Life distribution analysis based on Lévy subordinators for degradation with random jumps

Abstract

Abstract:For a component or a system subject to stochastic degradation with sporadic jumps that occur at random times and have random sizes, we propose to model the cumulative degradation with random jumps using a single stochastic process based on the characteristics of Lévy subordinators, the class of nondecreasing Lévy processes. Based on the inverse Fourier transform, we derive a new closed-form reliability function and probability density function for lifetime, represented by Lévy measures. The reliability function derived using the traditional convolution approach for common stochastic models such as gamma degradation process with random jumps, is revealed to be a special case of our general model. Numerical experiments are used to demonstrate that our model performs well for different applications, when compared with the traditional convolution method. More importantly, it is a general and useful tool for life distribution analysis of stochastic degradation with random jumps in multidimensional cases.

Multistream sensor fusion-based prognostics model for systems with single failure modes

“…There are various types of prognostic models that focus on single sensor applications. Examples include using random coefficients models [9,49], Brownian motion process [31,47,48], Gamma process [20,51,50], and Markov chains [1,13]. The second category are the models focusing on multi-sensor settings.…”

Markov additive processes for degradation with jumps under dynamic environments

“…Abdel‐Hameed (1984) studied the life distribution properties of devices subject to Lévy degradation. Under deterministic environments, Shu et al (2015, 2016) gave explicit results of reliability function for degradation described by Lévy subordinators and their functional extensions as a class of nondecreasing processes. Their results demonstrated the advantage of using Lévy subordinators as a realistic model for many physical degradation phenomena.…”

“…Considering external factors, Wiener‐based stochastic covariate models in Ebrahimi (2001), Markov modulated linear processes and Markov modulated compound Poisson processes in Kharoufeh et al (Kharoufeh, 2003; Kharoufeh et al, 2006, 2013; Kharoufeh & Cox, 2005; Kharoufeh & Mixon, 2009) were studied recently. Poisson process is a special case of Lévy process, thus the linear‐based and Poisson‐based stochastic models are not flexible in general cases (Shu et al, 2015, 2016, 2019).…”

Image-Based Prognostics Using Penalized Tensor Regression

“…Numerous prognostic methodologies have been developed in the literature. Examples of some modeling approaches include random coefficients models (Gebraeel et al, 2005;Ye and Chen, 2014), models that utilize the Brownian motion process (Ye, Chen and Shen, 2015;Chen et al, 2015) and gamma process (Shu, Feng and Coit, 2015;Zhang and Liao, 2015), and models based on functional data analysis (Fang, Zhou and Gebraeel, 2015;Zhou et al, 2014). These approaches are well-suited for time-series signals, but it is not clear how they can be extended to model image streams.…”