLC All Rights Reserved1. Select Options2. Un-check Randomize runs(for teaching purposes only)3. Select “OK”310-17

20、 Copyright 2001-2004Six Sigma Academy International LLC All Rights Reserved310-18 Copyright 2001-2004Six Sigma Academy International LLC All Rights Reserved310-19 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedThis is the Standard order for a 4 X 3 X 2 designThe StdOrder C

21、olumn shows the order of the runs if the design is not randomizedThe RunOrder column shows the order of the runs if the design is randomizedNote: Since we did not check the Randomize box when we created the design, both StdOrder and RunOrder are the same310-20 Copyright 2001-2004Six Sigma Academy In

22、ternational LLC All Rights ReservedCreate both a randomized and non-randomized MINITAB design (1 replicate) for the following:-The factors and respective levels are:FactorLEVELS Customer TypeC&I ConsumerSystemLegacy SAPWarehouseAtlanta DallasSt LouisOvertime Hours0 100The response is on-time deliver

23、yBe prepared to discuss your results310-21Replication, Repeats and RandomizationDesign for Six Sigma310-22 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedA Replicate is:-Total run of all treatment combinationsUsually in random order-All experiments will have one replicateT

24、wo replicates are two complete sets of experiment runsEach replicate is another repetition of the entire experimentWhen there are two or more replicates, the complete set of runs is generally randomized if the randomization is done only for the first replicate, and each run is repeated 2 or more tim

25、es, these are called repeats-Statistically best experimental scenarioMultiple replicates increase statistical power of experiment310-23 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedMINITAB handles replicating the design easilyActual factor level change between runs is at

26、 the discretion of the experimenter-MINITAB provides treatment combination-Randomization or information needed is part of strategy of experiment310-24 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedCreate a 2 x 3 Full Factorial with two non randomized replicatesTool Bar Me

27、nu Stat DOE Factorial Create Factorial Design310-25 Copyright 2001-2004Six Sigma Academy International LLC All Rights Reserved310-26 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedClick Factors310-27 Copyright 2001-2004Six Sigma Academy International LLC All Rights Reserve

28、d310-28 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedSkip the other dialog optionsUn-check randomize box in Options310-29 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedFirst ReplicateSecond ReplicateResponse Y would be placed in C6310-30 Copyr

29、ight 2001-2004Six Sigma Academy International LLC All Rights ReservedResponse Y would be placed in C6310-31 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedLets discuss a plating etch bath.The output of concern is etch rate higher is better.Someone wants to evaluate if addi

30、ng a stirrer to the bath will increase etch rate.We tell the supervisor to evaluate etch rate 20 times for both stirrer on and stirrer off.We are in a hurry and tell him that he has one day to do the test.What do we get?310-32 Copyright 2001-2004Six Sigma Academy International LLC All Rights Reserve

31、d4030201011010090807060IndexEtch RateONOFFAvg Off = 91.70Avg On = 74.50If higher is better Ran 20 with stirrer “off” then 20 with it “on” 310-33 Copyright 2001-2004Six Sigma Academy International LLC All Rights Reserved4030201011010090807060IndexEtch Rate1offonoffonononoffoffonoffoffononoffonoffonof

32、fonononoffoffoffoffonoffonononoffonoffononoffoffonoffoffAvg Off = 82.0Avg On = 88.6If higher is better Ran 20 “on”, 20 “off” with Randomization 310-34 Copyright 2001-2004Six Sigma Academy International LLC All Rights ReservedWhich tells the truth about the value of stirring?The degradation of the ba

33、th over the day is called a “lurking variable”.While this one would have been easy to predict, not all lurking variables are so obvious.Randomize whenever feasible310-35AssumptionsDesign for Six Sigma310-36 Copyright 2001-2004Six Sigma Academy International LLC All Rights Reserved Full Factorials us

34、e ANOVA to analyze the data. Thus, the assumptions are the same as for One-Way ANOVA:-The residuals are Independent Normally distributed With equal variance In addition, since Full Factorials have more than one factor, we have another assumption:-The factors are independent of each other310-37 Copyr

