Warranty servicing for special class of multi-state deteriorating products under renewing free-replacement warranty

We develop a replacement-repair model to study a renewing free replacement warranty (RFRW) for a class of multi-state deteriorating repairable products. Each product may experience N different working states with different hazard functions, before the warranty contract expires. Once the item enters working state j(j = 1, 2,..., N), it can either fail or move t any of the subsequent states. In the former case, the best rectification action, replacement or minimal repair, regarding the failure status, should be done to put the item into operation. In each working state there is a determined probability for transition to each of the subsequent working states. After a replacement the product warranty is renewed. There are two parameters that affect manufacturer's decision to minimally repair or replace a failed item: the product deterioration level at the time of the failure and the remaining warranty time. In order to minimise the expected warranty servicing cost per item sold, we use a simulation based optimization method that combines discrete event simulation and experimental design. We include numerical example to illustrate the effectiveness of the proposed methodology.