Narrow Results

This paper considers a periodic preventive maintenance policy under which each preventive maintenance (PM) reduces the hazard rate of the repairable system, while keeping the pattern of hazard rate unchanged. For this model, the hazard rate at a given time t is affected by the improvement factor which depends on the number of PMs conducted until t. In addition to the periodic preventive maintenance, the system undergoes the minimal repair at each failure between the preventive maintenances. We derive mathematical formulas to evaluate the expected cost rate per unit time by computing the expected number of failures depending on the hazard rate of the underlying life distribution of the system. Assuming that the system is replaced by a new one at the N-th preventive maintenance, the optimal values of N and the preventive maintenance period, which minimize the expected cost rate, are solved and thus the best schedules for the periodic preventive maintenance policy are established. Explicit solutions for the optimal schedule for the periodic preventive maintenance are presented when the failure times follow the Weibull distribution.

For a repairable product that fails under warranty, the manufacturer can choose between repair and replacement. Many different warranty servicing strategies involving these two types of rectification action have already been studied. In this paper, we propose two new servicing strategies involving minimal repair, each with two parameters that are selected optimally to minimize expected warranty servicing costs. We develop models to obtain the optimal parameter values for each new strategy and then carry out a comparison with a selection of the existing strategies through a numerical example.

A system subject to internal defects and external shocks is analyzed in this paper. Internal defects initiate following a nonhomogeneous Poisson process (NHPP) and they grow according to deterioration processes modeled as gamma processes. A corrective replacement is performed when the deterioration of a defect exceeds a failure threshold. The system is subject to external shocks. After an external shock, the system is replaced with probability 1 – p and is minimally repaired with probability p. The system is preventively replaced at the age of T. Costs are associated with the maintenance actions. The value of T that minimizes the expected cost rate is obtained analytically. Numerical examples are showed to illustrate the theoretical results.

This paper presents new sequential imperfect preventive maintenance (PM) models incorporating adjustment/improvement factors in hazard rate and effective age. The models are hybrid in the sense that they are combinations of the age reduction PM model and the hazard rate adjustment PM model. It is assumed that PM is imperfect: It not only reduces the effective age but also changes the hazard rate, while the hazard rate increases with the number of PMs. PM is performed in a sequence of intervals. The objective is to determine the optimal PM schedule to minimize the mean cost rate. Numerical examples for a Weibull distribution are given.

This paper deals with the problem of determining an optimal age replacement by incorporating minimal repair, planned replacement, and unplanned replacement into a k-out-of-n system subject to shocks. In particular, two kinds of solution procedures are discussed to obtain the optimal replacement age, one is a straightforward procedure, and the other is a graphical approach based on the Total Time on Test (TTT) concept. A statistical solution procedure for estimating the optimal replacement time is proposed, and the optimal policies are obtained directly from real data.

This paper develops a mathematical model to derive the optimal preventive maintenance warranty (PMW) policy for repairable products with age-dependent maintenance costs. Under a PMW, any product failures are rectified by minimal repair, and additional preventive maintenance actions are carried out within the warranty period. When the costs for preventive maintenance and minimal repair are age-dependent, the optimal number of preventive maintenance actions, corresponding maintenance degrees, and the maintenance schedule for designing a PMW policy are derived here such that the expected total warranty cost is minimized. Under some reasonable conditions, we show that there exists a unique optimal PMW policy in which the product is maintained periodically with the same preventive maintenance degree. Using this property, an efficient algorithm is provided to search for the optimal policy. Some related models developed in the literature are discussed and these models are in fact special cases of the model proposed in this paper. Furthermore, when the life-time distribution of a product is Weibull, a closed-form expression of the optimal policy is obtained. Finally, the impact of providing preventive maintenance is evaluated through numerical examples.

