Estimation of Trends in the Scram Rate at Nuclear Power Plants

Martz, Harry F.; Parker, Robert L.; Rasmuson, D.M.

doi:10.1080/00401706.1999.10485934

Cited by 8 publications

(10 citation statements)

References 19 publications

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“…1(a) indicates that there are some plants where the percentage of zero scrams are as high as 60% over 10 years). Martz et al (1999) stated that in year 1993 a third of all the plants experienced no unplanned scrams. The number of plants that did not have any unplanned scram increased from 1.5% in 1986 to 33.3% in 1993.…”

Section: Introductionmentioning

confidence: 98%

“…However, it is well known that hierarchical Bayes (HB) model usually accounts for all sorts of model uncertainty (for a given model) and hence instead of using a PEB method we employ a full HB model and obtain parameter estimates using the popular Markov Chain Monte Carlo (MCMC) methods. In addition to using a full HB approach, we also extend the framework of Martz et al (1999) by incorporating a zero-inflated model. Further, to account for auto-correlation among the scram rates (observed longitudinally for each plant) we use deterministic and stochastic time trend models.…”

Section: Introductionmentioning

confidence: 99%

“…However, it is to be noted that the models developed in this article is not restricted to this particular dataset and can be applied to analyze similar datasets involving count responses observed longitudinally over time and across several heterogeneous populations. Martz et al (1999) analyzed the data assuming a Poisson distribution on the number of unplanned scrams, a conjugate gamma prior, and an appropriate diffused hyper-prior. A parametric empirical Bayes (PEB) approximation was used.…”

Section: Introductionmentioning

confidence: 99%

“…In addition to excess zeros in the count response the dataset poses two other challenges, and those are how to model the auto-correlation among these scram rates and how to take into account plant-to-plant variation, both effects simultaneously within a model. This dataset has been previously analyzed by Martz et al (1999) and were originally obtained from a series of NRC annual reports (Office for Analysis and Evaluation of Operational Data, U.S. Regulatory Commission 1987Commission -1993. It consists of the annual number of unplanned scrams x ij in total critical hours T ij for plant i = 1 66 and coded year j = 1 10 (from 1984-1993).…”

Section: Introductionmentioning

confidence: 99%

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Estimation of SCRAM Rate Trends in Nuclear Power Plants Using Hierarchical Bayes Models

Mishra

Ghosh

2009

Communications in Statistics - Theory and Methods

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Nuclear reactors are equipped with reactor scram systems to ensure rapid shutdown of the system in the event of leaks, failure of power conversion systems, or other operational abnormalities. The U.S. Nuclear Regulatory Commission (NRC) collects data on scram rates from various nuclear power plants over time to estimate the trend of proper functioning of the plants which in turn is used to regulate them. The annual scram data obtained from 66 commercial nuclear power plants indicate an increase in the number of plants having no scrams from 1.5% in 1986 to 33% in 1993. To analyze correlated count data with excess zeros (e.g ., no scrams), a zeroinflated model that accounts for both temporal and plant-to-plant variation is being developed in this article. A wide class of possibly non-nested models was fitted usingMarkov Chain Monte Carlo (MCMC) methods and compared using a predictive criterion. Out-of-sample tests were also performed to study the performance of the models in predicting the scram rates of the plants. For the NRC data on scram rates, the stochastic time trend models that account for zero-inflation were found to provide a much better fit compared to the deterministic trend models.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Estimation of SCRAM Rate Trends in Nuclear Power Plants Using Hierarchical Bayes Models

Mishra

Ghosh

2009

Communications in Statistics - Theory and Methods

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“…Empirical Bayes methods have been applied in the fields of reliability (Sarhan 2003) and risk analysis (Martz et al 1999) and are regularly used to analyse accident occurrence patterns in road safety applications (Persaud and Lyon 2007 By using such homogenisation factors the estimates produced by pooling different event types using Empirical Bayes should become more accurate, in the sense that a more homogenous pool will attach more weight to the pooled average rather than the individual event experience. A reduction in error will be a consequence of greater reliance on a representative estimate derived from a larger sample size.…”

Section: Introductionmentioning

confidence: 99%

Merging expert and empirical data for rare event frequency estimation: Pool homogenisation for empirical Bayes models

Quigley¹,

Hardman²,

Bedford³

et al. 2011

Reliability Engineering & System Safety

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This version is available at https://strathprints.strath.ac.uk/27910/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the AbstractEmpirical Bayes provides one approach to estimating the frequency of rare events as a weighted average of the frequencies of an event and a pool of events. The pool will draw upon, for example, events with similar precursors. The higher the degree of homogeneity of the pool, then the Empirical Bayes estimator will be more accurate. We propose and evaluate a new method using homogenisation factors under the assumption that events are generated from a HomogeneousPoisson Process. The homogenisation factors are scaling constants which can be elicited through structured expert judgement and used to align the frequencies of different events, hence homogenising the pool. The estimation error relative to the homogeneity of the pool is examined theoretically indicating that reduced error is associated with larger pool homogeneity. The effects of misspecified expert assessments of the homogenisation factors are examined theoretically and through simulation experiments. Our results show that the proposed Empirical Bayes method using homogenisation factors is robust under different degrees of misspecification.

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Bayesian estimation of the rate at which a process, monitored by anX̄chart, goes out of control

Silver

Bischak

2004

International Journal of Production Research

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Estimation of Trends in the Scram Rate at Nuclear Power Plants

Cited by 8 publications

References 19 publications

Estimation of SCRAM Rate Trends in Nuclear Power Plants Using Hierarchical Bayes Models

Estimation of SCRAM Rate Trends in Nuclear Power Plants Using Hierarchical Bayes Models

Merging expert and empirical data for rare event frequency estimation: Pool homogenisation for empirical Bayes models

Bayesian estimation of the rate at which a process, monitored by anX̄chart, goes out of control

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