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GR&R - Destructive Testing


General Notes

Destructive Gauge R&R (DGR&R) is based on a nested, random effects model.  In most cases, the Gauge (Repeatability) term is confounded with the error (or trial) term.  In certain situations, it is possible to unconfound the Gauge term from the error term.
 

In some types of testing, the specimen is actually destroyed during the process of measurement. - meaning that it is not possible to take another measurement from that particular specimen.  In other types of testing, a specimen might be somehow altered during testing, but not destroyed; it is possible to take more than one measurement, but subsequent measurements reflect a change in the specimen due to the past measurement(s).  We tend to use DGR&R methods for both situations; however, for the latter situation we may want to consider the GR&R modeling approach where a regression model is created to account for the change in the specimen(s) over multiple measurements, and then GR&R is applied to the model residuals.


Sampling and Randomization considerations:
  • Trials within individual Samples should usually be as homogeneous as possible.  This will encourage more material variation to reside in the Sample variance component (where it belongs), and to prevent artificial inflation of the Gauge (Repeatability) variance component.
  • The material or process variation should be allocated randomly across the Sample term.
 


SAS code for a two-stage, hierarchically nested random effects model:

 
SAS
proc glm;
by material;
class operator direction obs;
model result = operator direction(operator) obs(direction*operator);
random operator direction(operator) obs(direction*operator) / test q;
test H = operator E = direction(operator);
test H = direction(operator) E = obs(direction*operator);
run;

proc nested;
by material;
class operator direction obs;
var result;
run;




Examples of opportunities to separate the Gauge repeatability term from the Trial term:


Measuring a known standard multiple times
  • Perhaps is available via calibration data
  • The standard used should have a value that is close to that of the MSA measurements (e.g. viscosity)


Use multiple gauges
  • This creates a 'gauge' term explicitly in the EMS table
  • While this may not be the exact equivalent of directly measuring gauge repeatability of any one particular gauge, it may give an indication of repeatability.





Assumptions
 
 


References

"Gauge R&R Studies For Destructive and Non-destructive Testing"; Mario Perez-Wilson; Advanced Systems Consultants; 2003; ISBN 1-883237-19-X 
 
Design and Analysis of Gauge R&R Studies – Making Decisions with Confidence Intervals in Random and Mixed ANOVA Models”, Montgomery, Douglas C., SIAM, 2005, ISBN 0-89871-588-1
 
For the hierarchically nested random effects model, see:
Design and Analysis of Experiments”, Montgomery, Douglas C., Wiley, 2001, ISBN 0-471-31649-0, pp. 519, 557

Fundamental Concepts in the Design of Experiments”, Hicks, Charles R, Oxford University Press, 1999, ISBN 0-19-512273-9, pp. 183, 190


 
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