Modeling and optimization of extended warranties using probabilistic design

Reliability engineers and actuaries from the insurance industry are increasingly being asked to collaborate in measuring, valuing and managing risk associated with extended warranties and long term service agreements. This interaction has resulted in the development of hybrid approaches that combine methods of quantifying uncertainty in the engineering domain (probabilistic design algorithms) with models that incorporate financial risk and uncertainty (actuarial loss models). One such hybrid algorithm is described in this paper. In this approach, the reliability of a structure is computed using a analytic, time-dependent stochastic-degradation code and its long term risk is assessed using a combination of renewal and actuarial loss models. Using these techniques, products can be optimally designed to meet an acceptable probability of survival as well as a predetermined cap on probabilistic financial exposure. The methods presented in this paper can also be used to value extended warranties. The algorithm and its potential applications are illustrated through a representative case study.