DOE及其应用.ppt
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1、DOE及其应用及其应用Fundamentals of Experiment DesignProcess ModelProcessControllable input factorsUncontrollable input factorsInputOutput)(xfyThe Concept of DOEw A designed experiment is a test or series of tests in which purposeful changes are made to the input variables of a process so that we may observe
2、 and identify corresponding changes in the output response.Screening Experiments to characterize the main factorsEvery controllable factors of the processScreeningDesignMain FactorsApplication of DOE To Process ImprovementQuality LevelDOEApplication of DOE in Choosing Between AlternativesFactor?Leve
3、l 1Level 2Level 3.Level 1Whether these levels have difference to the response?The steps of DOE?w Set objectivesw Select process variablesw Select an experimental designw Execute the designw Check whether the data are consistent with the experimental assumptionw Analyze and interpret the resultsw Use
4、 the results or lead to further DOEImportant Practical ConsiderationswCheck performance of gauges/measurement devices first. wKeep the experiment as simple as possible. wCheck that all planned runs are feasible. wWatch out for process drifts and shifts during the run.wAvoid unplanned changes (e.g.,
5、swap operators at halfway) Important Practical ConsiderationswPreserve all the raw data-do not keep only summary averages! wRecord everything that happens.wReset equipment to its original state after the experiment.Check The Assumptionsw Are the measurement systems capable for all of your responses?
6、w Is your process stable?w Are your responses likely to be approximated well by simple models?w Are the residuals well behaved?Residualsw Residuals are estimates of experimental error obtained by subtracting the observed responses from the predicted responses.How to select and scale the process vari
7、ables?w Include all important factorsw Be bold, but not foolish, in choosing the low and high factor levels. w Check the factor settings for impractical or impossible combinations w Include all relevant responses. w Avoid using only responses that combine two or more measurements of the process. Des
8、ign Selection GuidelineNumber of FactorsC o m p a r a t i v e ObjectiveS c r e e n i n g ObjectiveR e s p o n s e S u r f a c e Objective11-factor completely randomized design 24Randomized block designFull or fractional factorialC e n t r a l composite or Box-Behnken5 or moreRandomized block designF
9、ractional factorial o r P l a c k e t t -BurmanScreen first to reduce number of factorsCompletely Randomized Design with One Primary Factorw k = number of factors (= 1 for these designs)w L = number of levelsw n = number of replicationsw and the total sample size (number of runs) is N = k x L x n.w
10、Compare a single factor that has a different levels using the completely randomized disigns.Example with 3 levels and 3 replicationsThe run order of trials are completely randomized, thus the effective of experiment order can be eliminated. As in this example, there are all 9! Ways to run this exper
11、iment. The levels of the factor is called “1”, “2” and “3”.X1 Response3 1 2 2 1 3 1 2 3 Result AnalysiserrorrandomtheismeanoveralltheiseffectfactoriththeislevelithatnobservatiojththeisywhereyijiijijiijAnalysis of Variancew H0:w H1:Otherwisea.21FactorTEaiiFactorainjijTSSSSSSyySSyySS12121)()(Table of
12、ANOVAEFactorMSMSS o u r c e o f VariationS u m o f SquaresDegrees of FreedomM e a n SquareF0B e t w e e n factor levelsSSFactora-1MSFactorF0=Error(within factor levels)SSEa(n-1)MSE TotalSSTan-1 w If F0Fa-1,a(n-1)(0.05) then we can conclude the factor-level means are different. I.e. we reject the H0R
13、andomized Block Designw When we can not control nuisance factors, an important technique known as blocking can be used to reduce or eliminate the contribution to experimental error contributed by nuisance factors.A RBD TableThe model for a RBDw Yi,j = + Ti + Bj + random errorw wherenYi,j is any obse
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