Optimal periodic replacement policy for a GPP repairable product under the free-repair warranty

Abstract

This article provides an extension study on the optimal periodic replacement policy for repairable products under the free-repair warranty. A new and more general type of repair, called the ‘GPP repair’, is applied in this study, which is defined based on the Generalized Polya Process and which is more close to practical situations than the ‘minimal repair’. Under the GPP repair assumption, the future reliability performance of a product becomes worse as the number of system failures that occurred in the past increases. Cost models from the user’s perspective are developed for both a GPP repairable product with free-repair warranty and without warranty, and the corresponding optimal replacement periods are derived such that the long-run expected cost rate is minimized. The difference and relationship between GPP repairable and minimal repairable products on the optimal replacement policies are analytically presented. Numerical examples are demonstrated for illustration and verification. Finally, a practical case is provided to explain the potential application areas of this study, and managerial implications and insights are addressed.