A perturbed inverse Gaussian process model with time varying variance-to-mean ratio

The inverse gaussian (IG) process has become a common model for reliability analysis of monotonic degradation processes. The traditional IG process model assumes that the degradation increment follows an IG distribution, and the variance-to-mean ratio (VMR) is constant with time. However, for the degradation paths of some practical applications, e.g., the GaAs laser degradation data that motivated to propose the IG process, the VMR is actually time varying. Confronted with this, we propose an IG process model with measurement errors that depend on the actual degradation level. According to different forms or parameter values of the dependence function, the VMR of the degradation paths can display different time varying patterns. The maximum likelihood estimation method is developed in a step-by-step way, combined with numerical integration method and heuristic optimization method. Finally, the GaAs laser example is revisited to illustrate the effectiveness of the proposed model, which indicates that the introduction of statistically dependent measurement error can provide better fitting results and lifetime evaluation performance.