AN OPPORTUNITY-BASED AGE REPLACEMENT POLICY CONSIDERING WARRANTY

A general lost-sales Economic Manufacturing Quality (EMQ) model with machine breakdowns, minimal repairs and planned replacements is considered. When the machine fails, minimal repair is performed in negligible time and production is resumed immediately. It is assumed that resumption cost is lower than the set-up cost incurred at the beginning of each production cycle. Other cost components include inventory holding cost, operating cost, lost-sales cost and the preventive replacement (overhaul) cost. Both time to failure and the time to perform an overhaul are assumed to be generally distributed random variables. The objective is to find the optimal lot-sizing/ preventive replacement policy minimising the long-run expected average cost per unit time. The problem is formulated in the framework of semi-Markov decision processes. It is shown that the optimal lot size is a function of the operating age of the machine and the optimal preventive replacement is an age replacement. An EMQ model with lost sales is studied under the assumption of a constant production lot size. It is shown that a good approximation to the optimal policy can be found by solving two nonlinear equations.

Age replacement policies are investigated. When a unit reaches age T, a preventive replacement is made. If a failure occurs prior to age T and if the random repair cost is less than a fixed constant, a minimal repair is made. Otherwise the unit is replaced at failure.

In this paper, a two-unit system with failure interactions is studied. The system is subject to two types of shocks (I and II) and the probabilities of these two shock types are age-dependent. A type I shock, rectified by a minimal repair, causes a minor failure of unit A and type II shock causes a complete system failure that calls for a replacement. Each unit A minor failure also results in an amount of damage to unit B. The damages to unit B caused by type I shocks can be accumulated to trigger a preventive replacement or a corrective replacement action. Besides, unit B with cumulative damage of level z may become minor failed with probability \(\pi (z)\) at each unit A minor failure and rectified by a minimal repair. We consider a more general replacement policy. Under this policy, the system is preventively replaced at the Nth type I shock, or at the time when the total damage to unit B exceeds a pre-specified level Z (but less than a failure level K where \(K>Z\)) or is replaced correctively at first type II shock or when the total damage to unit B exceeding a failure level K, whichever occurs first. To minimize the expected cost per unit time, the optimal replacement policy \((N^{*}\), \(Z^{*})\) is derived analytically and determined numerically. We also show that several previous maintenance models in the literature are special cases of our model.

A (τ, T) replacement policy is commonly used to prevent system failure. In previous research, it was assumed that the maintenance time can be ignored since it is negligibly short compared with operation time. However, neglecting maintenance time when optimizing maintenance policies for systems for which the maintenance time is not relatively short can lead to sub-optimal or even incorrect solutions to the problem, resulting in higher maintenance costs. An optimal (τ, T) replacement policy is presented for series systems in which the units deteriorate following different stochastic processes independently. The failure of each unit in the time interval [τ, T) occurs in accordance with a nonhomogeneous Poisson process, the failure is immediately removed by a minimal repair and the system continues operating. The failure of any unit in time interval [τ, T) causes the entire system to fail, which is immediately detected, and corrective maintenance is performed on the whole system. If a failure does not occur during time interval [τ, T), the system receives preventive replacement at T A (τ, T) replacement policy was formulated that considers both preventive and corrective maintenance times and that determines an optimal preventive replacement interval that minimizes the expected long-run cost per unit time. A numerical example illustrates that implementing the proposed (τ, T) replacement policy can effectively reduce maintenance costs.

An approach for simulating models of highly dependable systems with general failure and repair time distribution is described. The approach combines importance sampling with event rescheduling in order to obtain variance reductions in such rare event simulations. The approach is general in nature and allows a variety of features commonly arising in dependability modeling to be simulated effectively. It is shown how the technique can be applied to systems with redundant components and/or periodic maintenance. For different failure time distributions, the effect of the maintenance period on the steady-state availability is explored. The amount of component redundancy needed to achieve a certain reliability level is determined. >

This paper develops an optional replacement policy for the maintenance of two non-identical components connected in series configuration. In this policy, each component is replaced correctively whenever it fails and preventively only if its age reaches or exceeds a preventive replacement age T when the other component fails. Mathematical model is established to evaluate the expected maintenance cost per unit of time over an infinite horizon for a special case when one of the two components has an increasing failure rate whereas the second component has a constant failure rate. Optimal policy is derived from the mathematical model and validated using a simulation model. The simulation model is then extended to a general case when the two components have increasing failure rates. Numerical examples are carried out to illustrate the special and the general cases of the considered optional replacement policy.

