A servicing strategy involving imperfect repair for two-dimensional warranties

We consider a product sold with two-dimensional warranties - such cars, trucks, etc. In the last decade, the manufacturer offers a greater age and mileage coverage in the warranty term - e.g. a car is warranted for maximum of 5 years or 10×103 miles. The greater warranty coverage results in a higher product competitiveness, but that will increase the warranty cost to the manufacturer for servicing the warranty. This will become a major interest to the manufacturer to reduce the warranty cost. An appropriate servicing strategy involving replacement or imperfect repair reduces the warranty cost significantly. A variety of such servicing strategies has been studied in the literature, but most of them deal with one dimensional warranties and the number of replacement or imperfect repair allowed at most one. For a product sold with a greater age and mileage warranty coverage, two or more imperfect repairs will be needed in order to reduce the warranty cost. In this paper, we study servicing strategies which allows more then one imperfect repairs for the case of two dimensional warranties. Numerical examples are presented to illustrate the optimal solution (in term of the optimal parameter values of the servicing strategies studied and the corresponding expected warranty costs) and then compare the results with those of the servicing strategy with only one imperfect repair.