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.