Preventive Replacement Policy and Imperfect Maintenance Model with Random Working Times

Abstract—This article proposes the preventive replacement policy for an operating system which may continuously work for N jobs with random working times and be 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 bivariate replacement policy is considered in which the system is replaced preventively at an operating time T, at number N of working times, or replaced correctively after any type-II failure, whichever occurs first. 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 model extends several existing results. Keywords-preventive replacement; imperfect maintenance; random working time; optimization; reliability I