On the reliability and optimal maintenance of systems under a generalized mixed δ-shock model

Bohlooli-Zefreh, Mohsen; Asadi, Majid; Parvardeh, Afshin

doi:10.1177/1748006x211002306

Cited by 9 publications

(4 citation statements)

References 32 publications

(47 reference statements)

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“…This model and some of its generalizations were studied by Refs. 1–9 Sarada and Sangeetha 10 analyzed a quasi-renewal process model with δ -shock for a degenerative repairable supply chain with a single supplier source. Jiang 11 investigated a new δ -shock model for a system subject to multiple failure types and its optimal order-replacement policy.…”

Section: Introductionmentioning

confidence: 99%

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

Lorvand

Kelkinnama

2022

Proceedings of the Institution of Mechanical Engineers, Part O:

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Consider a k-out-of- n system which is subject to shocks that arrive at random times. This study develops [Formula: see text]-shock model, among the variants of well-known shock models, for such system which consists of independent components. In a [Formula: see text]-shock model, the system fails when the inter-arrival between two consecutive shocks is less than a critical threshold value of [Formula: see text]. Depending on the number of components that fail due to the occurrence of the shocks, we introduce two [Formula: see text]-shock models. The reliability function and mean time to failure of the system are discussed when the time between shocks has an arbitrary distribution. Furthermore, the problem of finding the optimal preventive time concerned with minimizing a mean cost per unit time is investigated. Numerical examples based on a simulation study are also provided to illustrate theoretical achievement.

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Section: Introductionmentioning

confidence: 99%

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

Lorvand

Kelkinnama

2022

Proceedings of the Institution of Mechanical Engineers, Part O:

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“…The Mixed shock model was introduced by Gut 26 by combining two extreme and cumulative shock models. Other examples of this model were provided by Parvardeh and Balakrishnan 27 and Bohlooli-Zefreh et al 28 with a combination of δ and extreme shock models. In this regard, Lorvand et al 29,30 have also discussed a generalization of mixed δ -shock model for the multi-state 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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“…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. For example, Montoro-Cazorla and Pe´rez-Oco´n 13 studied a CSM where the arrivals of random shocks follow a batch Markovian arrival process.…”

Section: Introductionmentioning

confidence: 99%

“…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, 5–7 extreme shock models 8,9 and mixed shock models. 10–12…”

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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On the reliability and optimal maintenance of systems under a generalized mixed δ-shock model

Cited by 9 publications

References 32 publications

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

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

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

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

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