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Rejoinder: Methods for planning repeated measures accelerated degradation tests

Rejoinder: Methods for planning repeated measures accelerated degradation tests 1 Hong and Xu The methods presented in our paper apply only to linear mixed effects models. As suggested by Hong and Xu, some degradation models cannot be transformed to have linear degradation paths required for our methods. Linear degradation paths typically arise from zero‐order kinetics. Nonlinear paths with an asymptote arise from first‐order kinetics. For example, and give examples of first‐order degradation models that have asymptotes. The idea of using implicit differentiation followed by numerical evaluation of derivatives is promising. Even when the dimension is low, however, evaluation of numerical derivatives is challenging and must be performed with care. Divided differences should be used, and the interval size needs to be chosen carefully (if not dynamically). Barton describes some of the issues. 2 Reese and Wilson Reese and Wilson (RW hereafter) have raised some interesting points in their discussion. We certainly agree that using modern Bayesian estimation can provide important advantages, especially in degradation models with random effects describing unit‐to‐unit variability (and most applications we have encountered have such variability). Specifically, in temperature‐accelerated testing applications, we have seen that there is often prior information about the effective activation energy in the Arrhenius relationship (but generally little or http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Stochastic Models in Business and Industry Wiley

Rejoinder: Methods for planning repeated measures accelerated degradation tests

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References (13)

Publisher
Wiley
Copyright
Copyright © 2014 John Wiley & Sons, Ltd.
ISSN
1524-1904
eISSN
1526-4025
DOI
10.1002/asmb.2096
Publisher site
See Article on Publisher Site

Abstract

1 Hong and Xu The methods presented in our paper apply only to linear mixed effects models. As suggested by Hong and Xu, some degradation models cannot be transformed to have linear degradation paths required for our methods. Linear degradation paths typically arise from zero‐order kinetics. Nonlinear paths with an asymptote arise from first‐order kinetics. For example, and give examples of first‐order degradation models that have asymptotes. The idea of using implicit differentiation followed by numerical evaluation of derivatives is promising. Even when the dimension is low, however, evaluation of numerical derivatives is challenging and must be performed with care. Divided differences should be used, and the interval size needs to be chosen carefully (if not dynamically). Barton describes some of the issues. 2 Reese and Wilson Reese and Wilson (RW hereafter) have raised some interesting points in their discussion. We certainly agree that using modern Bayesian estimation can provide important advantages, especially in degradation models with random effects describing unit‐to‐unit variability (and most applications we have encountered have such variability). Specifically, in temperature‐accelerated testing applications, we have seen that there is often prior information about the effective activation energy in the Arrhenius relationship (but generally little or

Journal

Applied Stochastic Models in Business and Industry – Wiley

Published: Jan 1, 2014

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