Remaining useful life estimation on the non-homogenous gamma with noise deterioration based on Gibbs filtering: A case study

Prognostic of system lifetime is a basic requirement for condition-based maintenance in many application domains where safety, reliability, and availability are considered of first importance. Assessment of residual lifetime of component is always taken as one of important tasks of prognostic. In the framework of prognostic, the non-probabilistic approaches are mostly considered because of their connection to the scientific community that first developed the research area corresponding to the prognostic problem and started it from a very operational point of view. However, more and more probabilistic approaches such as hidden Markov model, life cycle data analysis, proportional hazards models, etc. have been applied to prognostic. In this paper, a probabilistic approach is considered where a lifetime distribution or a stochastic process is associated to the sys tem or component under consideration. This study considers the simulated noisy observations set corresponding to a Gamma process with additive Gaussian noise which is associated to the deterioration phenomenon. The presence of the Gaussian noise is due to the noisy and irregularly sampled observations data. In order to propose a remaining useful lifetime estimation, first by a stochastic filtering with Gibbs sampler the hidden degradation state is estimated. Since this latter evolves according to a gamma process, based on the gamma process properties the remaining useful life distribution is calculated. The interest of our probabilistic method is pointed out.