A deteriorating cold standby repairable system with priority in use

In this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. In this system, it is assumed that the working time distributions and the repair time distributions of the two components are both exponential and component 1 is given priority in use. After repair, component 2 is “as good as new” while component 1 follows a geometric process repair. Under these assumptions, using the geometric process and a supplementary variable technique, some important reliability indices such as the system availability, reliability, mean time to first failure (MTTFF), rate of occurrence of failure (ROCOF) and the idle probability of the repairman are derived. A numerical example for the system reliability R(t) is given. And it is considered that a repair-replacement policy based on the working age T of component 1 under which the system is replaced when the working age of component 1 reaches T. Our problem is to determine an optimal policy T^∗ such that the long-run average cost per unit time of the system is minimized. The explicit expression for the long-run average cost per unit time of the system is evaluated, and the corresponding optimal replacement policy T^∗ can be found analytically or numerically. Another numerical example for replacement model is also given.     

Opportunity-based age replacement with a one-cycle criterion

In this paper age replacement (AR) and opportunity-based age replacement (OAR) for a unit are considered, based on a one-cycle criterion, both for a known and unknown lifetime distribution. In the literature, AR and OAR strategies are mostly based on a renewal criterion, but in particular when the lifetime distribution is not known and data of the process are used to update the lifetime distribution, the renewal criterion is less appropriate and the one-cycle criterion becomes an attractive alternative. Conditions are determined for the existence of an optimal replacement age T^* in an AR model and optimal threshold age T_opp^* in an OAR model, using a one-cycle criterion and a known lifetime distribution. In the optimal threshold age T_opp^*, the corresponding minimal expected costs per unit time are equal to the expected costs per unit time in an AR model. It is also shown that for a lifetime distribution with increasing hazard rate, the optimal threshold age is smaller than the optimal replacement age. For unknown lifetime distribution, AR and OAR strategies are considered within a nonparametric predictive inferential (NPI) framework. The relationship between the NPI-based expected costs per unit time in an OAR model and those in an AR model is investigated. A small simulation study is presented to illustrate this NPI approach.     

An imperfect maintenance model with block replacements

We consider a model in which when a device fails it is either repaired to its condition prior to failure or replaced. Moreover, the device is replaced at times kT, k = 1, 2, … The decision to repair or replace the device at failure depends on the age of the device at failure. We find the optimal block time, T₀, that minimizes the long-run average cost of maintenance per unit time. Our results are shown to extend many of the well known results for block replacement policies.     

The Optimum Repair Limit Replacement Policies

This paper considers a single unit system which is first repaired if it fails. If the repair is not completed up to the fixed repair limit time then the unit under repair is replaced by a new one. The cost functions are introduced for the repair and the replacement of the failed unit. The optimum repair limit replacement time minimizing the expected cost per unit of time for an infinite time span is obtained analytically under suitable conditions. Two special cases where the repair cost functions are proportional to time and are exponential are discussed in detail with numerical examples.     

Quantifying the risk in age and block replacement policies

Preventive maintenance policies have been studied in the literature without considering the risk due to the cost variability. In this paper, we consider the two most popular preventive replacement policies, namely, age and block replacement policies under long-run average cost and expected unit time cost criteria. To quantify the risk in the preventive maintenance policies, we use the long-run variance of the accumulated cost over a time interval. We numerically derive the Risk-sensitive preventive replacement policies and study the impact of the Risk-sensitive optimality criterion on the managerial decisions. We also examine the performance of the expected unit time cost criterion as an alternative to the traditional long-run average cost criterion.     

On a Replacement Problem of a Cumulative Damage Model

Items are assumed to fail only by degradation. An appropriate stochastic model of such items is a cumulative process in which an item can fail only when the total amount of damage exceeds a prespecified failure level. This paper introduces a replacement policy in which an item is replaced at a certain level of damage before failure or at failure, whichever occurs first. The optimum replacement level of damage which will minimize the total expected cost per unit of time for an infinite time span is obtained. A numerical example is also presented. The total expected cost for a finite time span is also discussed.     

Cost optimal replacement of monotone,repairable systems

In this paper we study the optimal replacement problem of a monotone system comprising n components, where the components are “minimally” repaired at failures. The optimality function studied is the long run expected cost per unit of time. Different categories of replacement policies are investigated.     

Replacement Policies for Components that Deteriorate

For many industrial processes the cost of a component failing in service is sufficient to warrant replacement before failure, but intensive operation of the processes restricts replacement opportunities. A model is proposed where at each opportunity replacement is optional. Dynamic programming methods are used to show that for components that deteriorate as they are used, the best policy is to replace the component if its age exceeds a control limit otherwise to defer replacement.Numerical results are given when the time to failure of the component has a gamma distribution and replacement opportunities occur at random, or are entirely regular. A "rule of thumb" is given for calculating the control limit, and it is shown to be nearly optimal.     

An optimal repair–replacement policy for a cold standby system with use priority

In this paper, the maintenance problem for a cold standby system consisting of two dissimilar components and one repairman is studied. Assume that both component 1 and component 2 after repair follow geometric process repair and component 1 is given priority in use when both components are workable. Under these assumptions, using geometric process repair model, we consider a replacement policy N under which the system is replaced when the number of failures of component 1 reaches N. Our purpose is to determine an optimal replacement policy N1 such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit expression for the average cost rate of the system is derived and the corresponding optimal replacement policy N1 can be determined analytically or numerically. Finally, a numerical example is given to illustrate some theoretical results and the model applicability.     

Maintenance policies under imperfect information

This paper presents a continuous time maintenance problem where deterioration is Markovian and the state of the system is not directly observable except by means of an inspection. The costs incurred are inspection costs, state occupancy costs and replacement costs. We examine the problem of minimizing the expected average cost per unit time.