Please implement a GR&R study for the data given in the Excel file \"Battery_Lif

Question

Please implement a GR&R study for the data given in the Excel file "Battery_Life GR_R" Which of the followings is true regarding the analysis?

Part Number Appraiser Measurement 1 1 1.559723593 1 1 1.695248617 1 1 1.621688077 2 1 1.659250543 2 1 1.53751403 2 1 1.559204762 3 1 1.785088168 3 1 1.648493808 3 1 1.737259888 4 1 1.672934999 4 1 1.526511912 4 1 1.686235501 5 1 1.620080265 5 1 1.43960835 5 1 1.561806914 6 1 1.759381975 6 1 1.49326138 6 1 1.951731626 7 1 1.588225411 7 1 1.315146555 7 1 1.699441916 8 1 1.739190883 8 1 1.565933337 8 1 1.632919856 9 1 1.554428711 9 1 1.680132476 9 1 1.67141645 10 1 1.857534035 10 1 1.521701163 10 1 1.756692117 1 2 1.85208902 1 2 1.806011044 1 2 1.481990687 2 2 1.699747462 2 2 1.665022659 2 2 1.615101976 3 2 1.661169554 3 2 1.665433325 3 2 1.668484468 4 2 1.564390251 4 2 1.586095136 4 2 1.821379855 5 2 1.781057905 5 2 1.721084203 5 2 1.857011551 6 2 1.652462719 6 2 1.758077834 6 2 1.504760007 7 2 1.688983798 7 2 1.588230467 7 2 1.589494571 8 2 1.86270832 8 2 1.740327041 8 2 1.687458511 9 2 1.611768809 9 2 1.679070374 9 2 1.67922271 10 2 1.515563748 10 2 1.60215531 10 2 1.577547837 1 3 1.69067731 1 3 1.760806669 1 3 1.699250984 2 3 1.653759306 2 3 1.67536444 2 3 1.704209853 3 3 1.679821158 3 3 1.652101326 3 3 1.662237046 4 3 1.683531982 4 3 1.588171128 4 3 1.719702698 5 3 1.510902456 5 3 1.765313503 5 3 1.586160643 6 3 1.780835603 6 3 1.5988428 6 3 1.658686945 7 3 1.667978467 7 3 1.566262328 7 3 1.672902476 8 3 1.581983383 8 3 1.632893784 8 3 1.665895574 9 3 1.590762806 9 3 1.58409008 9 3 1.495796714 10 3 1.696420105 10 3 1.764178499 10 3 1.711164669

Explanation / Answer

GR&R study talks about the variation of the measurements so we shall conduct a 2 way anova in statistical package R to answer this . The R snippet is as follows

# read the data into R dataframe
data.df<- read.csv("C:\Users\586645\Downloads\Chegg\parts.csv",header=TRUE)
str(data.df)

data.df$Part.Number<-as.factor(data.df$Part.Number)
data.df$Appraiser<-as.factor(data.df$Appraiser)

a<-aov(lm(Measurement~Part.Number*Appraiser,data=data.df))

summary(a)

The results are

> summary(a)
Df Sum Sq Mean Sq F value Pr(>F)
Part.Number 9 0.0758 0.008418 0.828 0.593 # not signifcant
Appraiser 2 0.0197 0.009870 0.971 0.385 # not signifcant
Part.Number:Appraiser 18 0.2427 0.013482 1.326 0.205 # not signifcant
Residuals 60 0.6100 0.010166

The p values are not less than 0.05 , hence none of the variation come out to be significant enough to take any action. Hence Appraisers and part number do not have any statisitcally signifcant effect on the measurements

and we conclude that

The measurement system is reliable.

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