Reliability modeling for systems with multiple degradation processes using inverse Gaussian process and copulas

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.