Mathematics and System Engineering Faculty Publications

Document Type

Article

Publication Title

Axioms

Abstract

In this paper, we study a reliability system subject to occasional random shocks hitting an underlying device in accordance with a general marked point process with position dependent marking. In addition, the system ages according to a linear path that eventually fails even without any external shocks that accelerate the total failure. The approach for obtaining the distribution of the failure time falls into the area of random walk analysis. The results obtained are in closed form. A special case of a marked Poisson process with exponentially distributed marks is discussed that supports our claim of analytical tractability. The example is further confirmed by simulation. We also provide a classification of the literature pertaining to various reliability systems with degradation and shocks. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

DOI

10.3390/axioms10030199

Publication Date

2021

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