Reliability analysis and optimal replacement for a <i>k</i>-out-of-<i>n</i> system under a δ-shock model

Lorvand, H.; Kelkinnama, Maryam

doi:10.1177/1748006x221082762

Cited by 7 publications

(8 citation statements)

References 29 publications

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“…If each lamp is considered a component and electric impulses with high magnitudes are considered as shocks, then one can associate this problem with the model introduced in this paper. This example is borrowed from Lorvand and Kelkinnama [19].…”

Section: Model Descriptionmentioning

confidence: 99%

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On survival of coherent systems subject to random shocks

Goyal

Hazra

Finkelstein

2022

Preprint

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We consider coherent systems subject to random shocks that can damage a random number of components of a system. Based on the distribution of the number of failed components, we discuss three models, namely, (i) a shock can damage any number of components (including zero) with the same probability, (ii) each shock damages, at least, one component, and (iii) a shock can damage, at most, one component. Shocks arrival times are modeled using three important counting processes, namely, the Poisson generalized gamma process, the Poisson phase-type process and the renewal process with matrix Mittag-Leffler distributed inter-arrival times. For the defined shock models, we discuss relevant reliability properties of coherent systems. An optimal replacement policy for repairable systems is considered as an application of the proposed modeling.

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Section: Model Descriptionmentioning

confidence: 99%

“…Wang et al [25] have introduced a novel mixed shock model for a multi-state weighted k-outof-n system by considering system's resistance against shocks. Lorvand and Kelkinnama [19] have studied some reliability properties of k-out-of-n systems subject to random shocks under the δ-shock model.…”

Section: Introductionmentioning

confidence: 99%

On survival of coherent systems subject to random shocks

Goyal

Hazra

Finkelstein

2022

Preprint

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“…Transition rule (5) describes that when the j th shock is non-damaging, the component fails after suffering the j + 1 ð Þ th shock. Transition rule (6) depicts that when the j th shock is damaging, the component fails after the arrival of the j + 1 ð Þ th shock.…”

Section: Reliability Assessment For Componentsmentioning

confidence: 99%

“…For analyzing the failure process of the systems suffering shocks, a great many of shock models for them have been built based on different system structures, failure criteria, shock impacts and so on. Generally, the classic shock models can be classified into the following five types: cumulative shock models, 1,2 run shock models, 3,4 delta-shock models, [5][6][7] extreme shock models 8,9 and mixed shock models. [10][11][12] Cumulative shock models (CSMs) are modeled as that the systems break down when the cumulative damage from shocks exceeds a 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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“…Goyal et al 24 have discussed a δ -shock model that the threshold failure is a function of the arrival times and the magnitudes of shocks. Lorvand and Kelkinnama 25 developed the δ -shock model for multi-component systems.…”

Section: Introductionmentioning

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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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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Reliability analysis and optimal replacement for a k-out-of-n system under a δ-shock model

Cited by 7 publications

References 29 publications

On survival of coherent systems subject to random shocks

On survival of coherent systems subject to random shocks

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

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

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