Warranty strategy accounts for bathtub failure rate and random minimal repair cost

This investigation presents a novel repair-replacement warranty strategy. The strategy involves splitting the warranty period into two intervals in which only minimal repairs can be undertaken, separated by a middle interval in which no more than one replacement is allowed. The cost of the i^th minimal repair at age y depends on the random part C(y) and the deterministic part, c_i(y). Distribution functions of failure rates, with a bathtub shape over the lifetime of the product, are also considered. The form of the optimal repair-replacement strategy that minimizes the expected cost of servicing the warranty over the warranty period is discussed as well.