Degradation analysis based on an extended inverse Gaussian process model with skew-normal random effects and measurement errors

As an important degradation model for monotonic degradation processes, the inverse Gaussian (IG) process model has attracted a lot of attention. To characterize random effects among test samples, the traditional IG process model usually assumes a normal distributed degradation rate. However, the degradation rates in some applications may manifest some asymmetric and non-normal behaviors, such as the GaAs laser degradation data. Therefore, we propose an extended inverse Gaussian (EIG) process model by incorporating skew-normal random effects, and derive its analytical lifetime distribution. Furthermore, considering that available studies about IG process models are limited on the aspect of measurement errors, parameter estimation methods for the proposed degradation model are developed for two scenarios, i.e., the maximum likelihood estimations (MLEs) for perfect measurements, and an extended Monte Carlo (MC) integration algorithm for the MLEs for perturbed measurements. Then a simulation study is adopted to show the effectiveness of the proposed MLEs, and two illustrative examples of GaAs laser degradation and fatigue crack growth are provided to illustrate the advantages of the proposed EIG process model, i.e., the improvement in degradation data fitting performance and lifetime evaluation accuracy by incorporating skew-normal random effects and measurement errors.