Partially observed competing degradation processes: modeling and inference

Abstract

International audienceThe aim of the present paper is the stochastic modeling and statistical inference of a component which deteriorates over time, for prediction purpose. The deterioration is due to defects which appear one by one and next independently propagate over time. The motivation comes from an application to passive components within electric power plants, where (measurable) aw indications rst initiate (one at a time) and next grow over time. The available data come from inspections at discrete times, where only the largest aw indication is measured together with the total number of indications on each component. Though detected, too small indications cannot be measured, leading to censored observations. Taking into account this partial information coming from the eld, a specic stochastic model is proposed, where the aw indications initiate according to a Poisson process and next propagate according to competing independent gamma processes. A parametric estimation procedure is developed, tested on simulated data and then applied to the industrial case. The tted model is next used to make some prediction over the future deterioration of each component and over its residual operating time until a specied critical degradation level is reached

Characterizations of Probability Distribution by Some Sequential Relative Reliability Measures: An Application of Completeness in a Hilbert Space

“…In fact, it has been widely acknowledged that a stochastic process is partially observable. For example, in degradation models in which the lifetime is considered to be the first-passage time of some stochastic process (see, for example, Bordes et al [43]). Therefore, the random relative residual lives and their averages measured in some sequences of random time such as order statics or record values may be practically beneficial.…”

Imperfect condition-based maintenance for a gamma degradation process in presence of unknown parameters

“…copies (X (i) t ) t ø 0 of the gamma process (X t ) t ø 0 . Thus, before the first inspection, we have 8t 2 ½0, t), Y t = X (1) t . At the first inspection, we could have: if Y t À \ L, no action is performed and then Y t = Y t À = X (1) t À .…”

“…At the first inspection, we could have: if Y t À \ L, no action is performed and then Y t = Y t À = X (1) t À . if L4Y t À \ M, an imperfect PM (ARD ' ) is performed and then the degradation level is reduced of rX (1) t and thus Y t = (1 À r)X (1) t À . if Y À t .…”

“…Stochastic processes, such as Le´vy processes, Markov processes, counting processes, birth processes are complex and exhaustive models to describe the degradation indicator evolution in time. 1,2 Frequently, gamma and Wiener processes are considered to model the evolution of gradual degradation for monotone and non-monotone phenomenon respectively. [3][4][5] In the framework of this paper, a gamma process is adopted for monotonous degradation modelling.…”

Optimal harvesting policy of an inland fishery resource under incomplete information

“…Yang and Xiao analyzed a financial management problem with and without complete information, where the information cost is considered in the latter. Bordes et al addressed stochastic process modeling and statistical inference of deteriorating systems under incomplete information. Management problems of deteriorating items under incomplete information have also been considered in the work of Jin in the context of Markov decision processes.…”