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

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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.
LanguageEnglish
Pages933-941
Number of pages9
JournalReliability Engineering and System Safety
Volume96
Issue number8
DOIs
Publication statusPublished - Aug 2011

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Empirical Bayes
Bayes
System Design
Systems analysis
Engineering
Stochastic models
Product Development
Approximation
Industrial Application
Prior distribution
Granularity
Efficient Implementation
Product development
Estimate
Industrial applications
Stochastic Model
Counting
Innovation
Partition
First-order

Keywords

  • empirical bayes inference
  • reliability engineering
  • variant system designs

Cite this

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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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