Reliability analysis under Marshall–Olkin run shock model

Ozkut, Murat; Eryılmaz, Serkan

doi:10.1016/j.cam.2018.09.022

Cited by 46 publications

(15 citation statements)

References 21 publications

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“…Furthermore, [14] studied asymptotics in a mixed run and cumulative shock model. Ozkut and Eryilmaz [15] studied a so-called Marshall-Olkin run shock model that stemmed from Marshall and Olkin [16,17]. This system consists of two components that are subject to shocks from three different sources such that the shocks from the first and second source damage the first and second component, respectively, while the shocks from the third source affect either component.…”

Section: Run Shock Modelsmentioning

confidence: 99%

Random Walk Analysis in a Reliability System under Constant Degradation and Random Shocks

Dshalalow

White

2021

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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.

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Section: Run Shock Modelsmentioning

confidence: 99%

Random Walk Analysis in a Reliability System under Constant Degradation and Random Shocks

Dshalalow

White

2021

Axioms

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“…. have a phase-type distribution with X ji ∼ P H c (α j , A j ), j = 1, 2, ..., n, and i = 1, 2, .... [6] derived the individual lifetime random variable S j as…”

Section: Reliability Of Anmentioning

confidence: 99%

“…[5] generalizes the linear consecutive k-out-of-r-from-n: G system to multi-state case. Recently, [6] combined and studied run shock and Marshall-Olkin models.…”

Section: Introductionmentioning

confidence: 99%

On the coherent systems subject to Marshall-Olkin type shocks

Ozkut

Kan

2020

Mathematical Sciences and Applications E-Notes

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Coherent systems and Marshall-Olkin run shock models are combined. Coherent systems consisting of n components receive some kind of shocks from n + 1 different sources similar to Marshall-Olkin type. More precisely, when the component j receive k consecutive fatal shocks from the source j or k consecutive fatal shocks from the source n + 1, it fails, j = 1,. .. ,n. When the interarrival time of shocks has phase-type distribution, reliability, mean time to failure (MTTF) and mean residual life (MRL) function of the coherent systems are studied. Numerical examples and graphical representations are provided.

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“…In a cumulative shock model, a system failure occurs when the cumulative damage caused by shocks exceeds a given level (e.g., Gong et al, 2020; Kijima & Nakagawa, 1991; Ranjkesh et al, 2019). In a run shock model, the system fails only when the magnitudes of a specified number of consecutive shocks are greater than a preset threshold, which was first proposed by Mallor and Omey (2001), and further studied by Gong et al (2018), Ozkut and Eryilmaz (2019), and so on.…”

Section: Introductionmentioning

confidence: 99%

Two novel critical shock models based on Markov renewal processes

Cui

Qiu

2021

Naval Research Logistics

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In this paper, we investigate systems subject to random shocks that are classified into critical and noncritical categories, and develop two novel critical shock models. Classical extreme shock models and run shock models are special cases of our developed models. The system fails when the total number of critical shocks reaches a predetermined threshold, or when the system stays in an environment that induces critical shocks for a preset threshold time, corresponding to failure mechanisms of the developed two critical shock models respectively. Markov renewal processes are employed to capture the magnitude and interarrival time dependency of environment‐induced shocks. Explicit formulas for systems under the two critical shock models are derived, including the reliability function, the mean time to failure and so on. Furthermore, the two critical shock models are extended to the random threshold case and the integrated case where formulas of the reliability indexes of the systems are provided. Finally, a case study of a lithium‐ion battery system is conducted to illustrate the proposed models and the obtained results.

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Reliability analysis under Marshall–Olkin run shock model

Cited by 46 publications

References 21 publications

Random Walk Analysis in a Reliability System under Constant Degradation and Random Shocks

Random Walk Analysis in a Reliability System under Constant Degradation and Random Shocks

On the coherent systems subject to Marshall-Olkin type shocks

Two novel critical shock models based on Markov renewal processes

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