Bayes inference for a non-homogeneous Poisson process with power intensity law (reliability)

Guida, Maurizio; Calabria, R.; Pulcini, Gianpaolo

doi:10.1109/24.46489

Cited by 99 publications

(51 citation statements)

References 9 publications

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“…Section 3 presents posterior densities for the parameters a and/3 and compares these results with those obtainable from the frequency approach. These posterior densities are similar to those previously obtained by Guida et al (1989) and Kyparisis and Singpurwalla (1985), but include both failure and time truncation data. Section 4 discusses prediction of the number of failures in some specified time interval and of future failure times.…”

Section: Introductionsupporting

confidence: 75%

“…From a Bayesian perspective, Guida et al (1989) discuss point and interval estimation for a and ~3 assuming failure truncation data and using several different choices of priors, both informative and noninformative. Kyparisis and Singpurwalla (1985) analyse both interval and failure truncation data by employing informative priors on a and ~ and derive prediction distributions of future failure times and the number of failures in some future time interval.…”

Section: Introductionmentioning

confidence: 99%

“…The case 7 = 1 is most commonly used (Box and Tiao (1973)). The prior (a/3) -1 has been used by Guida et al (1989).…”

Section: Introductionmentioning

confidence: 99%

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Bayesian inference for the power law process

1992

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Section: Introductionsupporting

confidence: 75%

Section: Introductionmentioning

confidence: 99%

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Bayesian inference for the power law process

1992

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“…See, for example, Crow 14 , Finkelstein 15 , Guida et al 16 , MIL-HDBK-781 17 or Bain et al 18 . In fact, in García-Escudero et al 2 , we have already successfully used this process in the analysis of this sort of data.…”

Section: Systems That Are Improvingmentioning

confidence: 97%

Warning procedures for systems that are improving

García-Escudero

Fernández

Duque

et al. 2007

Quality & Reliability Eng

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Nowadays it is quite usual that systems are correctly maintained. This leads to a decreasing number of failures for the system. In this paper we discuss how to establish warning procedures that take into account features giving the chance of detecting eventual changes of trend in the systems and allowing taking measures before too much damage has actually happened. The proposed procedure is applied to the study of the reliability and maintenance of the railway electric supply system. In this kind of systems, complex and extended, testing the performance of the system and effectiveness of the maintenance tasks has special interest.

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“…In such situations, a Bayesian method that utilities expert opinions and information from a similar system currently in operation can be employed to improve decision making (see [13,26]). Guida et al [12] conducted a Bayesian inference for the parameters of the Weibull power law intensity function of an NHPP and compared the result with the corresponding maximum likelihood estimation. Mazzuchi and Soyer [19] presented a Bayesian analysis for determining the optimal replacement strategies for both the block replacement protocol with minimal repair and the traditional age replacement protocol.…”

Section: Introductionmentioning

confidence: 99%

Nonperiodic preventive maintenance for repairable systems

Lin

Huang

2010

Naval Research Logistics

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As a complex system with multiple components usually deteriorates with age, preventive maintenance (PM) is often performed to keep the system functioning in a good state to prolong its effective age. In this study, a nonhomogeneous Poisson process with a power law failure intensity is used to describe the deterioration of a repairable system, and the optimal nonperiodic PM schedule can be determined to minimize the expected total cost per unit time. However, since the determination of such optimal PM policies may involve numerous uncertainties, which typically make the analyses difficult to perform because of the scarcity of data, a Bayesian decision model, which utilizes all available information effectively, is also proposed for determining the optimal PM strategies. A numerical example with a real failure data set is used to illustrate the effectiveness of the proposed approach. The results show that the optimal schedules derived by Bayesian approach are relatively more conservative than that for non-Bayesian approach because of the uncertainty of the intensity function, and if the intensity function are updated using the collected data set, which indicates more severe deterioration than the prior belief, replacing the entire system instead of frequent PM activities before serious deterioration is suggested.

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Bayes inference for a non-homogeneous Poisson process with power intensity law (reliability)

Cited by 99 publications

References 9 publications

Bayesian inference for the power law process

Bayesian inference for the power law process

Warning procedures for systems that are improving

Nonperiodic preventive maintenance for repairable systems

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