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

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.

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, we study renewals in a system with two components connected in series. Both components can undergo corrective maintenance (i.e., either full replacement/perfect repair or minimal repair) when a failure occurs. When one of the units fails and is correctively maintained, the other one is either preventively replaced (if cost-feasible) or simply left working as is. When a component is minimally repaired or left working as is, its remaining lifetime is reevaluated (“memory effect”) and is taken into consideration in calculating the next renewal. A “coupled” lifetime that combines the lifetimes of the two serially connected components is proposed to represent the joint lifetime of the system. We develop renewal functions based on the coupled lifetimes and show that they follow the classical or generalized renewal theory depending on whether the components work without memory or not. Approximation formulas for the new renewal functions are also obtained and validated by Monte Carlo simulations for various combinations of distributions, and a comparative cost analysis is conducted.

A minimal repair replacement model with two types of failure and a safety constraint

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.

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.

This paper presents a novel reliability-centered multilevel maintenance optimization model tailored for multicomponent systems subjected to stochastic dependent (s-dependent) competing risks (CRs). Four types of maintenance actions, including minimal repair (MR), medium preventive maintenance (MPM), overhaul preventive maintenance (OPM), and preventive replacement (PR), are incorporated into the development of the multilevel maintenance model. The Copula function is utilized to quantify the s-dependence among failure risks, and subsequently, all unknown parameters are estimated via the inference function for margins (IFM) method. Three types of decision variables are designed to minimize the long-run expected cost rate of the system. Finally, sequential decision process method is utilized to solve the model, and a numerical example of a metro door system illustrates the effectiveness of our proposed model.

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.

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

An optimal planned replacement time based on availability and cost functions for a system subject to three types of failures

An age replacement policy with increasing minimal repair cost

A generalization of the block replacement policy (BRP) is proposed and analysed. Under such a policy, an operating system is preventively replaced at timeskT(k= 1, 2, 3, ···), independently of its failure history. At failure an operating system is either replaced by a new or a used one or minimally repaired or remains inactive until the next planned replacement. The cost of theith minimal repair of the new subsystem at ageydepends on the random partC(y) and the deterministic partci(y). The mathematical model is defined and general analytical results are obtained.

This paper investigates the optimal threshold values of age to perform preventive maintenance (PM) actions for leased equipment within the lease period. In this paper, we use age reduction method to describe the degree of PM and construct the maintenance cost function. For repairable leased equipment, two maintenance models are proposed: (i) maintenance policy of single-phase and (ii) maintenance policy of two-phase. During the lease period, PM actions are carried out when the age of equipment reaches a certain threshold value. Any failure of the leased equipment is rectified by a minimal repair within the lease period. Under these maintenance schemes, the mathematical models of the expected total cost for maintenance policies of single-phase and two-phase are established, and the optimal maintenance policies are derived such that the expected total cost is minimized. Finally, the features of the optimal maintenance policy are illustrated through numerical examples.

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

In this paper, we consider a production-inventory control problem for an Economic Manufacturing Quantity (EMQ) model with machine breakdowns and planned preventive replacement (overhaul) of the production unit. Two types of failure are considered. When type I failure occurs (major failure), the unit is replaced by a new one and the interrupted lot is aborted. Starting a new lot after a replacement or after a complete production run incurs a setup cost. Type II failures (minor failures) are corrected by minimal repairs which take negligible time. After performing a minimal repair, production can be resumed immediately at a cost lower than the setup cost. It is assumed that both preventive and failure replacement times are random and the demand that cannot be satisfied during these replacement times is lost.