In a typical gauge R&R experiment, each operator () makes multiple observations on each of several similar parts () from a monitored process. The statistical model used to describe the response variable is the balanced twofactor crossed random model with interaction
where is an unknown constant, and are jointly independent normal random variables with means of zero and variances and , respectively. The corresponding SAS statements are as follows:
proc varcomp method=grr; class P O; model y = PO; run;
The first random effect in the MODEL statement is assumed to be the "Part" effect and the second is "Operator."
The ANOVA table for the preceding model is shown in Table 108.2.
Table 108.2: GRR Analysis of Variance
Source 
DF 
Mean Square 
Expected Mean Square 

Parts(P) 



Operators(O) 



PO 



Error(E) 



The gauge R&R parameters of interest are given in Table 108.3 in terms of and
Table 108.3: Gauge R&R Parameters
Parameter 
Formula 

Mean of population of measurements 

Variance of the monitored process 

Variance of the measurement system 

Total variance of the response variable 

Ratio of process variance to measurement variance 

Proportion of total variance due to the process 

Proportion of total variance due to the measurement 

Signaltonoise ratio 

Discrimination ratio 

For a oneway model, and for a twoway model with no interaction,
If you use the SPECLIMITS option to give specification limits, the two parameters in Table 108.4 will also be estimated and displayed.
Table 108.4: Gauge R&R Parameters Related to Specification Limits
Parameter 
Formula 

Precisiontotolerance ratio 

Process capability ratio 

Here, USL and LSL are the specification limits, and the value k corresponds to the number of standard deviations between the "natural" tolerance limits of a normal process.
If you use the RATIO option, the ratios in Table 108.5 will also be estimated and displayed.
Table 108.5: Gauge R&R Ratios
Ratio 
Formula 

Ratio of process variance to total variance 

Ratio of operator variance to total variance 

Ratio of process by operator variance to total variance 

Ratio of process variance to residual variance 

Ratio of operator variance to residual variance 

Ratio of process by operator variance to residual variance 