It is commonplace to replicate critical components in order to increase system lifetimes and reduce failure rates. The case of a general N-plexed system, whose failures are modeled as N identical, independent nonhomogeneous Poisson process (NHPP) flows, each with rocof (rate of occurrence of failure) equal to λ(t), is considered here. Such situations may arise if either there is a time-dependent factor accelerating failures or if minimal repair maintenance is appropriate. We further assume that system logic for the redundant block is 2-out-of-N:G. Reliability measures are obtained as functions of τ which represents a fixed time after which Maintenance Teams must have replaced any failed component. Such measures are determined for small λ(t)τ, which is the parameter range of most interest. The triplex version, which often occurs in practice, is treated in some detail where the system reliability is determined from the solution of a first order differential-delay equation (DDE). This is solved exactly in the case of constant λ(t), but must be solved numerically in general. A general means of numerical solution for the triplex system is given, and an example case is solved for a rocof resembling a bathtub curve.

This paper takes up managerial maintenance policies during different phases for mission executions. When a mission execution is divided into two phases and three phases respectively, replacement, minimal repair and keeping failure status become alternatives for managerial maintenance policies. Further, we give approximations of the above managerial maintenance policies to make the computations simple. In this paper, keeping failure status is considered as the last choice for the last phase of mission executions. We aim to minimize the expected maintenance costs for the total mission executions. All of the discussions are made analytically and their numerical examples are given.

We propose a maintenance policy for new equipment on a repair-refund maintenance strategy in this paper and derive the optimal lease period from the lessor’s perspective based on independent and identical distribution of historical failure data which obey power law process. The cost model of a full refund and a proportional refund is studied, and the corresponding optimal leasing period is determined by reducing the expected total cost rate to the largest extent. We use a numerical example to illustrate the proposed cost model and analyze the sensitivity of related parameters. Furthermore, we show that the proportional refund policy is preferable than a full refund to the lessor. Finally, according to the simulation outcome, the proposed methods are effective and instructions for lessor in regard to equipment lease are provided.

A reliability-based design (RBD) of a mixed series–parallel system with deteriorative components for minimal life cycle cost is presented in this paper. Two formulations are presented based on the type of preventive maintenance modeling. These formulations incorporate the effects of preventive maintenance and minimal repairs to adjust the system failure rate. Genetic Algorithms are used to obtain an optimal system design. The economic life of the designed system is also evaluated. The results have practical applications in the area of computer integrated manufacturing where a system must perform below a given failure rate.

The opportunistic maintenance of a k-out-of-n:G system is studied in this paper. In many applications, it spends less cost and time to perform maintenance on several components jointly than on each component separately. Based on this fact, two new (τ, T) opportunistic maintenance models with the consideration of reliability requirements are proposed. In these two models with two decision variables τ ≤ T, only minimal repairs are performed on failed components before time τ, and corrective maintenance of all failed components are combined with preventive maintenance (pm) of all functioning but deteriorated components after τ; if the system survives to time T without perfect maintenance, it will be subject to pm at time T. Considering maintenance time, asymptotic system cost rate and availability are derived. The results obtained generalize and unify some previous research in this area. Application to aircraft engine maintenance is presented.

In this note, a pseudodynamic cost limit replacement policy presented by Park¹ is considered. Park¹ showed that the pseudodynamic policy is inferior to constant repair cost limit policy. In this note, the correct mean cost rate under the same assumption in the Park's model is obtained and the pseudodynamic policy is shown to be better than the constant repair cost limit policy² through the same numerical examples of Park.¹

Production systems are generally subjected to failures, which are not self-announcing. These failures may not bring the system to a complete halt but may cause its malfunction, which would affect the quality of output. Inspections at intervals are required to detect such failures. After a failure, the system would continue to produce degraded output unless corrective action (minimal repair) is taken after detecting the failure during inspection. These minimal repairs do not bring the system to "as good as new" condition, but restore its condition to the level prior to the failure. A replacement/overhaul of the system after operation for a long time will make it "as good as new." The paper presents optimal inspection models for such a production system. The system is replaced or overhauled at predetermined times, marking the end of a cycle, while inspections are periodically done within a cycle. An entire output during an interval is scrapped, if inspection reveals a failure during the interval. Dynamic programming formulation has been used to optimize expected profit per cycle. The model is suitable when prior sales commitments exist and failure of the system is not self-announcing.