Optimal maintenance level for second-hand product with periodic inspection schedule

This paper formulates a periodic inspection/upgrade model under free non-renewable warranty policy with a fixed length of warranty period for the second-hand product and derives an optimal number of inspections required and an optimal improvement level to minimize the expected total warranty cost from the perspective of the dealer during the warranty period. At each inspection, the product is taken an upgrade action in order to reduce its failure rate, which is characterized by an improvement level. It is true in general that the higher improvement level and more frequent inspections increase the warranty cost but lower the chance of product failures. In this paper, we propose an optimal strategy with respect to the inspection/upgrade action for the dealer to lower the total warranty cost. Firstly, we define an inspection/upgrade action, which reduces the product's failure rate proportionally to the improvement level at each inspection and then evaluate the expected total warranty cost. Secondly, the optimal solutions for the decision variables and its uniqueness are discussed in general. Numerical results are presented when the failure distribution follows a Weibull distribution under the proposed model.