DOEexample_minitab

1、Generating Full-Factorial Models in MinitabWe want to generate a design for a 23 full factorial model. 2 x 2 x 2 = 8 runsClick on down arrow and select number of factors. For this example its 3.Highlight desired design from list. For 3 factors, there are two options. Enter 2 replicates. Generating F

2、ull-Factorial Models in MinitabAfter selecting the design, you can name the factors (Xs)and define their low and high valuesClick on Factors buttonGenerating Full-Factorial Models in MinitabAfter entering your factors,Click on the Options button& De-Select the “Randomize runs”Then click “OK”twic

3、eWhat Do You SeeNotice Minitab gives you the values you need to run your experimentnot 1 and +1.Since we didntrandomize and we made StartAngle factor C,we only need tochange startangle once.It is recommended to RANDOMIZEYOUR EXPERIMENTNotes: 1) A new worksheet will be created for the design.2) The M

4、initab default is to randomize the run order.For our DesignAnalyzing the Results of the DOE: Step 9Lets look at some graphsAnalyzing the Results of the DOE: Step 9Click on the doublearrow button to transferall available terms intoselected termsMake sure you have “Distance” in the Responses boxPerfor

5、m these stepsin both setupMain Effects & InteractionsAnalyzing the Results of the DOE: Step 9It looks like Start Angle and Pin Position had a big effecton our Y-DistanceAnalyzing the Results of the DOE: Step 9Since the lines are nearly parallel, the two-way interactions will probably be insignif

6、icant Analyzing the Results of the DOE: Step 9Go to StatDOEAnalyze Factorial DesignAnalyzing the Results of the DOE: Step 92. Click on Graphs3. Then Pareto withAlpha = 0.054. Finally click Ok1. Put Distance in Responses:3. Click on these 3 PlotsAnalyzing the Results of the DOE: Step 91. Then click o

7、n Storage2. Select Fits & Residuals3. Then Ok and OkAnalyzing the Results of the DOE: Step 9These 3 graphs give you a good idea about whats going onAnalyzing the Results of the DOE: Steps 10 & 11Steps 10 & 11: Plot & Interpret the Residuals Residuals are the difference between the ac

8、tual Y value and the Y value predicted by the regression equation. Residuals should be randomly and normally distributed about a mean of zero not correlate with the predicted Y not exhibit trends over time (if data chronological) Stat DOE Analyze Factorial Design, Graphs button Selectnormal plot of

9、residualsresiduals against fitsresiduals against order Any trends or patterns in the residual plots indicates inadequacies in the regression model, such as missing Xs or nonlinear relationships. Analyzing the Results of the DOE: Steps 10 & 11Lets look at each graph individuallyAnalyzing the Resu

10、lts of the DOE: Steps 10 & 11But first lets perform a Normality test on The residuals by going to:StatBasic StatisticsNormality TestIn variable, select RESI1Then click OkAnalyzing the Results of the DOE: Steps 10 & 11-3-2-10123-1.5-1.0-0.50.00.51.01.5Normal ScoreResidualNormal Probability Pl

11、ot of the Residuals(response is Distance)Average: 0.0000000StDev: 1.49443N: 16Anderson-Darling Normality TestA-Squared: 0.322P-Value: 0.497-202.001.01.05.20.50.80.95.99.999ProbabilityRESI1Normal Probability PlotResiduals Look normalP-value: 0.497If residuals are not normal, your modelmay not predict

12、 very wellAnalyzing the Results of the DOE: Steps 10 & 11246810121416-3-2-10123Observation OrderResidualResiduals Versus the Order of the Data(response is Distance)No trends in this graphAnalyzing the Results of the DOE: Steps 10 & 11100110120130140150160170180190-3-2-10123Fitted ValueResidu

13、alResiduals Versus the Fitted Values(response is Distance)This graph indicates there might be more variability in the smaller distances, but with only two reps, well press on!Analyzing the Results of the DOE: Step 12Examine the Factor EffectsWell keepAnything withA low P-valueLower than 0.05Since we

14、re keeping the 3-way interaction, we need to include stop position in the modelAnalyzing the Results of the DOE: Step 12Examine the Factor EffectsGo back in StatDOEAnalyze Factorial Design and click on Terms, then remove the two-way interactionsPut 2-wayinteractionsback in Available TermsStep 13: De

15、velop Prediction ModelsCoefficients for theCoded model Coefficients for the Uncoded modelY = 145.4 11.3A + 0.7B + 29.2C 1.31ABCY = -339.4 9.4A + 2.9B + 2.9C For the Coded ModelY = 145.4 11.3A + 0.7B + 29.2C 1.31ABC145 = 145.4 11.3 (Pin Position) + 0.7(Stop Position) + 29.2(Start Angle) 1.3(ABC) Lets

16、 just arbitrarily set A & B to some value since they are discreteSet Pin Position to 0 (coded) which equates to 2 (actual: what you set in your design)Stop Position at 1 (coded) which equates to 2 (actual: what you set in your design) Lets figure out Start Angle145 = 145.4 11.3(0) + 0.7(-1) + 29

17、.2 (Start Angle) 1.31(0*-1*C)145 = 145.4 0 0.7 + 29.2(Start Angle) - 0 145 145.4 + 0.7 = 29.2(Start Angle) 0.3 = 29.2(Start Angle)0.01 = Start AngleConverting from the coded units: 160180-1+11700170.10.01For the Un-coded ModelY = -339.4 9.4A + 2.9B + 2.9C 0.0ABC145 = -339.4 9.4 (Pin Position) + 2.9(Stop Position) + 2.9(Start Angle) Lets just arbitrarily set A &a