35、ight 2001-2004Six Sigma Academy International LLC All Rights Reserved Independent Data No trends, patterns, or clustering- Most statistical modeling techniques assume that the residuals are independent (including ANOVA and regression)- The value of a point should not help predict the value of the ne

36、xt point Independent Variables No correlation- Most statistical modeling techniques assume that the factors or predictor variables are independent of each other (including ANOVA and regression) Independence is a critical assumption - lack of independence: - Can bias the results of a study- Can resul

37、t in extremely unstable prediction models310-38 Copyright 2001-2004Six Sigma Academy International LLC All Rights Reserved Sampling QuestionsMost problems related to sample data come back to the sampling method:Was sample data collected randomly?Were sampling techniques clearly outlined?Does the ord

38、er in which the data were collected matter? Correlated Factors or PredictorsOrthogonal designs used in DOE ensure independent factors310-39 Copyright 2001-2004Six Sigma Academy International LLC All Rights Reserved Independent Data or ResidualsOrder is importantRun chart or I Chart of data or residu

39、als will show trends, patterns, clustersThese charts have tests for trends and clustering use themThe data should be random, with no repeated cycles or long term trends If the data is random with no trends, then the data is independent and stableOrder is not important-If trends or patterns are detec

40、ted, ignore them (order is not important). Example: Due to cost, we did not randomize our design, we hope that our data will show a strong pattern as we ran all of the tests at one setting before changing to new setting. We hope that one setting will show an improvement310-40 Copyright 2001-2004Six

41、Sigma Academy International LLC All Rights ReservedIndependent Variables or FactorsScatter plots (or matrix plots) show relationship between variablesIf variables are correlated, select one that:Is easy to measureHas the most intuitive relationship with Y310-41 Copyright 2001-2004Six Sigma Academy I

42、nternational LLC All Rights Reserved The vast majority of statistical tests (ANOVA included) are theoretically based upon the assumption of normality Non-normality affects the calculations for p-values and Power Power decreases with non-normal data, and p-values are reported as being smaller than ac

43、tual The vast majority of statistical tests (ANOVA included) are also quite robust to departures from normality, especially for large samples Transformations can often be used to “normalize” dataFor more information on the normality assumption, refer to the paper “Normality Assumption” in the Suppor

44、t Files310-42 Copyright 2001-2004Six Sigma Academy International LLC All Rights Reserved Test the Right Data Remember, the assumption in ANOVA is that the residuals are normal therefore we test them, not the data Sample Size Histograms require large samples (50 or more recommended) Probability Plots

45、 dont require as large a sample Tests for normality require 25 or more observations, dont have much power unless n 50 As a result of the Central Limit Theorem, most hypothesis tests are robust to non-normality when sample size n 20Testing for normality almost always requires more data than the stati

46、stical tests that assume normality!310-43 Copyright 2001-2004Six Sigma Academy International LLC All Rights Reserved Nature of Non-NormalityHeavily skewed data is more of a concern than non-normal symmetric dataHeavily skewed data is easier to fix with a transformationLog, Box-Cox Power Transformati

47、on, Square Root, Arcsine, etc. Non-Parametric Alternatives: Does not apply for Full Factorials, except the special case when there are two factors Most non-parametric tests require symmetric data, and are just as sensitive to heavily skewed data as the parametric tests All non-parametric tests are f

48、ar less powerful than the corresponding parametric tests, unless sample size is very large (in which case the parametric tests are extremely robust anyway)If data is heavily skewed, it is better to try a transformation than a non-parametric alternative!310-44 Copyright 2001-2004Six Sigma Academy Int

49、ernational LLC All Rights Reserved Step 1: Test the right data (for 2k - test the residuals) Step 2: Graphical methodsHistogram of residualsNormal probability plot of residuals Step 3: Statistical testsAnderson-Darling test (preferred) Chi-Square goodness of fit testAlways use graphical tools when t

50、hey are appropriate!310-45 Copyright 2001-2004Six Sigma Academy International LLC All Rights Reserved Statistical modeling techniques (including ANOVA and regression) assume that the residuals have equal variance Unequal variances affect the calculations for p-values and Power Power decreases and re