Probabilistic and cost analyses of a renewable warranty with an inspection policy for a discrete operating item from a heterogeneous population

Abstract

This study considers an item that can be operated over an indefinitely long run operation cycle n (n = 1, 2, 3, …), where each operation period causes a random amount of damage to the item, where the damage is accumulated over time, and where the item fails when the cumulated damage/wear exceeds a failure level ξ0. For such an item, a warranty policy in a discrete-time form is considered. It is suggested that the discrete-type warranty policy that consists of a renewable free-replacement and one-inspection service can increase the probability of warranty success and decrease the costs due to the warranty contract. Under such a warranty policy, with a coverage period of N, items from a mixed population are inspected at an intermediate operation cycle M (< N), and if the observed level of the cumulated damage/wear exceeds the predetermined value ξ (< ξ0), it is screened out and replaced by a new one and the warranty is renewed, without any cost to the customer. Probabilistic and cost analyses of the model are performed, the optimal ξ* and M* that minimize the warranty costs are calculated, and illustrative examples are presented and discussed.