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Generalizations of the Poisson Process and Their Reliability Applications

In: Reliability Analysis and Maintenance Optimization of Complex Systems

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  • Ji Hwan Cha

    (Ewha Womans University)

Abstract

The Poisson process is a very useful tool for modeling random recurrent events. In general, the Poisson process is used to model the arrival process of recurrent events. Especially in reliability area, the Poisson process is usefully applied to model the minimal repair process of repairable systems. Although the Poisson process is the most frequently applied point process model, it also has its own limitations. Specifically, the Poisson process possesses the independent increments property. Furthermore, at any point of time, the variance and expectation of the number of event occurrences are the same. These can be critical restrictions in the application of the Poisson process to the practical situations where such restrictive conditions do not hold. Recently, there have been approaches to extend the Poisson process to more generalized models. In this paper, some generalized models of the Poisson process and their reliability applications are introduced and reviewed.

Suggested Citation

  • Ji Hwan Cha, 2025. "Generalizations of the Poisson Process and Their Reliability Applications," Springer Series in Reliability Engineering, in: Qian Qian Zhao & Il Han Chung & Junjun Zheng & Jongwoon Kim (ed.), Reliability Analysis and Maintenance Optimization of Complex Systems, pages 85-95, Springer.
    • Handle: RePEc:spr:ssrchp:978-3-031-70288-4_6
    DOI: 10.1007/978-3-031-70288-4_6
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