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

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

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Article ID: iaor201528966
Volume: 62
Issue: 6
Start Page Number: 483
End Page Number: 492
Publication Date: Sep 2015
Journal: Naval Research Logistics (NRL)
Authors: , ,
Keywords: simulation, stochastic processes, supply & supply chains, statistics: distributions
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.

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