A Bayesian Statistical Inference Approach to Automotive Reliability Estimation

Grohowski, G.; Hausman, W. C.; Lamberson, Leonard R.

doi:10.1080/00224065.1976.11980746

Cited by 11 publications

(4 citation statements)

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“…The Bayesian approach can be used to combine subjective opinion with data obtained from testing, to compute a system's reliability [26,49]. Bayesian inferential analysis is straightforward when one represents prior information via a conjugate prior distribution.…”

Section: Bayesian Statisticsmentioning

confidence: 99%

“…From (5.12), the minimal tests for a series system, n ser , is the closest integer value that is larger than or equal to the real-valued solution of the following equations 25) for any value of α, and (5.13) yields 26) for integer values of α. If n is large compared to a positive integer α, with β = 0 and p close to 1 then, using the same justifications used in Section 3.2, n ser is close…”

Section: Reliability Demonstration For Multiple Tasks Of One Typementioning

confidence: 99%

“…For example, for the reliability requirement with p = 0.95 and for Q = 1, 000, this leads to the optimal solution of installing y = 4 components and n = (12, 12, 15) zero-failure tests. If we increase the cost per component to Q = 3, 000 in the same setting, the optimum solution is y = 3 components with n = (26,28,35) tests. If we consider a 2-out-of-2 system for this case, the optimal zero-failure test numbers are (296, 322, 454).…”

Section: Optimal Testing and Redundancy Levelmentioning

confidence: 99%

“…Hausman [26] present the Bayesian approach which quantifies prior information in order to estimate reliability. They support the selection of Gamma distributions as prior distributions for their conjugacy to the Poisson distribution.…”

Section: Bayesian Statisticsmentioning

confidence: 99%

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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: Bayesian Statisticsmentioning

confidence: 99%

Section: Reliability Demonstration For Multiple Tasks Of One Typementioning

confidence: 99%

Section: Optimal Testing and Redundancy Levelmentioning

confidence: 99%

Section: Bayesian Statisticsmentioning

confidence: 99%

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