Optimal overhaul–replacement policy for a multi-degraded repairable system sold with warranty


1 Department of Industrial Engineering, Institut Teknologi Nasional Bandung (Itenas), Bandung, 40124, Indonesia

2 Department of Industrial Engineering, Institute Technology of Bandung (ITB), Bandung, 40132, Indonesia


In this research, we study an optimal overhaul–replacement policy of a multi-degraded repairable system sold with a free replacement warranty. In the proposed replacement policy, a maintenance action and failure are dependent on a system degradation level and the system age, and hence the replacement model will provide more effective maintenance decisions. Failure of the system is modeled using a rate of occurrence of failure for the system, which is as a function of a degradation level of the system and its age. We develop the optimal replacement policy for a multi-degraded repairable system from the buyer’s point of view, who plans to use the system for a horizon planning T. The buyer conducts a periodic evaluation and selects an appropriate maintenance option based on the revealed system condition together with the system operational age. At each evaluation point, three alternative decisions are available, i.e., keep running the system, overhaul, or replace it with a new one. We formulate the sequential decision (keep, overhaul, or replace) problem as a dynamic programming model and obtain an optimal policy that minimizes total cost over T. Numerical examples are presented using several hypothetical data sets to illustrate the structure of optimal solution and its sensitivity against the change in parameter values. The main contribution of the paper is to offer a decision tool that will help in deciding the overhaul–replacement action based on the degradation level and the operational age of the system.