A Generalized Block-Replacement Policy

Beichelt, Frank

doi:10.1109/tr.1981.5221021

Cited by 46 publications

(21 citation statements)

References 3 publications

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“…Over the past few decades, a number of researchers have studied simplified PM/OM policies, namely, group maintenance policy (Okumoto and Elsayed, 1983) and block replacement policy (Beichelt, 1981). The simplified PM/OM policies have a common disadvantage in that they may result in replacing an almost new unit.…”

Section: Overview Of Pm/om Modelsmentioning

confidence: 99%

Transient analysis of maintenance intervention of continuous multi-unit systems

et al. 2008

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The requirement for self-diagnosing and fault-tolerant systems and the need to conserve dwindling natural resources have led to an increased emphasis on design for reusability, survivability and maintainability. Existing research on failure and maintenance processes focus mostly on steady-state operation. A methodology for intervention analysis of a continuous multi-unit system under transient response is now presented. For modeling convenience, a continuous process without buffers is considered. A delay function is used in the determination of the optimum preventive maintenance policy for the individual units. The cost saving which arises when an opportunistic maintenance policy is adopted is investigated. The approach has three major thrusts. First, the development of analytical models based on the renewal theoretic framework that incorporate maintenance costs in formulating the Maintenance Decision Problem (MDP). Second, numerical methods for solving the results from the proposed formulation using differential and integral equations. Third, the embedded Binary Integer Programming (BIP) formulation that is used to optimize the resulting solutions because of the strong dynamic and unimodularity feature of the MDP problem. Data from an Aluminum Hot Roll Line consisting of three component parts is used to demonstrate proof of concept and to verify the problem formulation. Sensitivity analyses are performed on the resulting BIP model to provide optimum arrangement for the opportunistic maintenance problem.

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Section: Overview Of Pm/om Modelsmentioning

confidence: 99%

Transient analysis of maintenance intervention of continuous multi-unit systems

et al. 2008

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“…In the works of Beichelt and Fischer [3] and Beichelt [4,5], some generalized replacement policies for the general failure model were considered. In those researches, it was noted that a sufficient condition for the existence of the finite optimal replacement policy is that both r T (t) and p(t) are strictly increasing functions.…”

Section: Application To the General Failure Modelmentioning

confidence: 99%

“…In the literature a minor failure that can be removed by a minimal repair is called a Type I failure, whereas a catastrophic one that can be removed only by a complete repair (or a replacement) is called a Type II failure. These models have been considered by many researchers (see, for example, [3][4][5]). Recently, there has been much research on burn-in procedures for the general failure model (see [6 -9]).…”

Section: Introductionmentioning

confidence: 99%

“…In this research, some specific shapes on the probability function p(t) are assumed. For example, p(t) is a constant function in [3-6, 8, 9], p(t) is a non-decreasing (or strictly increasing) function in [3][4][5]9], or it is a bathtubshape function in [7,9]. The shape of the probability function p(t) takes an important role in deriving the main theorems therein.…”

Section: Introductionmentioning

confidence: 99%

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Some probability functions in reliability and their applications

Hwan

2006

Naval Research Logistics

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There has been much research on the general failure model recently. In the general failure model, when the unit fails at its age t, Type I failure (minor failure) occurs with probability 1 Ϫ p(t) and Type II failure (catastrophic failure) occurs with probability p(t). In the previous research, some specific shapes (constant, non-decreasing, or bathtub-shape) on the probability function p(t) are assumed. In this article, general results on some probability functions are obtained and applied to study the shapes of p(t). The results are also applied to determining the optimal inspection and allocation policies in maintenance problems.

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“…Préventive maintenance policies with minimal repair have, of late, attracted the attention of several authors. Many contributions to such préventive maintenance policies with minimal repair have been made by Barlow and Hunter [1], Muth [12], Beichelt and Fisher [3], Beichelt [4], Boland and Proschan [10], Boland [9], Berg and Cléroux [5], Tilquin and Cléroux [21], Cléroux, Dubuc and Tilquin [11], Berg, Bienvenu and Cléroux [6], Block, Borges and Savits [8], Nakagawa and Kowada [13], Sheu [16,17,18], Tahara and Nishida [20], Sheu, Kuo and Nakagawa [19] and others, Muth [12] suggested minimal repairs for a period of length t and then replacement at the first failure after t. Tahara and Nishida [20] considered a generalization of Muth's policy and suggested the following 0, T) policy. "Replace a system when the first failure after t hours operating or the total operating time reachs T(0<t^T), whichever occurs first.…”

Section: Introductionmentioning

confidence: 99%