Bayesian prediction for two-parameter weibull lifetime models

Evans, I. G.; Nigm, A. A.

doi:10.1080/03610928008827909

Cited by 34 publications

(15 citation statements)

References 7 publications

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“…In this section, a byes approach is proposed to predict, on the basis of a fixed Although such relations have been easily derived from a basic result of the order statistic theory and are independent froin the underlying distribution, it appears that no paper dealing with the Bayesian prediction problem of the filtnre failure times has used these relations to derive the Bayesian predictive distrib~~tion on h f ( x l , x 2 ) (see, for Weibull samples, Evans and Nignl (1980a, 1980b), Tziafetas (1987 and Nigin (1989Nigin ( , 1990). …”

Section: Joint Posterior Density On Parametersmentioning

confidence: 99%

“…Recent examples are the paper of Moore and Beckman (1988), where approximate tolerance bounds on the number of failures using Poisson regression are given, and the paper of Bar-Lev et al (1992), who analyse from a Bayesian viewpoint repairable systems whose failure pattern is modeled by a Power-Law process. I-Iowever, it appears that no paper provides prediction intervals on the number of failures when the failure times are Weibull distributed, although a large nurnbrr of papers deal with prediction problems for Weibull samples (see, for example, the papers of Mann (1970) and Lawless (1973), who used the classical approach, and the papers of Evans and Nigm (1980a,1980b), Tziafetas (1987 and Nigm (1989Nigm ( ,1990, who follow the Bayesian approach).…”

Section: Introductionmentioning

confidence: 98%

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Bayes prediction of number of failures in weibull samples

Calabria

Pulcini

1995

Comm. in Stats. - Theory & Methods

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This work is concerned with the Bayesian prediction problem of the number of components which will fail in a future time interval, when the failure times are Weibull distributed. Both the I-sample and the 2-sample prediction problems are dealed with, and some choices of the prior densities on the distribution parameters are discussed which are relatively easy to work with and allow different degrees of knowledge on the failure mechanism to bc incorporated in thc predictive procedure. Useful relations betwern the predictive distribution on the number of future failures and the predictive distribution on the future failure times arc derived. Numerical examples are also gixrcn.

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Section: Joint Posterior Density On Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Bayes prediction of number of failures in weibull samples

Calabria

Pulcini

1995

Comm. in Stats. - Theory & Methods

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“…Moreover, the Bayesian approach to problems involving Weibull distributions has been applied in many recent papers. Soland (1969), Cavanos & Tsokos (1973), Papadopoulos & Tsokos (1976) and Evans & Nigm (1980) all used Bayesian methods in their analysis. More recently, Chen et al (1985) use Bayesian methods in their analysis of survival data on cancer patients.…”

Section: Introductionmentioning

confidence: 99%

Numerical Prediction for the Two-Parameter Weibull Distribution

Δελλαπόρτας¹,

Wright²

1991

The Statistician

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“…Investigations of Kingston and Patel (1981), Ascher and Feingold (1984 ) evaluated the reliability oftile WeibuH distribution, while Evans and Nigin (1980) examined the Bayesian predictions for the Weibull Type-2 model. In short, we expect the flow events to meet a specified threshold level.…”

Section: Performance Indicatorsmentioning

confidence: 99%

A Bootstrap Approach and Reliability of Time Varying Design

Logan

Ponnambalam

Zhou³

1999

JWMM

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A pollution control strategy encourages better management of wastewater discharges to the receiving streams. This is necessary to protect the aquatic species against high levels of toxic contaminants. The primary concern is to prevent violation of water quality objectives. Protection has been based on controls using frequency of extreme minimum flows and a constant design load. A statistical method to evaluate reliability of a stream under varying design loads is proposed. In it, we applied a Bootstrap compute-intensive technique to investigate the use of extreme-value probability distribution on seasonal flows.'I'he Wei bull Type-3 model is demonstrated to be suitable for design purposes.lt was possible to link this approach to a system reliability concept, to assess the vulnerable nature of a stream. IntroductionStreamflow quantity dilutes and plays a major role in assimilating wastewater. These phenomena are congruent with satisfYing requirements of water quality objectives. Essentially, streamflow events are stochastic and non-stationary, and by tradition a design flow for waste load allocations relies on probability distribution of extreme minimum flows. Gumbel (1963) and Engelhardt and Bain -------------------------

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Bayesian prediction for two-parameter weibull lifetime models

Cited by 34 publications

References 7 publications

Bayes prediction of number of failures in weibull samples

Bayes prediction of number of failures in weibull samples

Numerical Prediction for the Two-Parameter Weibull Distribution

A Bootstrap Approach and Reliability of Time Varying Design

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