Optimal repair-cost limit for a consumer following expiry of a warranty

This paper develops a methodology for obtaining the optimalrepair-cost limit for the repair-replace decision that a consumerfaces on the expiry of a product warranty, where the producthas been minimally repaired on failure during the warranty.Three cases are considered; (i) an exponentially distributedtime to failure with an arbitrary repair-cost distribution,(ii) an exponentially distributed time to failure with a uniformrepair-cost distribution, and (iii) a Weibull-distributed timeto failure with a beta-distributed repair cost. Numerical optimizationsare performed for the third case, and conclusions drawn as tothe sensitivity of the optimal repair-cost limit on the parametervalues of the distributions involved.     

Costing minimal-repair replacement policies over finite time horizons

An integral-equation technique is used to evaluate the expectedcost of maintaining a system functioning over the period (O,t] using two minimal-repair replacement policies. These costfunctions provide appropriate criteria to determine T^*, theoptimal scheduled replacement period over this finite time horizon.For both policies, it is shown that significant cost savingscan be achieved by using the T^* values predicted by the newmodels with a finite time horizon rather than those obtainedfrom the established asymptotic formulations. An adaptive finiteminimal-repair replacement policy is also formulated using dynamicprogramming, and the expected cost of this policy is shown tobe only slightly less than that of the best stationary policy.     

A comparison of adaptive and stationary repair-cost limit criteria for a producer's warranty

A producer sells a product together with a warranty valid fora specified duration.Whenever the product fails during the warrantyperiod, the producer is responsible for making the product functional,either by replacing or repairing the equipment,according towhether the anticipated repair cost exceeds or does not exceeda specified repair-cost limit. It is assumed that repairs areminimal repairs, and that the distribution of repair costs isknown, as is the time-to-failure distribution of the product.In this paper, we compare two models in discrete time. The firstone involves an adaptive repair-cost limit which is set dynamicallyaccording to the age of the product, and the length of warrantyremaining. The second model assumes a constant or stationaryrepair-cost limit throughout the warranty period. Empiricalresults are summarized.