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Collaborative Opportunity: Inverse Prediction with Multiple Measurements per Pair

  

Notes before we get to a brand new collaboration request, from Willis Jensen of W. L. Gore & Associates.

1. You can now find all ISVC posts by using the following link:

http://community.amstat.org/isvc

2. So far, we've received two responses to Peter Parker's collaboration request, one from Steve Gilmour and another from Tom Bzik. If you are in industry--or even academia--with an interesting problem related to industrial statistics, please e-mail Byran Smucker at smuckerb@miamioh.edu. Same goes if you've done collaborative work with industry and would like to publicize it here.

Now on to Willis Jensen.

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Inverse Prediction with Multiple Measurements per Pair

Problem Motivation

Consider the situation where I can make product that has some final measurement response that relates to the quality of the product. The response has some pre-determined requirement (lower specification of 600) that is based on how well the product will perform for the customer. There is a desire to replace this current test method with a new test method which is simpler and easier to perform. What value do I need to measure with the new method to ensure that individual measurements will be above the specification of 600 with the old method?

Problem Statement

If both the old test method (Y) and new test method (X) are not destructive and you only have a single measurement per part, then naturally one could pair the measurements and fit a simple linear regression line. From the regression equation, one could predict what values of X would ensure that Y will be within the specification using inverse prediction. Thus instead of using the specification on Y to ensure good product, one uses a requirement on X.

However, in this case, there are multiple measurements where 3 operators measured each part 3 times. So there are 9 repeat measurements on the same location (3 operators times 3 repeats). We have 48 measured locations at our disposal that received the multiple measurements. Because of this testing variability due to operator and repeat measurements, we want to account for that variability in the analysis.

Previous Ideas and Solutions – Raw Data plot

There is a paper that talks about this general issue of inverse prediction for a simple case where you have a single measurement on each measured part. But it is not clear how to modify this approach for multiple measurements due to operator (random effect) and repeat measurements.

Parker, P.A., Vining, G., Wilson, S.R., Szarka, J.L. III, Johnson, N.G. (2010). “The Prediction Properties of Classical and Inverse Regression for the Simple Linear Calibration Problem”. Journal of Quality Technology 42(4) pp. 332-347.

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If interested in collaborating with Willis, comment on this post or contact him directly:

Willis Jensen
W. L. Gore & Associates
wjensen@wlgore.com

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