Empirical Bayes Estimation of the Reliability of Nuclear-Power-Plant Emergency Diesel Generators

Martz, Harry F.; Kvam, Paul H.; Abramson, Lee R.

doi:10.2307/1268899

Cited by 13 publications

(6 citation statements)

References 23 publications

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“…Notation c 1 , c 2 , c 3 covariances in the piston rings example E 0 , var 0 , cov 0 prior expectation, variance, and covariance E 1 , var 1 , cov 1 posterior expectation, variance, and covariance E k , var k , cov k expectation, variance, and covariance after observing Y k = y k f 0 ( ) a prior density function …”

Section: Appendixmentioning

confidence: 99%

“…Each combination of system and year in these data corresponds to a Poisson random variable with a mean specific to that system and that year. In reference [3] the number of successes by individual motors in a collection of emergency diesel generators (EDGs) for nuclear power stations followed a binomial distribution. The number of trials was the number of demands for that EDG and the unknown parameter of interest was the probability that the EDG started successfully.…”

Section: Introductionmentioning

confidence: 99%

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Bayes linear kinematics in the analysis of failure rates and failure time distributions

Wilson

Farrow

2010

Proceedings of the Institution of Mechanical Engineers, Part O:

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Collections of related Poisson or binomial counts arise, for example, from a number of different failures in similar machines or neighbouring time periods. A conventional Bayesian analysis requires a rather indirect prior specification and intensive numerical methods for posterior evaluations. An alternative approach using Bayes linear kinematics in which simple conjugate specifications for individual counts are linked through a Bayes linear belief structure is presented. Intensive numerical methods are not required. The use of transformations of the binomial and Poisson parameters is proposed. The approach is illustrated in two examples, one involving a Poisson count of failures, the other involving a binomial count in an analysis of failure times

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Section: Appendixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bayes linear kinematics in the analysis of failure rates and failure time distributions

Wilson

Farrow

2010

Proceedings of the Institution of Mechanical Engineers, Part O:

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show abstract

“…In order to check the robustness of the proposed methodology when the a priori hypotheses about the NLG component reliabilities are not valid, the Beta distribution has been adopted to characterize component reliabilities, because this is the most commonly used distribution as an a priori for reliability values (Martz and Waller, 1982;Martz et al, 1993;1996). The analytical expression of the Beta pdf, as a function of the values r assumed by a rv R in (0,1), is:…”

Section: Robustness Analysismentioning

confidence: 99%

Negative Log‐Gamma distribution for data uncertainty modelling in reliability analysis of complex systems ‐ Methodology and robustness

Allella

Chiodo

Lauria

et al. 2001

International Journal of Quality &Amp; Reliability Management

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In the paper, the problem of uncertain data in reliability analysis of complex systems is examined. The analysis is addressed to system reliability assessment with imprecise knowledge of component reliabilities, an item becoming more and more important for systems affected by considerable technological change. Starting from component uncertain data, a new method for the whole system reliability uncertainty description, based upon a Bayesian approach and not depending on the reliability model of each component, is proposed. The reliability value of each component is considered as a random variable described by a Negative Log-Gamma distribution. The proposed methodology makes it possible to compute the features of system reliability uncertainty (i.e. reliability distribution, confidence intervals, etc.) as functions of component uncertain data, thus characterizing the propagation of uncertainty from the components to the system. Numerical applications, related to a test system, are presented to show the validity of the method and its``robustness'', i.e. it is shown that it yields satisfactory results also when component reliabilities are not Negative Log-Gamma but Beta distributed.

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“…For example, Gelfand, Dey, and Chang (1992) propose a crossvalidation approach in which conditional residuals are plotted to reveal failures in the modeling assumptions regarding G. On the other hand, Gelman et al (1995) consider an omnibus goodness-of-fit test which requires calculating the corresponding Bayes p-value. Martz, Kvam, and Abramson (1996) also present an omnibus goodness-of-fit test based on the use of a randomized Kolmogorov-Smirnov test statistic. The omnibus test we consider here is an extension of common classical chi-square goodness-of-fit tests in the sense that we directly test whether or not the observed data come from the marginal distributional family corresponding to the given sampling model and assumed prior.…”

Section: Parametric Empirical Bayes Prior Validationmentioning

confidence: 99%

A chi-square goodness-of-fit test for non-identically distributed random variables: with application to empirical Bayes

Conover

Cox

Martz

1997

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Empirical Bayes Estimation of the Reliability of Nuclear-Power-Plant Emergency Diesel Generators

Cited by 13 publications

References 23 publications

Bayes linear kinematics in the analysis of failure rates and failure time distributions

Bayes linear kinematics in the analysis of failure rates and failure time distributions

Negative Log‐Gamma distribution for data uncertainty modelling in reliability analysis of complex systems ‐ Methodology and robustness

A chi-square goodness-of-fit test for non-identically distributed random variables: with application to empirical Bayes

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