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Mixing Bayes and empirical Bayes inference to anticipate the realization of engineering concerns about variant system designs

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  • Quigley, John
  • Walls, Lesley

Abstract

Mixing Bayes and Empirical Bayes inference provides reliability estimates for variant system designs by using relevant failure data – observed and anticipated – about engineering changes arising due to modification and innovation. A coherent inference framework is proposed to predict the realization of engineering concerns during product development so that informed decisions can be made about the system design and the analysis conducted to prove reliability. The proposed method involves combining subjective prior distributions for the number of engineering concerns with empirical priors for the non-parametric distribution of time to realize these concerns in such a way that we can cross-tabulate classes of concerns to failure events within time partitions at an appropriate level of granularity. To support efficient implementation, a computationally convenient hypergeometric approximation is developed for the counting distributions appropriate to our underlying stochastic model. The accuracy of our approximation over first-order alternatives is examined, and demonstrated, through an evaluation experiment. An industrial application illustrates model implementation and shows how estimates can be updated using information arising during development test and analysis.

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  • Quigley, John & Walls, Lesley, 2011. "Mixing Bayes and empirical Bayes inference to anticipate the realization of engineering concerns about variant system designs," Reliability Engineering and System Safety, Elsevier, vol. 96(8), pages 933-941.
    • Handle: RePEc:eee:reensy:v:96:y:2011:i:8:p:933-941
    DOI: 10.1016/j.ress.2011.02.011
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    Cited by:

    1. Rougé, Charles & Mathias, Jean-Denis & Deffuant, Guillaume, 2014. "Relevance of control theory to design and maintenance problems in time-variant reliability: The case of stochastic viability," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 250-260.
    2. Peng, Weiwen & Huang, Hong-Zhong & Li, Yanfeng & Zuo, Ming J. & Xie, Min, 2013. "Life cycle reliability assessment of new products—A Bayesian model updating approach," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 109-119.

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