A value-at-risk approach to optimisation of warranty policy

In the real world, a manufacturer may produce many products, which may have common components installed. Consequently, the frequencies of the warranty claims of those products are statistically dependent. Warranty policy optimisation in the existing research, however, has not considered such statistical dependence, which may increase bias in decision making. This paper is the first attempt to collectively optimises warranty policy for a set of different products, produced by one manufacturer, whose failures are statistically dependent, using tools borrowed from financial mathematics (i.e., value-at-risk theory and copula). We prove the existence of the optimal solutions for different scenarios. Numerical examples are used to validate the applicability of the proposed methods.