Persistent Link:
http://hdl.handle.net/10150/184647
Title:
RELIABILITY GROWTH MODELS FOR ATTRIBUTES (BAYES, SMITH).
Author:
SANATGAR FARD, NASSER.
Issue Date:
1982
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
In this dissertation the estimation of reliability for a developmental process generating attribute type data is examined. It is assumed that the process consists of m stages, and the probability of failure is constant or decreasing from stage to stage. Several models for estimating the reliability at each stage of the developmental process are examined. In the classical area, Barlow and Scheuer's model, Lloyd and Lipow's model and a cumulative maximum likelihood estimation model are investigated. In the Bayesian area A.F.M. Smith's model, an empirical Bayes model and a cumulative beta Bayes model are investigated. These models are analyzed both theoretically and by computer simulation. The strengths and weaknesses of each are pointed out, and modifications are made in an attempt to improve their accuracy. The constrained maximum likelihood estimation model of Barlow and Scheuer is shown to be inaccurate when no failures occur at the final stage. Smith's model is shown to be incorrect and a corrected algorithm is presented. The simulation results of these models with the same data indicate that with the exception of the Barlow and Scheuer's model they are all conservative estimators. When reliability estimation with growth is considered, it is reasonable to emphasize data obtained at recent stages and de-emphasize data from the earlier stages. A methodology is developed using geometric weights to improve the estimates. This modification is applied to the cumulative MLE model, Lloyd and Lipow's model, Barlow and Scheuer's model and cumulative beta Bayes model. The simulation results of these modified models show considerable improvement is obtained in the cumulative MLE model and the cumulative beta Bayes model. For Bayesian models, in the absence of prior knowledge, the uniform prior is usually used. A prior with maximum variance is examined theoretically and through simulation experiments for use with the cumulative beta Bayes model. These results show that the maximum variance prior results in faster convergence of the posterior distribution than the uniform prior. The revised Smith's model is shown to provide good estimates of the unknown parameter during the developmental process, particularly for the later stages. The beta Bayes model with maximum variance prior and geometric weights also provides good estimates.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Reliability (Engineering) -- Mathematical models.; Reliability (Engineering) -- Statistical methods.; Reliability (Engineering) -- Computer programs.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Systems and Industrial Engineering; Graduate College
Degree Grantor:
University of Arizona

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleRELIABILITY GROWTH MODELS FOR ATTRIBUTES (BAYES, SMITH).en_US
dc.creatorSANATGAR FARD, NASSER.en_US
dc.contributor.authorSANATGAR FARD, NASSER.en_US
dc.date.issued1982en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractIn this dissertation the estimation of reliability for a developmental process generating attribute type data is examined. It is assumed that the process consists of m stages, and the probability of failure is constant or decreasing from stage to stage. Several models for estimating the reliability at each stage of the developmental process are examined. In the classical area, Barlow and Scheuer's model, Lloyd and Lipow's model and a cumulative maximum likelihood estimation model are investigated. In the Bayesian area A.F.M. Smith's model, an empirical Bayes model and a cumulative beta Bayes model are investigated. These models are analyzed both theoretically and by computer simulation. The strengths and weaknesses of each are pointed out, and modifications are made in an attempt to improve their accuracy. The constrained maximum likelihood estimation model of Barlow and Scheuer is shown to be inaccurate when no failures occur at the final stage. Smith's model is shown to be incorrect and a corrected algorithm is presented. The simulation results of these models with the same data indicate that with the exception of the Barlow and Scheuer's model they are all conservative estimators. When reliability estimation with growth is considered, it is reasonable to emphasize data obtained at recent stages and de-emphasize data from the earlier stages. A methodology is developed using geometric weights to improve the estimates. This modification is applied to the cumulative MLE model, Lloyd and Lipow's model, Barlow and Scheuer's model and cumulative beta Bayes model. The simulation results of these modified models show considerable improvement is obtained in the cumulative MLE model and the cumulative beta Bayes model. For Bayesian models, in the absence of prior knowledge, the uniform prior is usually used. A prior with maximum variance is examined theoretically and through simulation experiments for use with the cumulative beta Bayes model. These results show that the maximum variance prior results in faster convergence of the posterior distribution than the uniform prior. The revised Smith's model is shown to provide good estimates of the unknown parameter during the developmental process, particularly for the later stages. The beta Bayes model with maximum variance prior and geometric weights also provides good estimates.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectReliability (Engineering) -- Mathematical models.en_US
dc.subjectReliability (Engineering) -- Statistical methods.en_US
dc.subjectReliability (Engineering) -- Computer programs.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineSystems and Industrial Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.committeememberRamberg, Johnen_US
dc.contributor.committeememberSchultz, Donalden_US
dc.contributor.committeememberWang, Chiangen_US
dc.contributor.committeememberDietrich, Duaneen_US
dc.identifier.proquest8227367en_US
dc.identifier.oclc682948782en_US
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