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Investigation of robustness in Bayes optimal designs for accelerated life testing.

机译：研究贝叶斯（Bayes）优化设计的健壮性，以加快寿命测试。

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摘要

Accelerated Life Testing (ALT), the testing of systems under more severe environments than those experienced in actual use, is a standard practice used to reduce test time and cost. Increasing limitations on test sample sizes have now focused attention on the incorporation of Bayesian methods and Design of Experiments (DOE) in ALT. The former uses prior subjective input to offset the small sample sizes and the latter provides efficiency due to optimal test design.;The focus of this dissertation is the exploration of the robustness of Bayesian ALT designs under this new procedure. Specifically, designs constructed using the major univariate and bivariate time transformation functions with the Weibull and Exponential life distributions are analyzed. The Basic Sensitivity Theorem is used to characterize the optimal solution robustness. The general expression of the optimal design as a function of the perturbation of prior information is developed as is the general expression for the optimal pre-posterior variance.;The research shows that the Basic Sensitivity Theorem estimates provide a useful approximation of pre-posterior risk. Additionally, the pre-posterior risk is found to be robust though the optimal designs are not as robust.;Because DOE is model dependent, choice of a life length distribution or even its parameter values can influence the optimal test design. Within the Bayesian paradigm, selection of model parameters is based on subjective prior information. To date, literature which addresses robustness of Bayesian ALT designs with respect to prior information has centered on Normal distribution theory due to mathematical convenience in addressing the common DOE optimality criteria of minimizing the pre-posterior variance. Recently, however, an inference procedure for life length statistics has been developed for ALT using Linear Bayes Estimation. This procedure relies on the specification of a linear time transformation function for relating failures at severe environment to those at use environments and of the mean and variance-covariance matrix of prior parameters. Using this method, pre-posterior variance expressions may be developed for a wider class of life distribution used in ALT design; however, analysis of design robustness in these instances remains a difficult and unexplored problem.
机译：加速寿命测试（ALT）是在比实际使用中更严苛的环境下进行系统测试的标准做法，旨在减少测试时间和成本。对测试样本大小的限制越来越大，现在已将注意力集中在将贝叶斯方法和实验设计（DOE）纳入ALT中。前者使用先前的主观输入来抵消较小的样本量，而后者则通过优化测试设计来提高效率。;本论文的重点是在这种新程序下探索贝叶斯ALT设计的鲁棒性。具体来说，分析了使用主要的单变量和双变量时间转换函数以及Weibull和指数寿命分布构造的设计。基本灵敏度定理用于表征最佳解决方案的鲁棒性。最优设计的一般表达式是先验信息扰动的函数，是最优后验方差的一般表达式。研究表明，基本敏感性定理估计值提供了后验风险的有用近似值。此外，尽管最佳设计没有那么稳健，但后验风险仍然很稳健。；由于DOE取决于模型，因此寿命长度分布甚至其参数值的选择都可能影响最佳测试设计。在贝叶斯范式中，模型参数的选择基于主观先验信息。迄今为止，由于贝叶斯ALT设计在先验信息方面的鲁棒性的文献已经集中在正态分布理论上，这是由于数学上的便利，它解决了将后验方差最小化的常见DOE最优性标准。但是，最近，使用线性贝叶斯估计已经为ALT开发了寿命统计的推断程序。此过程依赖于线性时间变换函数的规范，该函数用于将严重环境下的故障与使用环境下的故障相关联，以及先前参数的均值和方差-协方差矩阵。使用这种方法，可以开发出后方差异表达式，以用于ALT设计中使用的更广泛的生命分布。然而，在这些情况下对设计稳健性的分析仍然是一个困难且尚未探索的问题。

著录项

  • 作者

    Lund, Lorin Michael.;

  • 作者单位

    The George Washington University.;

  • 授予单位 The George Washington University.;
  • 学科 Operations research.;Materials science.;Industrial engineering.
  • 学位 D.Sci.
  • 年度 1997
  • 页码 173 p.
  • 总页数 173
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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