Semiparametric and nonparametric evaluation of first-passage distribution of bivariate degradation processes

Abstract In system engineering, the reliability of a system depends on the reliability of each subsystem. Those subsystems have their own performance characteristics (PCs) which can be dependent. The degradation of those dependent PCs of the subsystems is used to access the system reliability. Parametric frameworks have been developed to model bivariate degradation processes in the literature; however, in practical situations, the underlying degradation process of a subsystem is usually unknown. Therefore, it is desired to develop semiparametric and nonparametric approaches to model bivariate degradation processes. Here, different semiparametric and nonparametric methods are proposed to estimate the first-passage time distribution of dependence bivariate degradation data. The saddlepoint approximation and bootstrap methods are used to estimate the marginal FPT distributions empirically and the empirical copula is used to estimate the joint distribution of two dependence degradation processes nonparametrically. A Monte-Carlo simulation study is used to demonstrate the effectiveness and robustness of the proposed semiparametric and nonparametric approaches. A numerical example is presented to illustrate the methodologies developed in this paper.

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