A Perturbed Inverse Gaussian Process Model with Time Varying Variance-To-Mean Ratio

Songhua Hao (1, 2) , Jun Yang (1, 2) , Christophe Bérenguer (3)

1 School of Reliability and Systems Engineering [Beijing]
2 BUAA - Beihang University
3 GIPSA-SAIGA - GIPSA - Signal et Automatique pour la surveillance, le diagnostic et la biomécanique

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.

Mots clés: GaAs Laser; Time varying VMR; Measurement Error; Inverse Gaussian Process

Domaines: Automatique / Robotique; Applications [stat.AP]

Songhua Hao, Jun Yang, Christophe Bérenguer. A Perturbed Inverse Gaussian Process Model with Time Varying Variance-To-Mean Ratio. ESREL 2019 - 29th European Safety and Reliability Conference, Sep 2019, Hannover, Germany. pp.739-745, ⟨10.3850/978-981-11-2724-3_0144-cd⟩. ⟨hal-02324834⟩