A non-Markov model for the optimum replacement of self-repairing systems subject to shocks

Rangan, A.; Grace, R. Esther

doi:10.1017/s0021900200041012

Cited by 8 publications

(4 citation statements)

References 10 publications

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“…Shanthikumar and Sumita (1983), Abdel-Hameed (1986), Aven and Gaader (1987), Anderson (1987Anderson ( , 1988, Rangan and Grace (1988), Gut (1990), Lai and Yuan (1993), Gut and Husler (1999), and Li et al (1999) are just a few. Shanthikumar and Sumita (1983), Abdel-Hameed (1986), Aven and Gaader (1987), Anderson (1987Anderson ( , 1988, Rangan and Grace (1988), Gut (1990), Lai and Yuan (1993), Gut and Husler (1999), and Li et al (1999) are just a few.…”

Section: Introductionmentioning

confidence: 99%

Preventive replacement policy with cumulative repair-cost limit for a system under increasing failure rate shock model

Lai

Hung

2012

IJPQM

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A system is subject to shocks and these shocks are divided into two types: non-lethal and lethal shocks. Non-lethal shocks increase the failure rate of the system along with the age of the system and make the system eventually into a minor failure. Lethal shock whenever occurs makes the system critical failure. This shock process is called an increasing failure rate shock model. A minor failure is corrected by minimal repair, while a critical failure is rectified by replacement. In this paper, we propose a periodical replacement policy for a system, incorporating with the concept of cumulative repair-cost limit. While carrying out minimal repair, the repair cost and the accumulated repair cost are calculated. The system is replaced at age T or a minor failure at which the accumulated repair cost exceeds a predetermined threshold L or at a critical failure. The minimum-cost replacement policy is studied and a sensitivity analysis is conducted to evaluate the effect of model parameters on the optimal T*.Keywords: periodical replacement policy; increasing failure rate shock model; cumulative repair-cost limit; minimal repair.Reference to this paper should be made as follows: Lai, M-T. and Hung, C-W. (2012) 'Preventive replacement policy with cumulative repair-cost limit for a system under increasing failure rate shock model', Int.

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Section: Introductionmentioning

confidence: 99%

Preventive replacement policy with cumulative repair-cost limit for a system under increasing failure rate shock model

Lai

Hung

2012

IJPQM

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“…Tapiero and Venezia (1979) treated the variance of the cost as a risk factor to study a maintenance problem. Rangan and Grace (1988) used variance optimisation criterion to obtain the optimal replacement cycle for systems. However, both works only considered periodic replacement policy.…”

Section: Introductionmentioning

confidence: 99%

Optimal variability sensitive condition-based maintenance with a Cox PH model

Chen

et al. 2011

International Journal of Production Research

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Condition based maintenance (CBM) is an important maintenance strategy in practice. In this paper, we propose a CBM method to effectively incorporate system health observations into maintenance decision making to minimise the total maintenance cost and cost variability. In this method, the system degradation process is described by a Cox PH model and the proposed framework includes simulation of failure process and maintenance policy optimisation using adaptive nested partition with sequential selection (ANP-SS) method, which can adaptively select or create the most promising region of candidates to improve the efficiency. Different from existing CBM strategies, the proposed method relaxes some restrictions on the system degradation model and taking the cost variation as one of the optimisation objectives. A real industry case study is used to demonstrate the effectiveness of our framework.

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“…As a result, this model is easier to implement than control-limit policies. Boland and Proschan [3], Abdel-Hameed [1], Lai and Yuan [6], Puri & Singh [12], and Ragan and Grace [13] have studied such a model. (4) Increasing failure rate model: in this type of model, whenever a shock occurs, it damages the system with the increases of failure rate.…”

Section: Introductionmentioning

confidence: 99%

Economic discrete replacement policy subject to increasing failure rate shock model

Lai

Shih

Tang

2005

Int J Adv Manuf Technol

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This paper presents an economic discrete replacement model for a single-unit system subjected to external shocks. In this model, the system is affected by both external shocks and its ageing process. The external shocks are divided into two types, namely non-lethal and lethal, depending on their effect to the system. A non-lethal shock damages the system by increasing the failure rate of a certain degree, while a lethal shock causes the system into instantaneous failure. The failure rate also increases with the system's ageing process. The system is replaced at the instant of the nth non-lethal shock, or on failure, whichever occurs first. The research proposed a model where the long run expected cost per unit time is formulated by introducing relative costs and derived as a criterion of optimality. By minimizing the cost, an optimal number, n * , is then found. The optimal number, n * , is also verified to be finite and unique under certain conditions.Keywords Ageing process · Failure rate · Prevention maintenance model · Replacement policy · Shock · Single-unit system Notation:Intensity rate of a Poisson process {N(t)} t 0 pThe probability that an external shock occurs is a nonlethal shock r j (t) Failure rate of the system when the age of the system is t and the number of non-lethal shocks incurred over [0, t] P j (t) The probability that there is just j non-lethal shocks incurred over [0, t] r(t, pλ) Failure rate of the system without lethal shocks F p (t) Survival function of the system at age t without lethal shocks G(t)Survival function of the occurrence time of lethal shock Y 1The time to first type I failure of the system with survival function F p (t) without lethal shocks X 1The time to first type II failure of the system with survival function G(t) without non-lethal shocks ZThe time to first failure (type I or type II) of the system,The occurrence time of the nth non-lethal WThe time to replacement, W = min(T n , Z) E(R 1 ) The expected cost incurred during a replacement cycle time E(W 1 ) The expected replacement cycle time C p (n) The long-run expected cost per unit time

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A non-Markov model for the optimum replacement of self-repairing systems subject to shocks

Cited by 8 publications

References 10 publications

Preventive replacement policy with cumulative repair-cost limit for a system under increasing failure rate shock model

Preventive replacement policy with cumulative repair-cost limit for a system under increasing failure rate shock model

Optimal variability sensitive condition-based maintenance with a Cox PH model

Economic discrete replacement policy subject to increasing failure rate shock model

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