Optimal Age Policy for a Used System with Imperfect Preventive Maintenance and Cumulative Damage Model

In this article, the concept of imperfect preventive maintenance is discussed and an age maintenance policy is developed based on the cumulative damage model for a used system with initial variable damage. The deterioration of the system is assumed to suffer the non-homogeneous Poisson shocks which can be divided into two types with stochastic probability: Type-I shock (minor) yields a random amount of additive damage of the system, or Type-II shock (catastrophic) causes the system to fail. An age preventive maintenance policy T is presented in which the system undergoes preventive maintenance at a scheduled lifetime T, or corrective maintenance at first Type-II shock and the total damage exceeds a threshold level, whichever occurs first. The objective is to determine the optimal preventive maintenance schedule such that the expected cost rate is minimized. The optimal solution is derived analytically and discussed numerically.     

Optimal scheduling replacement policies for a system with multiple random works

From the economical viewpoint in reliability theory, this paper addresses a scheduling replacement problem for a single operating system which works at random times for multiple jobs. The system is subject to stochastic failure which results the imperfect maintenance activity based on some random failure mechanism: minimal repair due to type-I (repairable) failure, or corrective replacement due to type-II (non-repairable) failure. Three scheduling models for the system with multiple jobs are considered: a single work, N tandem works, and N parallel works. To control the deterioration process, the preventive replacement is planned to undergo at a scheduling time T or the job's completion time of for each model. The objective is to determine the optimal scheduling parameters (T^* or N^*) that minimizes the mean cost rate function in a finite time horizon for each model. A numerical example is provided to illustrate the proposed analytical model. Because the framework and analysis are general, the proposed models extend several existing results.     

Optimal preventive policies for imperfect maintenance models with replacement first and last

ABSTRACT

This paper proposes preventive replacement policies for an operating system which may continuously works for N jobs with random working times and is imperfectly maintained upon failure. As a failure occurs, the system suffers one of the two types of failures based on some random mechanism: type-I (repairable or minor) failure is rectified by a minimal repair, or type-II (non repairable or catastrophic) failure is removed by a corrective replacement. A notation of preventive replacement last model is considered in which the system is replaced before any type-II failure at an operating time T or at number N of working times, whichever occurs last. Comparisons between such a preventive replacement last and the conventional replacement first are discussed in detail. For each model, the optimal schedule of preventive replacement that minimizes the mean cost rate is presented theoretically and determined numerically. Because the framework and analysis are general, the proposed models extend several existing results.     

Stochastic Algorithms for the Estimation of an Optimal Solution of a LP Problem. Convergence and Central Limit Theorem

In this article, we consider a Linear Programming (LP) problem with unknown objective function. We introduce a class of stochastic algorithms to estimate an optimal solution of the LP problem. The almost sure convergence and the speed of convergence of these algorithms are analyzed. We also prove a central limit theorem for the estimation errors of the algorithms.     

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

In this article, a two-dissimilar-component cold standby repairable system with one repairman is studied. Assume that the repair after failure for each component is delayed or undelayed. Component 2 after repair is “as good as new” while Component 1 after repair is not, but Component 1 has priority in use. Under these assumptions, using a geometric process, we consider a replacement policy N based on the failure number of Component 1. An optimal replacement policy N* is determined by minimizing the average cost rate C(N) of the system. Finally, a numerical example is given to illustrate some theoretical results and the model applicability.