Reliability assessment of interactive competing failure processes under the generalized Pólya shock

Lina Bian; Jiayi Wang; Lina Bian; Jiayi Wang

doi:10.3934/era.2026208

Electronic Research Archive

2026, Volume 34, Issue 7: 4725-4748. doi: 10.3934/era.2026208

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Research article

Reliability assessment of interactive competing failure processes under the generalized Pólya shock

Lina Bian ^{1,2
,
,},
Jiayi Wang ^1,2

1.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
2.
Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics, China

Received: 13 April 2026 Revised: 13 May 2026 Accepted: 26 May 2026 Published: 01 June 2026

In recent years, the competing failure processes gained significant attention as a way of modeling based on degradation and shock processes. A traditional independent competing failure process model assumes that soft failure and hard failure affect the life of the system independently. This modeling method is being improved by a new modeling method, that is, the interaction between soft failure and hard failure affects the life of the system. Therefore, a novel reliability modeling of systems that suffer from mutually dependent competing failure processes under the generalized mixed shock model is proposed. In reliability modeling, the external random shocks can immediately increase the degradation level and degradation rate to accelerate the system degradation. Meanwhile, the internal degradation can continuously change the hard failure threshold to weaken the system strength. Under the above assumptions, analytical expressions for the reliability function for systems under the generalized Pólya process have been derived using the stochastic process theory and probabilistic techniques based on the proposed mixed shock model. Additionally, simulation algorithms to compute the reliability based on the Monte Carlo method are provided. Finally, a case study is verified to illustrate the proposed model and the derived results.
- reliability function,
- interactive competing failure processes,
- state dependence,
- generalized Pólya process,
- generalized mixed shock model
Citation: Lina Bian, Jiayi Wang. Reliability assessment of interactive competing failure processes under the generalized Pólya shock[J]. Electronic Research Archive, 2026, 34(7): 4725-4748. doi: 10.3934/era.2026208

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Abstract

In recent years, the competing failure processes gained significant attention as a way of modeling based on degradation and shock processes. A traditional independent competing failure process model assumes that soft failure and hard failure affect the life of the system independently. This modeling method is being improved by a new modeling method, that is, the interaction between soft failure and hard failure affects the life of the system. Therefore, a novel reliability modeling of systems that suffer from mutually dependent competing failure processes under the generalized mixed shock model is proposed. In reliability modeling, the external random shocks can immediately increase the degradation level and degradation rate to accelerate the system degradation. Meanwhile, the internal degradation can continuously change the hard failure threshold to weaken the system strength. Under the above assumptions, analytical expressions for the reliability function for systems under the generalized Pólya process have been derived using the stochastic process theory and probabilistic techniques based on the proposed mixed shock model. Additionally, simulation algorithms to compute the reliability based on the Monte Carlo method are provided. Finally, a case study is verified to illustrate the proposed model and the derived results.

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