Lifetime properties of a cumulative shock model with a cluster structure

Bai, Jianming; Zhang, Zhe George; Li, Zehui

doi:10.1007/s10479-012-1255-6

Cited by 12 publications

(5 citation statements)

References 18 publications

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“…The application and theory of this model have been widely investigated by researchers. [2][3][4][5][6] Although this model has been introduced as one of the first shock models, it has still attracted the attention of researchers. For example, in a recent work by Ranjkesh et al 7 a new cumulative shock model presented in which shocks arriving in small intervals are more critical and lead to more serious damages to the system.…”

Section: Motivation and Related Literaturementioning

confidence: 99%

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On the occurrence time of an extreme damage in a general shock model

Bohlooli-Zefreh

Parvardeh

Asadi

2022

Proceedings of the Institution of Mechanical Engineers, Part O:

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In the literature of system reliability and other fields related to the time to occurrence of an event, shock models play an important role. In this paper, we assume that a system is subject to shocks that occur according to a counting process describing the number of shocks that arrive during a specified time interval. As the magnitude of the damage imposed to the system by each shock is a crucial parameter to the system’s survival, we investigate some important random variables related to this parameter. A random variable of interest associated with this process is the first time, after a pre-specified time [Formula: see text], at which the amount of a shock damage to the system gets greater than the maximum of damages imposed to the system until time [Formula: see text]. We obtain the reliability function of this random variable and investigate various properties of it and some other related random variables. In order to explore further the results, we examine two commonly used processes in the literature, that is, the non-homogeneous Poisson process and the Pólya process.

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Section: Motivation and Related Literaturementioning

confidence: 99%

“…Despite the fact that an NHPP has independent increments, the Po´lya process has dependent increments. In many cases in the context of shock models such as cluster shocks (see Bai et al 5 ), we deal with the processes with dependent increments. Hence, the Po´lya process can be utilized for such applications.…”

Section: Preliminariesmentioning

confidence: 99%

On the occurrence time of an extreme damage in a general shock model

Bohlooli-Zefreh

Parvardeh

Asadi

2022

Proceedings of the Institution of Mechanical Engineers, Part O:

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“…where ]( , ⋅) is a Lévy measure. A generalized cumulative shock model and its lifetime properties are already discussed in our latest work [13], where the system considered is subject to two types of shocks, called primary shocks and secondary shocks, respectively, and each primary shock causes a series of secondary shocks according to a "cluster" mechanism. Then, the shock process has a cluster structure and is a superposition of a primary (shock) process and a group of adjunct (shock) processes, and the system fails once the totally superposed effect of the primary and secondary shocks exceeds the threshold level.…”

Section: Local Cumulative Shock Model With Cluster Structurementioning

confidence: 99%

Limit Theorems for Local Cumulative Shock Models with Cluster Shock Structure

Bai

Chen

Yuan

et al. 2015

Mathematical Problems in Engineering

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This paper considers a more general shock model with insurance and financial risk background, in which the system is subject to two types of shocks called primary shocks and secondary shocks. Each primary shock causes a series of secondary shocks according to some cluster pattern. In reliability applications, a primary shock can represent an issue of insurance policies of an insurer company, and the secondary shocks then denote the relevant insurance claims generated by the policy. We focus on the local cumulative shock process where only a certain number of the most recent primary and secondary shocks are accumulated. This process is a very new topic in the available literature which is more flexible and realistic in modeling some more complex reliability situations such as bankrupt behavior of an insurance company. Based on the theory of infinite divisibility and stable distributions, we establish a central limit theorem for the local cumulative shock process and obtain the conditions for the process to converge to an infinitely divisible distribution or to anα-stable law. Also, by choosing the proper scale parameters, the process converges to a normal distribution.

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“…A system fails in cumulative shock deterioration process when total damages due to successive shocks exceed its failure threshold. 1 Bai et al 2 studied a generalized cumulative shock model with a cluster shock structure. They considered a system being subjected to primary and secondary types of shocks, such that each primary shock caused a series of secondary shocks.…”

Section: Introductionmentioning

confidence: 99%

“…A system fails in cumulative shock deterioration process when total damages due to successive shocks exceed its failure threshold 1 . Bai et al 2 . studied a generalized cumulative shock model with a cluster shock structure.…”

Section: Introductionmentioning

confidence: 99%

Reliability modeling of systems with random failure threshold subjected to cumulative shocks using machine learning method

Shamstabar,

Ebrahimmagham,

Samimi

et al. 2024

Quality & Reliability Eng

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Modeling and evaluation of a system reliability is a key issue in shock model analysis. In cumulative shock model, a system fails when the total damages caused by shocks exceeds the system failure threshold level. The reliability of a system with random failure threshold level under cumulative shocks is investigated in this work, considering the general dependency between inter‐arrival times of shocks and their damages magnitudes. Clustering, as one of the unsupervised machine learning methods, is utilized here by applying a genetic algorithm (GA) and particle swarm optimization algorithm (PSO) for its implementation. Phase‐type (PH) distributions and their properties are also applied for finding a system failure distribution functions, determining the convolutions, evaluating the integrals, and ultimately modeling the system reliability. An illustrative example is provided to demonstrate the implementation and effectiveness of the proposed modeling procedure and the suggested approach for computing the system reliability and remaining useful lifetime (RUL). Also, an example case study of X‐ray machine in healthcare industry is provided to demonstrate the application of the proposed model. Applying other machine learning methods for patterns recognition is an area for future research.

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Lifetime properties of a cumulative shock model with a cluster structure

Cited by 12 publications

References 18 publications

On the occurrence time of an extreme damage in a general shock model

On the occurrence time of an extreme damage in a general shock model

Limit Theorems for Local Cumulative Shock Models with Cluster Shock Structure

Reliability modeling of systems with random failure threshold subjected to cumulative shocks using machine learning method

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