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Discussion on Incorporating Bias in Response Surface Design Evaluation

A reflective discussion on extending FDS plots to include bias in response surface designs. The authors address model misspecification issues and propose a focus on the probability of failure using generalized linear models. The study extends VDGs and emphasizes the need for thorough literature review and model selection for reliability assessment.

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Discussion on Incorporating Bias in Response Surface Design Evaluation

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  1. Discussion of “Aspects of Bias, Prediction Variance and Mean Square Error” Geoff Vining Virginia Tech

  2. Construction and Evaluation of Response Surface Designs Incorporating Bias from Model Misspecification • Appreciate that the Authors Are Exxtending FDS Plots to Include Bias • Very Natural and Welcomed Extension • Reflections from a Very Quick Reading!

  3. Construction and Evaluation of Response Surface Designs Incorporating Bias from Model Misspecification • Looks Like the Authors Are Treating the Lack-of-Fit Coefficients as Random • Very Problematic • Actually, They Are Fixed but Unknown • Suggest a More Thorough Literature Review

  4. Construction and Evaluation of Response Surface Designs Incorporating Bias from Model Misspecification • Box and Draper (1959, 1963) • Lambda – Optimality (1980s) • Trace L – Optimality (1980s) • Vining and Myers (Technometrics, 1991) • Extends VDGs to Include Bias • Defines the Lack-of-Fit in Terms of Power • Avoids the Need for Looking at Individual Coefficients

  5. Prediction Based Model Selection for Reliability • Takes a Generalized Linear Models Approach to Reliability • Not Focused on “Time to Failure” • Focus on Probability of Failure • Binary Response • Probit Models • “Region of Interest” • “True Value” Comes from the “Full Model”

  6. Prediction Based Model Selection for Reliability • Issues: • General There Are Multiple Regions of Interest • “In any generalized linear model, … , the estimate from the full model converges in probability to the true model.” • If, and only if, the full model is,in fact, the full model!! • “All models are wrong; some models are useful.” • More closely related to Mallows Cp. • Number of Models to Evaluate

  7. Prediction Based Model Selection for Reliability • Comments • Interesting Approach • Serious Approach to Model Selection for Reliability • Some Concern about Reliance on the Full Model • Focus on Probability of Failure Seems Limiting • Perhaps Appropriate • Seems to ignore the physics of failure.

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