On optimal replacement-repair policy for multi-state deteriorating products under renewing free replacement warranty

In this paper a replacement‐repair model is developed to study a renewing free replacement warranty (RFRW) for a class of multi‐state deteriorating repairable products. After a replacement, the product warranty is renewed. Two parameters affect the manufacturer’s decision to minimally repair or replace a failed item: the product deterioration level at the time of failure and the remaining warranty time. We derive an optimal replacement‐repair policy to minimise the expected warranty servicing cost per item sold. In the case of a product with two different working states, we are able to explicitly find the optimal values of the replacement‐repair parameters using the Adomian decomposition method. In general, for $N>2$ , it is impossible to find the optimal parameter values analytically. Hence, a computational procedure for finding these optimal values is proposed. For more clarification, numerical examples are also presented.