Reliability analysis of inverse Gaussian processes with two-stage degenerate paths

For randomly degraded products undergoing a two-stage degradation process, traditional random effects models assume that the degradation rate follows a symmetrically normal distribution. However, certain products exhibit asymmetric degradation rates. In light of this, this paper proposes an approach for reliability analysis based on the inverse Gaussian (IG) degeneration process, which considers both asymmetric random effects and the two-stage nature simultaneously. To begin with, we establish a two-stage IG degradation process model that incorporates a skew normal random effect. Subsequently, we determine the location of change points using the Schwarz Information Criterion (SIC). The estimation of parameters is then conducted by combining Maximum Likelihood Estimations (MLEs) with the Genetic Algorithm (GA). Finally, we validate and demonstrate the practicality for the proposed model through Monte Carlo (MC) simulation and examples involving lithium batteries.