Bayesian Reliability Analysis of Complex Series/Parallel Systems of Binomial Subsystems and Components

Martz, Harry F.; Waller, R.A.

doi:10.2307/1270120

Cited by 45 publications

(56 citation statements)

References 6 publications

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“…We use predictive formulations for reliability requirements and related optimisation problems. Prior to the system's use in a process it can be tested, where we can use tasks as inputs without relying on a particular arrival process for the tasks [32,39,40,54,55]. We explicitly assume that testing reveals zero failures, which we share with Martz and Waller [37] and which has also been considered by Sandoh [53], in order for the system to be used in the process after testing.…”

Section: Overviewmentioning

confidence: 99%

“…Moreover, their analysis is limited to integer values for α and β, whereas in our approach α and β can be any positive constants, while we advocate the choice of α = 1 and β = 0, which we discuss in detail later in this thesis. We also share the use of a Binomial model for the tests, and a Beta prior distribution with Martz et al [40], Martz and Waller [39], and with Springer and Thompson [54,55].…”

Section: Learning From Testsmentioning

confidence: 99%

“…In this chapter, we consider redundancy where reliability prediction is only considered at the system level. The references [38][39][40]42] discuss reliability at system, subsystem and component levels. Components here are regarded as either functional or not (pass or fail components) [30,39,40], and we only consider systems consisting of exchangeable components.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Probabilistic Assessment Study of Channels Downstream Slopes Erosion in the Maritime Environment

Khalifa

Ganainy

Nasr

2009

Journal of Coastal Research

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We study required numbers of tasks to be tested for a technical system, including systems with built-in redundancy, in order to demonstrate its reliability with regard to its use in a process after testing, where the system has to function for different types of tasks, which we assume to be independent. We consider optimal numbers of tests as required for Bayesian reliability demonstration in terms of failure-free periods, which is suitable in case of catastrophic failures, and in terms of the expected number of failures in a process after testing. We explicitly assume that testing reveals zero failures. For the process after testing, we consider both deterministic and random numbers of tasks. We also consider optimal numbers of tasks to be tested when aiming at minimal total expected costs, including costs of testing and of failures in the process after testing. Cost and time constraints on testing are also included in the analysis. We consider such reliability demonstration for a single type of task, as well as for multiple types of tasks to be performed by one system. We also consider optimal Bayesian reliability demonstration testing in combination with flexibility in the system redundancy, where more components can be installed to reduce test effort. For systems with redundancy, we restrict attention to systems with exchangeable components, with testing only at the component level.We use the Bayesian approach with the Binomial model and Beta prior distributions for the failure probabilities. We discuss the influence of choice of prior distribution on the required zero-failure test numbers, where these inferences are very sensitive to the choice of prior distribution, which requires careful attention to the interpretation of non-informativeness of priors. DeclarationThe work in this thesis is based on research carried out at the Statistics and Probability Group, Department of Mathematical Sciences, University of Durham, England.No part of this thesis has been submitted elsewhere for any other degree or qualification and it is all my own work unless referenced to the contrary in the text.

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Section: Overviewmentioning

confidence: 99%

Section: Learning From Testsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Probabilistic Assessment Study of Channels Downstream Slopes Erosion in the Maritime Environment

Khalifa

Ganainy

Nasr

2009

Journal of Coastal Research

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“…To obtain an approximate 90% interval for the unreliability, approximate the distribution as a beta distribution having the mean and variance just found, and use the 5th and 95th percentiles of that beta distribution. This is the approximation advocated by Martz and Waller (1990). All this is easy to accomplish with a computer program that contains very small subprograms or macros, such as a macro to find the probability of the union of two independent events and a macro to find the variance of a product of independent random variables.…”

Section: I)mentioning

confidence: 99%

Constrained noninformative priors

Atwood¹

1994

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“…The history of BNs in reliability can (at least) be traced back to [12,13]; the first real attempt to use BNs in reliability analysis is probably the work of Almond [13], where he used the GRAPHICAL-BELIEF tool to calculate reliability measures concerning a low pressure coolant injection system for a nuclear reactor (a problem originally addressed by Martz [14]). BNs constitute a modelling framework which is particularly easy to use in interaction with domain experts, also in the reliability field [15].…”

Section: Introductionmentioning

confidence: 99%

Inference in hybrid Bayesian networks

Langseth

Nielsen

Rumí

et al. 2009

Reliability Engineering & System Safety

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a b s t r a c tSince the 1980s, Bayesian networks (BNs) have become increasingly popular for building statistical models of complex systems. This is particularly true for boolean systems, where BNs often prove to be a more efficient modelling framework than traditional reliability techniques (like fault trees and reliability block diagrams). However, limitations in the BNs' calculation engine have prevented BNs from becoming equally popular for domains containing mixtures of both discrete and continuous variables (the so-called hybrid domains). In this paper we focus on these difficulties, and summarize some of the last decade's research on inference in hybrid Bayesian networks. The discussions are linked to an example model for estimating human reliability.

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Bayesian Reliability Analysis of Complex Series/Parallel Systems of Binomial Subsystems and Components

Cited by 45 publications

References 6 publications

Probabilistic Assessment Study of Channels Downstream Slopes Erosion in the Maritime Environment

Probabilistic Assessment Study of Channels Downstream Slopes Erosion in the Maritime Environment

Constrained noninformative priors

Inference in hybrid Bayesian networks

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