2K DOE Residual Validation

Introduction

Recently, I conducted a training for 2K Full Factorial at one of ours customer site. The topic was 2K Full Factorial. As we all aware , generally steps for DOE can be classified as below:

DOE Planning Stage> DOE Creation Using Minitab Stage> DOE Execution Stage ( Data collection )> DOE Analyze Stage ( Analyze by eliminating insignificant terms in the model starting from higher order interaction group )> Validating the final model ( Examining the residual plots “Four In One Graphs ; In Minitab 15 )> Finding the optimum setting from the DOE model ( Using Factorial Plots )> Collecting new data of your process output using the BEST SETTING of SIGNIFICANT FACTORS> Comparing the result after improvement versus before improvement by ; Stability Check for both data distribution ( Before and After Improvement datasets) -> Normality Check for both data distribution ( Before and After Improvement datasets) -> Spread Study Comparison for both data distribution ( Before and After Improvement datasets) using 2-Variance Test -> Centering Study Comparison for both data distribution ( Before and After Improvement datasets) using 2-Sample T or Paired-T ; case by case

During the “Validating the final model (Examining the residual plots “Four In One Graphs”)” , in common we use our naked eye to judge Normality , Equal Variance , Random at the “Four In One Graphs” , thus at this stage of explanation , one of my student asked me , how can we be so sure if there is/are point/s that is/are slightly deviating from the others will not impact to the residual normality validation.  My answers to this question are as below:

(1)   Basically from my experience , if your DOE final model R-Sq is high ( > 70% ) and the difference of R-Sq - R-Sq adjusted less than 10% , the point/s that is/are slightly deviating from the others will not give a severe impact towards the normality of your residual study .

(2)   You can reconfirm (1) by using FAT PENSIL test or

(3)   You can store the calculated residual at Minitab worksheet and execute NORMALITY TEST on the stored residuals. Let’s see below example :

Above Graph is the “Four In One” graph output from Minitab 15 for a DOE case study final model. In this case only 1 point ( blue dot ) slightly deviate from the best fitted blue line for other residuals, for this particular case study the R-Sq = 73.5% and the difference of R-Sq and R-Sq adjusted = 7.85%. Generally based on R-Sq and the difference of R-Sq and R-Sq adjusted, the “blue dot” will not impact towards the residual normality. Of course to be sure about that you can execute NORMALITY TEST for the residuals and get the p-value for the NORMALITY TEST. To do that,
(1) Go to Stat> DOE> Factorial? Analyze Factorial Design> Storage and complete as below image> Click OK ( 2 times )

(2) Then minitab 15 will store the Residuals at your minitab worksheet as below:

(3) Then go to STAT> Basic Statistics> Normality Test and do as below image> Click OK

(4) You will get the result as below, with normality test p-value:

So now we can conclude, the “blue dot” which is observation 19 is not impacting the residual normality for the final DOE model (p-value > 0.05). As for observation 19, minitab already indicate as unusual observation in the window session( in this example ) as below:

Unusual Observations for Y
Obs Y Fit SE Fit Residual St Resid
19 71.0000 85.2500 3.2649 -14.2500 -2.52 R

However from above normality study it seems the unusual observation is not a harm to our DOE final model.
So this is how you can be firmed with the residual normality validation.
The same method can be applied during ANOVA, Regression, GFF and others tools that have the “Four In One Graphs” residual study.