An optimal geometric process model for a cold standby repairable system

In this paper a cold standby repairable system consisting of two identical components and one repairman is studied. Assume that each component after repair is not ‘as good as new'. Under this assumption, by using a geometric process, we consider a replacement policy N based on the number of repairs of component 1. Our problem is to determine an optimal replacement policy N* such that the long-run expected reward per unit time is maximized. The explicit expression of the long-run expected reward per unit time is derived and the corresponding optimal repair replacement policy can be determined analytically or numerically. Finally, a numerical example is given.     

A bivariate optimal replacement policy for a multistate repairable system

In this paper, a deteriorating simple repairable system with k+1 states, including k failure states and one working state, is studied. It is assumed that the system after repair is not “as good as new” and the deterioration of the system is stochastic. We consider a bivariate replacement policy, denoted by (T,N), in which the system is replaced when its working age has reached T or the number of failures it has experienced has reached N, whichever occurs first. The objective is to determine the optimal replacement policy (T,N)^* such that the long-run expected profit per unit time is maximized. The explicit expression of the long-run expected profit per unit time is derived and the corresponding optimal replacement policy can be determined analytically or numerically. We prove that the optimal policy (T,N)^* is better than the optimal policy N^* for a multistate simple repairable system. We also show that a general monotone process model for a multistate simple repairable system is equivalent to a geometric process model for a two-state simple repairable system in the sense that they have the same structure for the long-run expected profit (or cost) per unit time and the same optimal policy. Finally, a numerical example is given to illustrate the theoretical results.     

Cost—Optimal replacement policy (N, n) for a parallel system with common cause failure

The purpose of this article is to present an improved replacement model for a parallel system of N identical units, by taking common failure and repair and maintenance costs into consideration, and to develop the methods for obtaining the (1) optimal redundant units N^* for a fixed n, (2) optimal number of repairs n^* for a fixed N, and (3) optimal pair (N^*, n^*) simultaneously, respectively, under the condition that the system is allowed to undergo at most a prefixed number of repairs before being replaced. The results are illustrated by numerical examples.     

Opportunity-based age replacement policy with minimal repair

This paper proposes an opportunity-based age replacement policy with minimal repair. The system has two types of failures. Type I failures (minor failures) are removed by minimal repairs, whereas type II failures are removed by replacements. Type I and type II failures are age-dependent. A system is replaced at type II failure (catastrophic failure) or at the opportunity after age T, whichever occurs first. The cost of the minimal repair of the system at age z depends on the random part C(z) and the deterministic part c(z). The opportunity arises according to a Poisson process, independent of failures of the component. The expected cost rate is obtained. The optimal T^* which would minimize the cost rate is discussed. Various special cases are considered. Finally, a numerical example is given.     

An optimal replacement policy for a repairable system based on its repairman having vacations

This paper studies a cold standby repairable system with two different components and one repairman who can take multiple vacations. If there is a component which fails and the repairman is on vacation, the failed component will wait for repair until the repairman is available. In the system, assume that component 1 has priority in use. After repair, component 1 follows a geometric process repair, while component 2 can be repaired as good as new after failures. Under these assumptions, a replacement policy N based on the failed times of component 1 is studied. The system will be replaced if the failure times of component 1 reach N. The explicit expression of the expected cost rate is given, so that the optimal replacement time N^? is determined. Finally, a numerical example is given to illustrate the theoretical results of the model.     

Analysis for a two-dissimilar-component cold standby repairable system with repair priority

In this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. Assume that working time distributions and repair time distributions of the two components are both exponential, and Component 1 has repair priority when both components are broken down. After repair, Component 1 follows a geometric process repair while Component 2 obeys a perfect repair. Under these assumptions, using the perfect repair model, the geometric process repair model and the supplementary variable technique, we not only study some important reliability indices, but also consider a replacement policy T, 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 loss per unit time (i.e. average loss rate) of the system is minimized. The explicit expression for the average loss rate of the system is derived, and the corresponding optimal replacement policy T^? can be found numerically. Finally, a numerical example for replacement policy T is given to illustrate some theoretical results and the model's applicability.     

Joint hybrid repair and remanufacturing systems and supply control

The control of a stochastic manufacturing system that executes capital asset repairs and remanufacturing in an integrated system is examined. The remanufacturing resources respond to planned returns of worn-out equipment at the end of their expected life and unplanned returns triggered by major equipment failures. Remanufacturing operations for planned demand can be executed at different rates and costs corresponding to different replacement and repair modes. The replacement components inventory is provided by an upstream supply with random lead times. The objective is to determine a control policy for both the supply and remanufacturing activities that minimises the average repair/replacement, acquisition and inventory/shortage total cost over an infinite horizon. We propose a suboptimal joint remanufacturing and supply control policy, composed of a multi-hedging point policy (MHPP) for the remanufacturing stage and an (s, Q) policy for the replacement parts supply. The MHPP is based on two inventory thresholds that trigger the use of predefined remanufacturing modes. Control policy parameters are obtained combining analytical modelling, simulation experiments and response surface methodology. The effects of the distribution, mean and variability of the lead time are tested and a sensitivity analysis of cost parameters is conducted to validate the proposed control policy. We also show that our policy leads to a significant cost reduction as compared to a combination of a hedging point policy (HPP) and an (s, Q) policy.     

Reward optimization of a repairable system

This paper analyzes a system subject to repairable and non-repairable failures. Non-repairable failures lead to replacement of the system. Repairable failures, first lead to repair but they lead to replacement after a fixed number of repairs. Operating and repair times follow phase type distributions (PH-distributions) and the pattern of the operating times is modelled by a geometric process. In this context, the problem is to find the optimal number of repairs, which maximizes the long-run average reward per unit time. To this end, the optimal number is determined and it is obtained by efficient numerical procedures.     

Optimal maintenance policy for a Markovian system under periodic inspection

This study proposes a state-dependent maintenance policy R_i,j(T,N,α) for a multi-state continuous-time Markovian deteriorating system subject to aging and fatal shocks and with states 0 (new state) <1<2<…<L (failed-state). Under R_i,j(T,N,α), the system is inspected at each kT for k=1,2,3… to identify the current state as, say a, and then do-nothing, repair and replacement are taken immediately according to 0≤a≤i−1, i≤a≤j−1 and j≤a≤L−1, respectively in case i<j. Additionally, the replacement is carried out whenever L occurs due to fatal shocks. This policy includes numerous maintenance policies in the literature as special cases and can be applied quite generally. We then try to determine the optimal i^*, j^* and T^* such that the expected long-run cost rate is minimized. A numerical example is given to evaluate the performance of the policy.     

Optimal preventive maintenance strategy using two repair crews having different efficiencies: a quasi renewal process based modelling approach

This paper considers randomly failing, single-unit equipment subject to a periodic preventive maintenance (PM) policy. In case of failure between successive perfect PM actions (renewals), imperfect repairs are performed following a decreasing quasi-renewal process. One of two different maintenance crews can perform the repairs. One team is more experienced, and consequently more efficient than the other, but more costly. A mathematical model is developed in order to determine the PM period, T, and the kth repair, during a PM period, after which the repair team should be changed, minimising the average total cost per time unit over an infinite time span. It is also proved that an optimal solution in terms of the PM period always exists for any given system lifetime distribution and any set of maintenance costs. Numerical examples are presented and the obtained results are discussed.