Warranty cost analysis with an alternating geometric process

Abstract

In this study, we model the warranty claims process and evaluate the warranty servicing costs under non-renewing, renewing and restricted renewing free repair warranties. We assume that the repair time for rectifying the claims is non-zero and the repair cost is a function of the length of the repair time. To accommodate the ageing of the product and repair equipment, we use a decreasing geometric process to model the consecutive operational times and an increasing geometric process to model the consecutive repair times. We identify and study the alternating geometric process, which is an alternating process with cycles consisting of the item’s operational time followed by the corresponding repair time. We derive new results for the alternating geometric process in a finite horizon and use them to evaluate the warranty costs over the warranty period and over the life cycle of the product under a non-renewing free repair warranty, a renewing free repair warranty and a restricted renewing free repair warranty. Properties of the model are demonstrated using a simulation study and by fitting the models to real data from an automotive manufacturer.