Abstract
We develop a reliability model for systems with s-dependent degradation processes using copulas. The proposed model accommodates assumptions of s-dependence among degradation processes and allows for different marginal distributions. This flexibility makes the model more attractive compared with the multivariate distribution model, which lay on the limitation of the homogeneous marginal distribution and can only describe linear correlation. Marginal degradation process is modeled by the inverse Gaussian (IG) process with time scale transformation. Furthermore, we incorporate random drift to account for the possible heterogeneity in population. This paper also develops the statistical inference method using EM algorithm with two-stage procedure. The comparison results of the reliability estimation under both s-dependent and s-independent assumptions are illustrated in the illustrative example to demonstrate the applicability of the proposed method.
Highlights
For systems with high reliability, it is challenging to do reliability assessment in a timely manner because usually minor failures occur during such short time
We first use the inverse Gaussian (IG) process with random drift and time scale transformation to model the monotonic degradation process; we employ the copula method to fit the joint distribution of multiple degradation processes
This study has investigated reliability modeling method for systems with s-dependent degradation processes
Summary
For systems with high reliability, it is challenging to do reliability assessment in a timely manner because usually minor failures occur during such short time. The Wiener process and Gamma process have wide applications in degradation modeling, only these two classes of models cannot fit all degradation data well. Based on the bivariate Wiener degradation model, Wang et al [11] put forward an adaptive method for residual life estimation In their method, the dependence of degradation variables is characterized by the Frank copula function. Some researchers use copulas to model the dependence among degradation processes, which allows for different marginal distributions. We first use the IG process with random drift and time scale transformation to model the monotonic degradation process; we employ the copula method to fit the joint distribution of multiple degradation processes.
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