Séminaire LARIS - Antonio PISCOPO11h | Polytech Angers | B106 | 62 Notre Dame du Lac - 49000 Angers

Le 11 décembre 2025

Stochastic Models for Bathtub Shaped Degradation Rate Phenomena

Résumé :

This work deals with degradation processes characterized by a bathtub-shaped degradation rate function, meaning stochastic processes whose mean function has a first derivative with respect to time that has a bathtub-shaped degradation behaviour. Most stochastic models in the literature exhibit mean degradation functions whose derivative is monotonic, a feature that could limit their practical use because the degradation rate of many technological units typically has a three-phasic bathtub-shaped behavior, with a first decreasing phase (accommodation phase), a second nearly constant phase (steady-state phase), and a final increasing phase (degenerative phase). In most studies, monotonic degradation rate models are presented because available datasets often do not show all three phases, since degradation data are frequently collected over limited time horizons or under conditions where early or late phases are not observable. However, this is not the case for the metal-oxide-semiconductor field-effect transistors (MOSFET) dataset [1], whose empirical mean clearly exhibits all three phases of the bathtub-shaped behaviour.
The focus is on three processes that have been recently suggested in the literature: a Wiener process with two random effects [2], and two perturbed models, the gamma [3] and the inverse Gaussian process [4], both characterized by one random effect. The main features of these processes, which are not mathematically tractable, are presented and discussed. The remaining useful life distribution function and the residual reliability function are obtained through a failure threshold model.
The estimation of model parameters is addressed through the use of the maximum likelihood method. A combination of the expectation-maximization algorithm and the particle filter is employed to facilitate the maximization of the likelihood in the case of the perturbed processes. These degradation processes are applied to the MOSFET dataset. Examples of application prove the usefulness of the discussed models and the effectiveness of the related estimation procedures.

Bibliographie:

1. Wang X, Jiang P, Guo B, Cheng Z. 2014. Real-time reliability evaluation for an individual product based on change point gamma and Wiener process. Quality and Reliability Engineering International 30(4):513‐525.
2. Giorgio M, Piscopo A, Pulcini G. 2024. A new Wiener process with bathtub-shaped degradation rate in the presence of random effects, Applied Stochastic Models in Business and Industry 40:574-597
3. Piscopo A, Esposito N, Castanier B, Giorgio M. 2023. Remaining useful life estimation of gamma degrading units characterized by a bathtub-shaped degradation rate in the presence of random effect and measurement error. In: Brito MP, Aven T, Baraldi P, Čepin M, Zio E, editors. Proceedings of the 33rd European Safety and Reliability Conference (ESREL 2023), Research Publishing Services, Singapore; 1258–1265.
4. Esposito N, Piscopo A, Castanier B, Giorgio M. 2025. An inverse Gaussian process with bathtub-shaped degradation rate function in the presence of random effect and measurement error. In: Abrahamsen E B, Aven T, Bouder F, Flage R, Ylönen M, editors. To appear in: Proceedings of the 35th European Safety and Reliability Conference (ESREL 2025), Research Publishing Services, Singapore.

Antonio PISCOPO est en 3ème année de doctorat dans l'équipe SFD - Sûreté de Fonctionnement et outils d'aide à la Décision du LARIS. En co-tutelle avec l'Université Frederico II de Naples, ses directeurs de thèse sont Bruno Castanier et Massimiliano Giorgio ainsi que Mitra Fouladirad de l'Ecole Centrale Marseille en tant que co-encadrante.