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The VARCOMP Procedure

Example 94.2 Using the GRR Method

In this example from Houf and Burman (1988), the response variable is the thermal performance of a module measured in Celsius degrees per watt. Each of three operators measures 10 parts three times. It is assumed that parts and operators are selected at random from larger populations. The following statements produce Output 94.2.1.

   data Houf;
      input a b y @@;
      datalines;
   1  1 37    1  1 38    1 1 37
   1  2 41    1  2 41    1 2 40
   1  3 41    1  3 42    1 3 41
   2  1 42    2  1 41    2 1 43
   2  2 42    2  2 42    2 2 42
   2  3 43    2  3 42    2 3 43
   3  1 30    3  1 31    3 1 31
   3  2 31    3  2 31    3 2 31
   3  3 29    3  3 30    3 3 28
   4  1 42    4  1 43    4 1 42
   4  2 43    4  2 43    4 2 43
   4  3 42    4  3 42    4 3 42
   5  1 28    5  1 30    5 1 29
   5  2 29    5  2 30    5 2 29
   5  3 31    5  3 29    5 3 29
   6  1 42    6  1 42    6 1 43
   6  2 45    6  2 45    6 2 45
   6  3 44    6  3 46    6 3 45
   7  1 25    7  1 26    7 1 27
   7  2 28    7  2 28    7 2 30
   7  3 29    7  3 27    7 3 27
   8  1 40    8  1 40    8 1 40
   8  2 43    8  2 42    8 2 42
   8  3 43    8  3 43    8 3 41
   9  1 25    9  1 25    9 1 25
   9  2 27    9  2 29    9 2 28
   9  3 26    9  3 26    9 3 26
   10 1 35   10  1 34   10 1 34
   10 2 35   10  2 35   10 2 34
   10 3 35   10  3 34   10 3 35
   ;
   proc varcomp data=Houf method=grr (speclimits=(18,58) ratio);
      class a b;
      model y=a|b/cl;
   run;

You specify METHOD=GRR in this example to drive the VARCOMP procedure to produce a gauge repeatability and reproducibility analysis. With the option speclimits=(18 58), the parameters PTR and Cp are estimated and displayed. With the option ratio, certain additional ratios of variance components are also estimated and displayed.

Output 94.2.1 Class Level Information Using Method=GRR
Variance Components Estimation Procedure

Class Level Information
Class Levels Values
a 10 1 2 3 4 5 6 7 8 9 10
b 3 1 2 3

Number of Observations Read 90
Number of Observations Used 90

Dependent Variable: y

The "Class Level Information" table in Output 94.2.1 displays the levels of each variable specified in the CLASS statement.

Output 94.2.2 Analysis of Variance Using Method=GRR
GRR Analysis of Variance
Source DF Sum of Squares Mean Square Expected Mean Square
a 9 3935.955556 437.328395 Var(Error) + 3 Var(a*b) + 9 Var(a)
b 2 39.266667 19.633333 Var(Error) + 3 Var(a*b) + 30 Var(b)
a*b 18 48.511111 2.695062 Var(Error) + 3 Var(a*b)
Error 60 30.666667 0.511111 Var(Error)
Corrected Total 89 4054.400000    

The GRR analysis of variance in Output 94.2.2 is the same as for the Type I analysis when the design is balanced.

Finally, the estimates of the GRR parameters of interest and their confidence limits are displayed in Output 94.2.3.

Output 94.2.3 Parameter Estimates Using Method=GRR
GRR Estimates
Parameter Estimate 95% Confidence Limits
Var(a) 48.29259 22.69452 161.63918
Var(b) 0.56461 0.07296 25.75077
Var(a*b) 0.72798 0.33273 1.79272
Var(Error) 0.51111 0.36816 0.75754
Gamma Y 50.09630 24.48844 166.22217
Gamma P 48.29259 22.69452 161.63918
Gamma M 1.80370 1.20623 27.01724
Gamma R 26.77413 1.69168 105.60895
SNR 7.31767 1.83939 14.53334
PTR(18,58,6) 0.20145 0.16474 0.77967
Cp(18,58,6) 0.95933 0.52437 1.39942
DR 54.54825 4.38336 212.21791
Rho P 0.96400 0.62848 0.99062
Rho M 0.03600 0.0093801 0.37152
Var(a)/Gamma Y 0.96400 0.62848 0.99062
Var(b)/Gamma Y 0.01127 0.0008700 0.34151
Var(a*b)/Gamma Y 0.01453 0.0027083 0.04744
Var(a)/Var(Error) 94.48551 40.19199 327.32469
Var(b)/Var(Error) 1.10467 0.13662 50.37744
Var(a*b)/Var(Error) 1.42432 0.55232 3.74691

You can draw the following inferences from the results of the analysis. Most of the variation is due to differences between parts because of the relative larger value of Gamma R. The measurement system is nearly inadequate because the PTR exceeds 20%. However, the measurement system is of value in monitoring the process since the SNR is greater than five. Refer to Burdick, Borror, and Montgomery (2003) for more information about interpreting gauge R&R studies.

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