Balakrishnan, Narayanaswamy; Qin, Chengwei First passage time of a Lévy degradation model with random effects. (English) Zbl 1411.60069 Methodol. Comput. Appl. Probab. 21, No. 1, 315-329 (2019). Summary: 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. Cited in 3 Documents MSC: 60G51 Processes with independent increments; Lévy processes 62F10 Point estimation 62N05 Reliability and life testing Keywords:first-passage time; generalized methods of moments; Lévy subordinator; random effects; saddlepoint approximations; inverse Laplace transform Software:SPLIDA PDFBibTeX XMLCite \textit{N. Balakrishnan} and \textit{C. Qin}, Methodol. Comput. Appl. Probab. 21, No. 1, 315--329 (2019; Zbl 1411.60069) Full Text: DOI References: [1] Applebaum SD (2004) Lévy processes and stochastic calculus. Cambridge University Press, Cambridge · Zbl 1073.60002 [2] Belomestny D (2011) Statistical inference for time-changed lévy processes via composite characteristic function estimation. 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