In reality, most operating systems are repaired or replaced when they have failed. For such systems, it would be reliable to maintain them in a control-limit consideration of repairs or operations. This article addresses a system scheduling policy for preventive replacement with discrete control limits of minimal repair and random work. An operating system which works at random times for multiple jobs (N tandem jobs or N parallel jobs) is considered. The system subjects to two failure mechanisms and maintained imperfectly: type-I (minor) failure rectified by a minimal repair and type-II (catastrophic) failure removed by a corrective replacement. To control the deterioration process, the preventive replacement is planned to undergo before catastrophic failure at number n of minimal repairs or the completion of N multiple jobs. The objective is to determine the optimal discrete scheduling replacement parameters (n* or N*) that minimizes the mean cost rate function in a finite time horizon. Model analysis relating to the existence and uniqueness of optimal solutions is provided. A Numerical example is presented for illustrative purposes.

This paper proposes a bivariate (T, L2) replacement policy with double repair-cost limits for a system subject to increasing failure rate model. External shocks are divided into two types: type-I shock and type-II shock. Each type-II shock makes the system suffer a minor failure, while each type-I shock increases the failure rate of the system by a certain amount and it will induce the system into critical failure. When a minor failure occurs, the repair cost is evaluated and minimal repair is executed if the repair cost is less than a single repair-cost limit L1 and the accumulated repair cost is less than a cumulative repair-cost limit L2, otherwise, the system is replaced by a new one. In addition, the system is replaced at scheduled time T or at critical failure. By formulating the optimisation problem, the optimal T* and L2* which minimise the long-run expected cost per unit time are found, respectively. We develop the corresponding computational algorithm to obtain the optimal replacement policy and present a numerical example to illustrate the effectiveness of the proposed model.

WITHDRAWN: A trivariate optimal replacement policy for a deteriorating system based on cumulative damage and inspections

This paper investigates the effects of unsuccessful repairs on the optimal periodic replacement policy for a repairable product with multiple attempts of minimal repair under the free-repair warranty. The motivation for this study is based on the novel notion of ‘multi-attempt minimal repair’, first introduced by Cha and Finkelstein (2024a, 2024b), in which they highlighted various practical reasons and examples to illustrate that minimal repair attempts may sometimes fail and need to be repeated until success is achieved. Their repair model and useful properties served as the motivation for this study. For both the warranted and non-warranted products, cost models are developed from the user’s perspective, and the corresponding optimal replacement policies are derived to minimize the long-run expected cost rates. By comparing these optimal policies, we show that the optimal planned time for preventive replacement should be adjusted toward the end of the warranty period, and the effects of unsuccessful minimal repair produce different degrees of impact, respectively, on the warranted and non-warranted product. Finally, detailed numerical examples and computation results illustrate our findings, and some insightful observations about practical and managerial implications are concluded.

Different type of maintenance problems have been investigated during the past decades. With the growth in complexity of modern systems, the cost of purchasing new systems becomes higher ever than before. Surprisingly, very little attention in the literature has been paid to the failure replacement in these preventive maintenance models. However, in practice most systems incur increasingly expensive down time costs when the systems suffer the unexpected failures. The major changes to the standard maintenance model in this research are the addition of a failure replacement cost for a failed system and the reliability limit for which system has to be replaced. The overall objective of this research is to propose an efficient algorithm to obtain the optimal maintenance policy. The optimal preventive maintenance policy is investigated with incorporating the costs of minimal repair, imperfect preventive maintenance, failure replacement and preventive replacement. The specific maintenance actions for a repairable system are when to perform an imperfect preventive maintenance or to replace the system while the system is in the operating condition. In another case, the specific maintenance actions for a repairable system are whether to replace the system, or to perform a minimal repair when the system fails. The number of imperfect preventive maintenance and the control limits of the optimal maintenance policy are calculated under the expected average cost rate criterion.

Optimisation of a single-component maintenance system: A smoothed perturbation analysis approach

Optimal maintenance policy for multicomponent systems with periodic and opportunistic inspections and preventive replacements

Optimal maintenance–replacement policy of products with competing failures after expiry of the warranty

On discrete failure-time distributions