Characterization of the Generalized Pólya Process and its Applications

Hwan, Ji

doi:10.1017/s0001867800007588

Cited by 30 publications

(86 citation statements)

References 20 publications

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“…Before developing a bivariate preventive replacement policy for a system, we need to introduce the new repair type assumed in this paper, which is defined based on a new counting process model. Recently, in the work of Cha, the GPP has been introduced and its properties have been characterized. It was defined by the concept of stochastic intensity.…”

Section: Preliminariesmentioning

confidence: 99%

“…Lee and Cha have developed two periodic preventive maintenance models for a repairable deteriorating system and discussed the properties of the optimal policies assuming the GPP repair process. In the work of Cha, a simple age‐based preventive replacement policy was discussed assuming the GPP repair process. In the aforementioned work, the system is replaced when its age reaches T and it undergoes the GPP repairs at failures between replacements.…”

Section: Introductionmentioning

confidence: 99%

“…In the work of Cha, a simple age‐based preventive replacement policy was discussed assuming the GPP repair process. In the aforementioned work, the system is replaced when its age reaches T and it undergoes the GPP repairs at failures between replacements. In this paper, generalizing the work of Cha, a bivariate preventive replacement policy, which is based on the age T and the number of failures n , is developed and the corresponding optimal policy is studied.…”

Section: Introductionmentioning

confidence: 99%

“…In the aforementioned work, the system is replaced when its age reaches T and it undergoes the GPP repairs at failures between replacements. In this paper, generalizing the work of Cha, a bivariate preventive replacement policy, which is based on the age T and the number of failures n , is developed and the corresponding optimal policy is studied. It will be shown that the bivariate preventive replacement policy developed in this paper outperforms that considered in the work of Cha (see also the works of Gertsbakh and Kordonsky, Jack et al, and Baik and Murthy for the maintenance policies based on several time scales).…”

Section: Introductionmentioning

confidence: 99%

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A bivariate optimal replacement policy for a system subject to a generalized failure and repair process

Lee¹,

Hwan

2018

Appl Stoch Models Bus & Ind

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Traditionally, in the studies of the optimal maintenance policies for repairable systems, the nonhomogeneous Poisson process model, which corresponds to the minimal repair process, has been intensively applied. However, in many practical situations, the repair type is not necessarily minimal. In this article, a new repair process based on a new counting process model (so-called the generalized Polya process) is introduced. Then, the issue of the optimal replacement problem is discussed. A bivariate preventive replacement policy is developed and the properties of the optimal policy are studied. Illustrative examples are also presented. In addition, a comparison with a conventional replacement policy is performed.KEYWORDS dependent increments property, generalized Polya process, optimal maintenance policy, stochastic intensity, worse than minimal repair Appl Stochastic Models Bus Ind. 2019;35:637-650.wileyonlinelibrary.com/journal/asmb

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A bivariate optimal replacement policy for a system subject to a generalized failure and repair process

Lee¹,

Hwan

2018

Appl Stoch Models Bus & Ind

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“…It is shown in Cha 15 and Asfaw and Lindqvist 30 that probabilities of occurrence of n events in (0, t] can be described the corresponding negative binomial distribution:…”

Section: Some Stochastic Processes Of Failure/repairmentioning

confidence: 99%

On preventive maintenance under different assumptions on the failure/repair processes

Hwan

Finkelstein

2017

Quality & Reliability Eng

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We discuss models of preventive maintenance (PM) under different assumptions on the failure/repair processes. The main emphasis is on the PM modeling under the Brown-Proschan model for minimal/perfect repairs. We also present the generalization of this model for the failure/repair process governed by the generalized Polya process. Some comparisons with conventional PM models are discussed (Nonhomogeneous Poisson process, renewal process, and geometric process of failure/repairs). Several practical examples are considered. In this paper, we will discuss some optimal PM models that are already popular in practice and suggest some new ones. We will perform the corresponding analysis and comparisons under different assumptions with respect to the failure/repair processes. Our aim is to focus on some important issues of the PM modeling and comparisons for different settings rather than to present a thorough literature review and analysis of existing models. We will consider in detail the case when the failure/repair processes obey the Brown-Proschan imperfect repair model (Brown and Proscahn 13

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An overview of some classical models and discussion of the signature‐based models of preventive maintenance

Asadi

Hashemi

2022

Appl Stoch Models Bus & Ind

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In reliability engineering literature, a large number of research papers on optimal preventive maintenance (PM) of technical systems (networks) have appeared based on preliminary many different approaches. According to the existing literature on PM strategies, the authors have considered two scenarios for the component failures of the system. The first scenario assumes that the components of the system fail due to aging, while the second scenario assumes the system fails according to the fatal shocks arriving at the system from external or internal sources. This article reviews different approaches on the optimal strategies proposed in the literature on the optimal maintenance of multi‐component coherent systems. The emphasis of the article is on PM models given in the literature whose optimization criteria (cost function and stationary availability) are developed by using the signature‐based (survival signature‐based) reliability of the system lifetime. The notions of signature and survival signature, defined for systems consisting of one type or multiple types of components, respectively, are powerful tools assessing the reliability and stochastic properties of coherent systems. After giving an overview of the research works on age‐based PM models of one‐unit systems and k‐out‐of‐n systems, we provide a more detailed review of recent results on the signature‐based and survival signature‐based PM models of complex systems. In order to illustrate the theoretical results on different proposed PM models, we examine two real examples of coherent systems both numerically and graphically.

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Characterization of the Generalized Pólya Process and its Applications

Cited by 30 publications

References 20 publications

A bivariate optimal replacement policy for a system subject to a generalized failure and repair process

A bivariate optimal replacement policy for a system subject to a generalized failure and repair process

On preventive maintenance under different assumptions on the failure/repair processes

An overview of some classical models and discussion of the signature‐based models of preventive maintenance

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