Robust Bayesian estimation of system reliability for scarce and surprising data

ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng.

2018

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In reliability engineering, data about failure events is often scarce. To arrive at meaningful estimates for the reliability of a system, it is therefore often necessary to also include expert information in the analysis, which is straightforward in the Bayesian approach by using an informative prior distribution. A problem called prior-data conflict then can arise: observed data seem very surprising from the viewpoint of the prior, i.e., information from data is in conflict with prior assumptions. Models based on conjugate priors can be insensitive to prior-data conflict, in the sense that the spread of the posterior distribution does not increase in case of such a conflict, thus conveying a false sense of certainty. An approach to mitigate this issue is presented, by considering sets of prior distributions to model limited knowledge on Weibull distributed component lifetimes, treating systems with arbitrary layout using the survival signature. This approach can be seen as a robust Bayesian procedure or imprecise probability method that reflects surprisingly early or late component failures by wider system reliability bounds.

Section: Introductionmentioning

confidence: 67%

Robust Bayesian Reliability for Complex Systems under Prior-Data Conflict

Walter

ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng.

2018

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“…In this paper, we only considered test data with observed failure times for all tested components. If test data also contain right-censored observations, this can also be dealt with, both in the imprecise Bayesian and NPI approaches (Walter, Graham, & Coolen 2015, Coolen & Yan 2004, Maturi 2010) (more information about NPI is available from www.npi-statistics.com). This generalization is further relevant as, instead of assuming availability of test data, it allows us to take process data for the actual components in a system into account while this system is operating, hence enabling inference on the remaining time until system failure.…”

Section: Discussionmentioning

confidence: 99%

“…The paper ends with a brief discussion of research challenges, particularly with regard to upscaling the survival signature methodology for application to large-scale real-world systems and networks. framework of statistics, which can be applied with the assumption of a parametric distribution for the component failure times (Walter, Graham, & Coolen 2015) or in a nonparametric manner (Aslett, Coolen, & Wilson 2015). We briefly illustrate the latter approach.…”

Section: Introductionmentioning

confidence: 99%

Imprecise system reliability using the survival signature

Applied Mathematics in Engineering and Reliability

Coolen‐Maturi

Aslett

et al. 2016

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The survival signature has been introduced to simplify quantification of reliability of systems which consist of components of different types, with multiple components of at least one of these types. The survival signature generalizes the system signature, which has attracted much interest in the theoretical reliability literature but has limited practical value as it can only be used for systems with a single type of components. The key property for uncertainty quantification of the survival signature, in line with the signature, is full separation of aspects of the system structure and failure times of the system components. This is particularly useful for statistical inference on the system reliability based on component failure times. This paper provides a brief overview of the survival signature and its use for statistical inference for system reliability. We show the application of generalized Bayesian methods and nonparametric predictive inference, both these inference methods use imprecise probabilities to quantify uncertainty, where imprecision reflects the amount of information available. The paper ends with a discussion of related research challenges.

“…η u 0 (n) (s) < η u 0 (n) ( n 2 ) for n 2 < s < n. This means that y at η 0 + n, the gradual increase of y (n) H through the changing tangent slope is replaced by a different change mechanism, where increase of y (n) H is solely due to the shift of H (n) in the η 1 coordinate. Due to (4), y (n) H is then linear in s. In (12), the factor to the linear function is a n 2 −s+a . Here, we have to distinguish the two cases n 2 ≤ s < n 2 + a and s ≥ n 2 + a.…”

Section: Touchpoints For Arbitrary Updatesmentioning

confidence: 99%

“…[11] suggested a parameter set shape that balances tractability and ease of elicitation with desired inference properties. This approach has been applied in common-cause failure modelling [7] and system reliability [12]. We further refine this approach by complementing the increased imprecision reaction to prior-data conflict with further reduced imprecision if prior and data coincide especially well, which we call strong prior-data agreement.…”

Section: Introductionmentioning

confidence: 99%

Sets of Priors Reflecting Prior-Data Conflict and Agreement

Walter

Information Processing and Management of Uncertainty in Knowledge-Based Systems

2016

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In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge. This has the advantage that prior-data conflict sensitivity can be modelled: Ranges of posterior inferences should be larger when prior and data are in conflict. We propose a new method for generating prior sets which, in addition to prior-data conflict sensitivity, allows to reflect strong prior-data agreement by decreased posterior imprecision.Comment: 12 pages, 6 figures, In: Paulo Joao Carvalho et al. (eds.), IPMU 2016: Proceedings of the 16th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Eindhoven, The Netherland