A quasi renewal process and its applications in imperfect maintenance

Wang, Hongzhou; Pham, Hoang

doi:10.1080/00207729608929311

Cited by 126 publications

(73 citation statements)

References 9 publications

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“…Many models, including the geometric process (GP) and its variants (Lam, 1988;Wang & Pham, 1996;Wu & Clements-Croome, 2006), the generalised renewal process models (GRP) (Kijima & Sumita, 1986;Kijima, 1989;Doyen & Gaudoin, 2004), and the reduction of failure hazard models (Doyen & Gaudoin, 2004), have been developed for modelling imperfect repair. 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 The particular models themselves are defined as follows.…”

Section: Definitionsmentioning

confidence: 99%

Two new stochastic models of the failure process of a series system

Scarf

2017

European Journal of Operational Research

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Consider a series system consisting of sockets into each of which a component is inserted: if a component fails, it is replaced with a new identical one immediately and system operation resumes. An interesting question is: how to model the failure process of the system as a whole when the lifetime distribution of each component is unknown? This paper attempts to answer this question by developing two new models, for the cases of a specified and an unspecified number of sockets, respectively. It introduces the concept of a virtual component, and in this sense, we suppose that the effect of repair corresponds to replacement of the most reliable component in the system. It then discusses the probabilistic properties of the models and methods for parameter estimation. Based on six datasets of artificially generated system failures and a real-world dataset, the paper compares the performance of the proposed models with four other commonly used models: the renewal process, the geometric process, Kijima's generalised renewal process, and the power law process. The results show that the proposed models outperform these comparators on the datasets, based on the Akaike information criterion.Our responses are shown below, taking the reviewer comments one by one.In the revised paper, new text is coloured blue, deletions are indicated, and text we wish to emphasise to address a review comment is coloured red.Reviewer #1: This revised version significantly improves the first paper. I have still some comments that should be taken into account before acceptation.1. Throughout the paper, the components of the series systems are supposed to be independent. This assumption should be stated clearly. Response: We now state this clearly at the beginning of Proposition 1. Also, please note that the first sentence immediately under the heading of Section 2 says: "Consider a series system with a number of statistically independent components." (See the sentence in red on page 6).2. Answer to my comment 9. The proof (d) of the additivity of the CRIF is not really a proof. The additivity comes from the facts that the counting process of system failures is the sum of the counting processes of components failures, and that the probability of having more than one failure in an infinitesimal interval is zero because of the independence of the components. See considerations of that kind in reference 1. Response: Yes, we agree, and we have rewritten the text in part (d) there on page 8. In addition, the sentence starting with "Alternatively, …" shortly after is introduced to outline the idea of the proof and is in response to comment 1 of reviewer 3.3. Answer to my comment 15. You say that the sentence "and the oldest VC in the VSS will be renewed" has been removed. But in fact, it is still in the paper. You should explain this part more clearly. The fact that one component in the VSS is renewed seems contradictory with the initial assumption that the VSS is not maintained or minimally repaired. Response: We agree the explanation was ...

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Section: Definitionsmentioning

confidence: 99%

Two new stochastic models of the failure process of a series system

Scarf

2017

European Journal of Operational Research

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“…In this section, the univariate quasi-renewal processes proposed by Wang and Pham (1996b) are generalized to multivariate distributions to model n-dimensional warranties. For a failure process defined along n-dimensions, let X i = (X 1i , X 2i , .…”

Section: Multiple Quasi-renewal Processmentioning

confidence: 99%

The role of repair strategy in warranty cost minimization: An investigation via quasi-renewal processes

Samatlı-Paç

Taner

2009

European Journal of Operational Research

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a b s t r a c tMost companies seek efficient rectification strategies to keep their warranty related costs under control. This study develops and investigates different repair strategies for one-and two-dimensional warranties with the objective of minimizing manufacturer's expected warranty cost. Static, improved and dynamic repair strategies are proposed and analyzed under different warranty structures. Numerical experimentation with representative cost functions indicates that performance of the policies depend on various factors such as product reliability, structure of the cost function and type of the warranty contract.

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“…The geometric process (Lam, 1988) defines an alternative to the non-homogeneous Poisson process: a sequence of random variables {X k , k = 1, 2, · · · } forms a geometric process if the cumulative distribution function of X k is given byF (a k−1 t) for k = 1, 2, · · · , where a is a positive constant andF (t) is an arbitrary distribution function. Wang and Pham (1996) later refer to the geometric process as a quasi-renewal process. Wu and Clements-Croome (2006) extend the geometric process by replacing its parameter a k−1 with αa k−1 + βb k−1 , where a ≥ 1 and 0 < b ≤ 1.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, optimization of maintenance policy based on the geometric process has attracted considerable attention in the reliability literature (Lam and Zhang, 2004;Lam, 1988;Chen and Li, 2008;Wang and Pham, 1996;Wu and Clements-Croome, 2006). The geometric process (Lam, 1988) defines an alternative to the non-homogeneous Poisson process: a sequence of random variables {X k , k = 1, 2, · · · } forms a geometric process if the cumulative distribution function of X k is given byF (a k−1 t) for k = 1, 2, · · · , where a is a positive constant andF (t) is an arbitrary distribution function.…”

Section: Introductionmentioning

confidence: 99%

“…Wu and Clements-Croome (2006) extend the geometric process by replacing its parameter a k−1 with αa k−1 + βb k−1 , where a ≥ 1 and 0 < b ≤ 1. The geometric process has been applied to reliability analysis and maintenance policy optimization for various systems, see (Wang and Pham, 1996;Liang et al, 2012;Cheng and Li, 2012;Yu et al, 2013;Wang and Zhang, 2014), for example. In order to model the effectiveness of preventive maintenance (PM), Wu and Zuo (2010) review existing PM models, explore their interrelationships, and extend them to three new models: linear, nonlinear and their hybrid.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimisation of replacement policy for a one-component system subject to Poisson shocks

2015

International Journal of Systems Science: Operations & Logi

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A quasi renewal process and its applications in imperfect maintenance

Cited by 126 publications

References 9 publications

Two new stochastic models of the failure process of a series system

Two new stochastic models of the failure process of a series system

The role of repair strategy in warranty cost minimization: An investigation via quasi-renewal processes

Optimisation of replacement policy for a one-component system subject to Poisson shocks

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