Point Processes for Reliability Analysis

Hwan, Ji; Finkelstein, Maxim

doi:10.1007/978-3-319-73540-5

Cited by 63 publications

(59 citation statements)

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“…is given by (see, e.g., the proof of Theorem 1 in Cha and Finkelstein [9] and Cha and Finkelstein [10])…”

Section: Characterization Based On the Mixture Of Bppmentioning

confidence: 99%

On a Multivariate Generalized Polya Process Without Regularity Property

Hwan¹,

Badía²

2019

Prob. Eng. Inf. Sci.

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Most of the multivariate counting processes studied in the literature are regular processes, which implies, ignoring the types of the events, the non-occurrence of multiple events. However, in practice, several different types of events may occur simultaneously. In this paper, a new class of multivariate counting processes which allow simultaneous occurrences of multiple types of events is suggested and its stochastic properties are studied. For the modeling of such kind of process, we rely on the tool of superposition of seed counting processes. It will be shown that the stochastic properties of the proposed class of multivariate counting processes are explicitly expressed. Furthermore, the marginal processes are also explicitly obtained. We analyze the multivariate dependence structure of the proposed class of counting processes.

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“…is given by (see, e.g., the proof of Theorem 1 in Cha and Finkelstein [9] and Cha and Finkelstein [10])…”

Section: Characterization Based On the Mixture Of Bppmentioning

confidence: 99%

On a Multivariate Generalized Polya Process Without Regularity Property

Hwan¹,

Badía²

2019

Prob. Eng. Inf. Sci.

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“…We must now "integrate a random Z from (25)". The first guess, similar to the age-based PM case defined by (22), would be…”

Section: Heterogeneous Pmmentioning

confidence: 99%

“…Denote by F p ( t ) the cdf of the time between two consecutive perfect repairs. Then,

F_{p} ((), x) = 1 - exp ({}, - \int_{0}^{x} p ((), u) λ ((), u) d u) .

It also follows from the work of Cha and Finkelstein that the process of minimal repairs is the NHPP with rate q ( t ) λ ( t ). It is important to state that although there exist numerous imperfect repair models, minimal repair can be considered as the only one that combines practical importance (minimal repair often occurs in practice) with a very tractable mathematical description.…”

Section: Pm Under the Brown‐proschan Model: Homogeneous Systemsmentioning

confidence: 99%

Preventive maintenance for homogeneous and heterogeneous systems

Finkelstein

Levitin

2018

Appl Stoch Models Bus & Ind

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We consider optimal preventive maintenance for homogeneous and heterogeneous systems with major (critical) and minor (noncritical) failures. A major failure results in a replacement of a failed system, whereas minor failures can be minimally instantaneously repaired. Distinct from the homogeneous case, where the process of minimal repairs is the Poisson process, the process of minimal repairs in the heterogeneous case is the mixed Poisson process that does not possess the memoryless property. This enables considering the number of minimal repairs as the decision parameter for the corresponding optimal preventive maintenance policy. The proposed approach is theoretically justified, and the detailed illustrative numerical examples are presented. KEYWORDSBrown-Proschan model, heterogeneity, minimal repair, nonhomogeneous Poisson process, perfect repair, preventive maintenance 908

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“…Proposition in Ramlau-Hansen (1983, pp. 461).Consider a predictable process W n (t) and assume that for some 2 , asn → + ∞. First, we study the bias term, B(t).…”

Section: Appendix A: Proof Of Theoremmentioning

confidence: 99%

“…A typical reference is Ascher and Feingold 1 and an updated revision on the subject, including recent theoretical developments on point processes and applications on reliability analysis, is presented in Cha and Finkelstein. 2 The most commonly used models for the failure process of a repairable system are renewal processes (RP) and nonhomogeneous Poisson processes (NHPP). Lindqvist et al 3 and Lindqvist 4 study some generalizations of these models.…”

Section: Introductionmentioning

confidence: 99%

Data visualization for reliability analysis of repairable systems

Gámiz

López-Montoya

Martínez-Miranda

et al. 2018

Quality & Reliability Eng

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The objective of this paper is to find out possible patterns of failure occurrences in a repairable system. We develop a graphical exploratory tool and perform visual inference considering non‐parametric local linear kernel estimators for the rate of occurrence of failures (ROCOF) and its first derivative. The shape characteristics of the ROCOF function are distinguished from those which are merely an artefact of the sampling variability of the data through the construction of confidence intervals for the first derivative. The proposal is illustrated with several real data sets, and its performance is evaluated through an extensive simulation study.

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Point Processes for Reliability Analysis

Cited by 63 publications

References 0 publications

On a Multivariate Generalized Polya Process Without Regularity Property

On a Multivariate Generalized Polya Process Without Regularity Property

Preventive maintenance for homogeneous and heterogeneous systems

Data visualization for reliability analysis of repairable systems

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