Yuan Lin Zhang

Analysis of a two-component series system with a geometric process model

In this article, a geometric process model is introduced for the analysis of a two-component series system with one repairman. For each component, the successive operating times form a decreasing geometric process with exponential distribution, whereas the consecutive repair times constitute an increasing geometric process with exponential distribution, but the replacement times form a renewal process with exponential distribution. By introducing two supplementary variables, a set of partial differential equations is derived. These equations can be solved analytically or numerically. Further, the availability and the rate of occurrence of failure of the system are also determined.

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. The system after repair is not ‘as good as new’ and the deterioration of the system is stochastic. Under these assumptions, we study a replacement policy, called policy N, based on the failure number of the system. The objective is to maximize the long-run expected profit per unit time. The explicit expression of the long-run expected profit per unit time is derived and the corresponding optimal solution may be determined analytically or numerically. Furthermore, we prove that the model for the multistate system in this paper forms a general monotone process model which includes the geometric process repair model as a special case. A numerical example is given to illustrate the theoretical results.

A bivariate optimal replacement policy for a multistate repairable system

Abstract 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.

Optimal replacement policy for a deteriorating production system with preventive maintenance

This paper presents a new policy for determining the optimal replacement time of a deteriorating production system. The optimal replacement time is expressed in terms of the accumulated number of failures that the system has experienced. The provision of preventive maintenance is incorporated in the system model and the objective function is cost efficiency (i.e. the long-run average cost per unit working time). A numerical example is given in the paper. The basic concept used in this paper parallels the geometric process replacement policy N introduced by Lam in 1988. The work in this paper generalizes and modifies Lams 1988 work.

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

Abstract 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 models applicability.

A geometric process repair model for a repairable cold standby system with priority in use and repair

In this paper, a deteriorating cold standby repairable system consisting of two dissimilar components and one repairman is studied. For each component, assume that the successive working times form a decreasing geometric process while the consecutive repair times constitute an increasing geometric process, and component 1 has priority in use and repair. Under these assumptions, we consider a replacement policy N based on the number of repairs of component 1 under which the system is replaced when the number of repairs of component 1 reaches N. Our problem is to determine an optimal policy N* such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit equation of the average cost rate of the system is derived and the corresponding optimal replacement policy N* can be determined analytically or numerically. Finally, a numerical example with Weibull distribution is given to illustrate some theoretical results in this paper.

Reliability analysis for a circular consecutive-2-out-of-n:F repairable system with priority in repair

Abstract A circular consecutive-2-out-of- n :F repairable system with one repairman is studied in this paper. When there are more than one failed component, priorities are assigned to the failed components. Both the working time and the repair time of each component is assumed to be exponentially distributed. Every component after repair is as good as new. By using the definition of generalized transition probability and the concept of critical component, we derive the state transition probability matrix of the system. Methodologies are then presented for the derivation of system reliability indexes such as availability, rate of occurrence of failure, mean time between failures, reliability, and mean time to first failure.

Optimal replacement policy for a two-component cold standby system with repair priority

Abstract In this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is examined. It was assumed that both Component 1 and Component 2, were not as good as new after repair, and Component 1 had repair priority. Under these assumptions, using the geometric process repair model, a discrete replacement policy N under which the system is replaced when the number of failures of Component 1 reaches N is considered. The problem was to determine an optimal policy N∗ so that the long-run average loss per unit time L(N) of the system was minimized. The expression L(N) was explicitly derived, and the corresponding optimal policy N∗ can be determined by minimizing L(N) with respect to N. A numerical example and the associated MATLAB computer program are given to illustrate the model—s applicability. Finally, conclusions are drawn for this study.