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Article: Bayesian estimation and prediction for the power law process with left-truncated data

TitleBayesian estimation and prediction for the power law process with left-truncated data
Authors
KeywordsBayesian method
Nonhomogeneous Poisson process
Noninformative prior
Prediction intervals
Reliability growth
Issue Date2011
PublisherColumbia University, Department of Statistics. The Journal's website is located at http://www.jds-online.com/
Citation
Journal of Data Science, 2011, v. 9 n. 3, p. 445-470 How to Cite?
AbstractThe power law process (PLP) (i.e., the nonhomogeneous Poisson process with power intensity law) is perhaps the most widely used model for analyzing failure data from reliability growth studies. Statistical inferences and prediction analyses for the PLP with left-truncated data with classical methods were extensively studied by Yu et al. (2008) recently. However, the topics discussed in Yu et al. (2008) only included maximum likelihood estimates and confidence intervals for parameters of interest, hypothesis testing and goodness-of-fit test. In addition, the prediction limits of future failure times for failure-truncated case were also discussed. In this paper, with Bayesian method we consider seven totally different prediciton issues besides point estimates and prediction limits for xn+k. Specically, we develop estimation and prediction methods for the PLP in the presence of left-truncated data by using the Bayesian method. Bayesian point and credible interval estimates for the parameters of interest are derived. We show how five single-sample and three two-sample issues are addressed by the proposed Bayesian method. Two real examples from an engine development program and a repairable system are used to illustrate the proposed methodologies.
Persistent Identifierhttp://hdl.handle.net/10722/139715
ISSN

 

DC FieldValueLanguage
dc.contributor.authorTian, GLen_US
dc.contributor.authorTang, MLen_US
dc.contributor.authorYu, JWen_US
dc.date.accessioned2011-09-23T05:54:45Z-
dc.date.available2011-09-23T05:54:45Z-
dc.date.issued2011en_US
dc.identifier.citationJournal of Data Science, 2011, v. 9 n. 3, p. 445-470en_US
dc.identifier.issn1680-743X-
dc.identifier.urihttp://hdl.handle.net/10722/139715-
dc.description.abstractThe power law process (PLP) (i.e., the nonhomogeneous Poisson process with power intensity law) is perhaps the most widely used model for analyzing failure data from reliability growth studies. Statistical inferences and prediction analyses for the PLP with left-truncated data with classical methods were extensively studied by Yu et al. (2008) recently. However, the topics discussed in Yu et al. (2008) only included maximum likelihood estimates and confidence intervals for parameters of interest, hypothesis testing and goodness-of-fit test. In addition, the prediction limits of future failure times for failure-truncated case were also discussed. In this paper, with Bayesian method we consider seven totally different prediciton issues besides point estimates and prediction limits for xn+k. Specically, we develop estimation and prediction methods for the PLP in the presence of left-truncated data by using the Bayesian method. Bayesian point and credible interval estimates for the parameters of interest are derived. We show how five single-sample and three two-sample issues are addressed by the proposed Bayesian method. Two real examples from an engine development program and a repairable system are used to illustrate the proposed methodologies.-
dc.languageengen_US
dc.publisherColumbia University, Department of Statistics. The Journal's website is located at http://www.jds-online.com/-
dc.relation.ispartofJournal of Data Scienceen_US
dc.subjectBayesian method-
dc.subjectNonhomogeneous Poisson process-
dc.subjectNoninformative prior-
dc.subjectPrediction intervals-
dc.subjectReliability growth-
dc.titleBayesian estimation and prediction for the power law process with left-truncated dataen_US
dc.typeArticleen_US
dc.identifier.emailTian, GL: gltian@hku.hken_US
dc.identifier.authorityTian, GL=rp00789en_US
dc.description.naturelink_to_OA_fulltext-
dc.identifier.hkuros195636en_US
dc.identifier.volume9en_US
dc.identifier.issue3en_US
dc.identifier.spage445en_US
dc.identifier.epage470en_US
dc.publisher.placeUnited States-

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