Maintenance policies for a group of identical units

Abstract

Maintenance policies for stochastically failing units have been developed extensively in the past three decades. However, most of the previous works deal with one-unit maintenance problem, while most industries in practice operate not one but many units of the same type. In this dissertation, maintenance policies for a group of identical units are proposed. This study is divided into two parts according to whether the unit is repairable or nonrepairable. In the first part, a block replacement policy for a group of nonrepairable units is proposed. Each unit is individually replaced on failure during a specified time interval. Beyond the failure-replacement interval, failed units are left idle until a number of failures, then a block replacement is performed. The average cost rate for this two-phased block replacement policy is derived and analyzed. It is shown that the proposed policy, which involves the fleet size as a modeling parameter unlike the other block replacement models proposed thus far, yields lower mean cost rate than the other two block replacement policies published previously. In the second part, two types of two-phase group replacement policies for a group of identical repairable units are proposed. During the first" repair" phase, individual units are minimally repaired under both policies. During the second "waiting" phase, no repair is performed. However, in one policy, the duration of waiting phase is a fixed time interval, whereas in another policy, it lasts until a number of failures. At the end of the waiting phase, a group replacement is performed under both policies. The mean cost rate expression under each policy is derived. It is shown that the "failure counting" policy is better than the "waiting time" policy or the classical one-unit replacement policy in terms of mean cost rate. The methods for finding the optimum values of the policy variables are explored. Numerical examples are given to demonstrate the results.