First Passage Time of a Lévy Degradation Model with Random Effects

This paper introduces the weighted-convolution Lévy degradation process motivated by a multiple-sensor system. To estimate the first passage time (FPT) of this degradation model, the method based on inverse Laplace transform and the saddlepoint approximation is proposed to obtain the certain percentile of the FPT distribution which is generally taken as an important index regarding product reliability. Although the likelihood function of such a process is usually intractable because of its complexity, the parameter estimation can be alternatively realized by the generalized method of moments (GMM). As an example, the degradation model is assumed as the weighted convolution of two differently parameterized gamma processes incorporating random effects and its efficiency and applicability are evaluated by simulations and empirical data analysis.