Combining Gamma and Brownian processes for degradation modeling in presence of explanatory variables

Laurent Bordes (1) , Christian Paroissin (1) , Ali Salami (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

A new approach has been proposed recently to describe a system deterioration. In this new approach the authors have considered the degradation as the sum of a gamma process and a Brownian motion, independent of the gamma process. The Brownian motion may describe, for example, degradation measurement error. In this paper covariates are introduced in order to take into account environmental effects or systems heterogeneity. From the observation of $n$ independent items at regular instants over a finite time interval, the model parameters are estimated by a two-stage least-square method. Asymptotic properties of the estimators are provided. Finally both numerical simulations and real data applications are supplied to illustrate our method.

Mots clés: Gamma process; Wiener process; Covariates; Least-square estimators; Consistency; Asymptotic normality

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Méthodologie [stat.ME]

Laurent Bordes, Christian Paroissin, Ali Salami. Combining Gamma and Brownian processes for degradation modeling in presence of explanatory variables. 2010. ⟨hal-00535812⟩