Bayesian nonparametric system reliability using sets of priors

An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through bounds on the functioning probability. Given component level test...

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Bibliographic Details
Published in:International journal of approximate reasoning 2017-01, Vol.80, p.67-88
Main Authors: Walter, Gero, Aslett, Louis J.M., Coolen, Frank P.A.
Format: Article
Language:English
Subjects:
Bayesian nonparametrics
Imprecise probability
Prior–data conflict
Survival signature
System reliability
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Summary:An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through bounds on the functioning probability. Given component level test data these bounds are propagated to bounds on the posterior predictive distribution for the functioning probability of a new system containing components exchangeable with those used in testing. The method further enables identification of prior–data conflict at the system level based on component level test data. New results on first-order stochastic dominance for the Beta-Binomial distribution make the technique computationally tractable. Our methodological contributions can be immediately used in applications by reliability practitioners as we provide easy to use software tools. •System reliability bounds for arbitrarily complex system layouts.•Nonparametric modelling of component reliability functions.•Vague and partial specification of prior component reliability functions possible.•Wider reliability bounds on component and system level in case of prior–data conflict.•Freely available and easy to use software: implemented in R package Reliability Theory.
ISSN:0888-613X
1873-4731
DOI:10.1016/j.ijar.2016.08.005