Failure interaction model based on extreme shock and Markov processes

Meango, Toualith Jean-Marc; Ouali, Mohamed-Salah

doi:10.1016/j.ress.2020.106827

Cited by 23 publications

(3 citation statements)

References 28 publications

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“…In the extreme shock models (ESMs), a shock with the tremendous magnitude leads to the system failure and some related studies are as follows. Bohlooli-Zefreh 1 et al 15 investigated a random variable related to the ESM, which is the first time after s, at which the amount of a damage exerted on the system becomes larger than the maximal damage to the system until time s. Meango and Ouali 16 extended the ESMs by integrating the failure interaction as consecutive random events. Based on delta shock models (DSMs), the system breaks down when the time lag between two successive shocks is smaller than a critical threshold.…”

Section: Introductionmentioning

confidence: 99%

Generalized mixed shock model for multi-component systems in the shock environment with a change point

Wang

Ning

Zhao

2022

Proceedings of the Institution of Mechanical Engineers, Part O:

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The reliability of various systems under shock models has been explored extensively in the literature, where the constant mechanism of shock impact has always been studied. Nevertheless, engineering systems operate in a more complicated shock environment due to developments, and it is worth studying the reliability of such multi-component systems in a variable shock environment. Driven by the research gaps and practical situations, this paper constructs a reliability model of multi-component systems under a generalized mixed shock model with a change point. The multi-state components operate in the shock environment I initially and it may continue to run in the shock environment II after the random change point of the environment. Two novel shock impact mechanisms of the variable environment are put forward, where a series of failure criteria based on shocks are included. Four different structures of multi-component systems are considered in this paper. It can be proved that the proposed mixed shock model is a generalization of some transformed models. A multi-stage finite Markov chain imbedding approach is established to derive the probabilistic indices of the components and entire systems. Based on the engineering applications, illustrative examples are provided to verify the effectiveness of the proposed model.

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Section: Introductionmentioning

confidence: 99%

Generalized mixed shock model for multi-component systems in the shock environment with a change point

Wang

Ning

Zhao

2022

Proceedings of the Institution of Mechanical Engineers, Part O:

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“…In an extreme shock model, a system failure happens as soon as an individual shock magnitude exceeds a predetermined threshold value, which refers to the situation where the overload directly leads to the electromechanical system failure in load‐strength models. It was first studied by Shanthikumar and Sumita (1983) who employed a correlated pair

{false(X_{n}, Y_{n} false)}_{n = 0}^{\infty}

of renewal sequences where X n represents the n th shock magnitude and Y n represents the time interval between two consecutive shocks, followed by Gut and Hüsler (1999), Cha and Maxim (2011), Eryilmaz and Kan (2019), Meango and Ouali (2020) and so on, who developed various extreme shock models.…”

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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“…Cumulative shock models proposed by Esary 6 were subsequently studied in Ranjkesh et al 7 and Kijima and Nakagawa, 8 where system failures are resulted from cumulative damage of shocks exceeding thresholds. Extreme shock model was first considered in Shanthikumar and Sumita 9 and extended in Eryilmaz and Kan 10 and Meango and Ouali, 11 where system fails upon the occurrence of a shock with magnitude above a certain threshold. Run shock model was constructed in Mallor and Omey 12 and then developed in Ozkut and Eryilmaz, 13 where system fails if the number of consecutive shocks attains a certain threshold.…”

Section: Introductionmentioning

confidence: 99%

Reliability modeling for multi-state systems with a protective device considering multiple triggering mechanism

Zhao

Fan

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part O:

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Failures of safety-critical systems may result in irretrievable economic losses and significant safety hazards, thus enhancing the reliability of safety-critical system is crucial. As applied widely in engineering fields, protective devices are commonly equipped for the systems operating in shock environment to reduce external damage, which has not been taken into consideration in existing literatures. This paper investigates the reliability of multi-state systems with competing failure patterns supported by a protective device. According to the system failure modes, state-based and shock number-based triggering mechanism of the protective device are developed. That is, the protective device is triggered once the system state or cumulative number of shocks exceeds corresponding critical thresholds respectively. After being triggered, the protective device can reduce the probability of damaging shocks for the system. The protective device fails when the number of consecutive valid shocks reaches a threshold. Based on the constructed model, a finite Markov chain imbedding approach is employed to derive reliability indices including distribution functions of system lifetime and residual lifetime, together with expected operating time of the protective device. Moreover, two age-based replacement policies together with a condition-based replacement policy are developed to accommodate different maintenance scenarios and corresponding optimal solutions are acquired. Numerical illustrations based on the application of cooling systems in engines are presented to validate the results.

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Failure interaction model based on extreme shock and Markov processes

Cited by 23 publications

References 28 publications

Generalized mixed shock model for multi-component systems in the shock environment with a change point

Generalized mixed shock model for multi-component systems in the shock environment with a change point

Two novel critical shock models based on Markov renewal processes

Reliability modeling for multi-state systems with a protective device considering multiple triggering mechanism

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