An age replacement policy with increasing minimal repair cost

doi:10.1016/0026-2714(89)90563-5

Microelectronics Reliability

Volume 29, Issue 2, 1989, Pages 153-157

https://doi.org/10.1016/0026-2714(89)90563-5 Get rights and content

Abstract

A replacement policy for a system in which minimal repair cost increases in system age is considered. If a system fails before age T, it is minimally repaired. Otherwise, the system is replaced when if fails for the first time after age T. The mean cost rate is used as a criterion for optimization. It is shown that the optimal T minimizing the mean cost rate is finite and unique.

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Cited by (9)

Optimum component reallocation and system replacement maintenance for a used system with increasing minimal repair cost
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Motivated by the economics of a used system, the paper studies a component reallocation (CR) based maintenance policy for a used and repairable system with functionally interchangeable components. The policy, denoted as optimum CR and system replacement maintenance, incorporates the actions of CR and system replacement to minimize the expected maintenance cost per unit time. The components experience nonhomogeneous degradation with different failure rates and different minimal repair costs because of different position conditions. The minimal repair costs are increasing over time. The CR action reallocates the functionally interchangeable components to balance degradation. The system replacement action replaces system by a new or used one. A mixed binary nonlinear optimization model for the policy is established to determine the optimal time and assignment for CR and the optimal time for system replacement. Further, we analyze the expected maintenance cost per unit time over the used age of system and some special cases. Finally, specializing the failure rate by Weibull distribution and the minimal repair cost by inversely proportional to the component reliability, numerical examples show the efficiency of CR compared to the system replacement maintenance without CR.
A note on optimal replacement policy under general repair
1993, European Journal of Operational Research
An age replacement policy with minimal repair and general random repair cost
1992, Microelectronics Reliability
An age replacement policy is introduced which incorporates minimal repair, replacement, and general random repair costs. If an operating unit fails at age y<T, it is either replaced by a new unit with probability p(y) at a cost c₀, or it undergoes minimal repair with probability q(y) = 1−p(y). Otherwise, a unit is replaced when it fails for the first time after age T. The cost of the i-th minimal repair of an unit at age y depends on the random part C(y) and the deterministic part c_i(y). The aim of the paper is to find the optimal T which minimizes the long run expected cost per unit time of the policy. Various special cases are considered.
Optimal replacement of a system with imperfect repair
1991, Microelectronics Reliability
We consider a deteriorating system subject to random failure. At failure the system can be replaced or can undergo a repair with the following three possible outcomes: as good as new, returned to the functioning state just prior to failure or the system must be scrapped and replaced at additional replacement cost. We assume that the repair cost increases with the system's age and that both maintenance actions take negligible time. Viewing the repair/replacement process as a semi-Markov decision process, we prove that under certain assumptions the optimal replacement policy is an age-dependent policy proposed by Muth (5) for a system with constant repair cost and minimal repairs. The average cost function is then derived which can be minimized to obtain the optimal replacement time $T^{∗}$ . This generalizes previously obtained results for repairable systems with minimal repair.
Preventive maintenance models for technical systems
2019, Springer Series in Reliability Engineering
A survey of replacement models with minimal repair
2011, Springer Series in Reliability Engineering

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An age replacement policy with increasing minimal repair cost

Abstract

European J. of Operational Research

Optimal preventive maintenance policies

Oper. Res.

Periodic replacement when minimal repair costs vary with time

Naval Research Logistics Quarterly