The VARCOMP Procedure |
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.
Class Level Information | ||
---|---|---|
Class | Levels | Values |
a | 10 | 1 2 3 4 5 6 7 8 9 10 |
b | 3 | 1 2 3 |
The "Class Level Information" table in Output 94.2.1 displays the levels of each variable specified in the CLASS statement.
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.
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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