Life behavior of $$\delta $$ δ -shock models for uniformly distributed interarrival times

Eryılmaz, Serkan; Bayramoğlu, İsmihan

doi:10.1007/s00362-013-0530-1

Cited by 38 publications

(17 citation statements)

References 10 publications

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“…So far in the literature, various shock models have been defined and studied. The shock models can be classified in five groups: cumulative shock model [6], extreme shock model [17], run shock model [14], δ-shock model [4,11], and mixed shock model. The mixed shock model is obtained by combining two different shock models.…”

Section: Introductionmentioning

confidence: 99%

Assessment of a multi-state system under a shock model

Eryılmaz

2015

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 99%

Assessment of a multi-state system under a shock model

Eryılmaz

2015

Applied Mathematics and Computation

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“…For more information about the multi-state systems, and the multi-state systems under shock models, one can refer to Lisianski et al, 9 Natvig, 10 and Eryilmaz and Tuncel. 11 A special type of shock model is the d-shock model in which the system fails when the time between two successive shocks is less than a prefixed d. This model has been studied by Li et al, 12 Li and Kong, 13 Eryilmaz and Bayromoglu, 14 Parvardeh and Balakrishnan, 15 and Lorvand et al 16 Eryilmaz and Bayramoglu 14 have discussed the d-shock models when the time between shocks follows a uniform distribution. Their works have been extended by Parvardeh and Balakrishnan.…”

Section: Introductionmentioning

confidence: 99%

Reliability analysis of an extended shock model

Poursaeed

2021

Proceedings of the Institution of Mechanical Engineers, Part O:

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Suppose that a system is subject to a sequence of shocks which occur with probability p in any period of time [Formula: see text], and suppose that [Formula: see text] and [Formula: see text] are two critical levels ([Formula: see text]). The system fails when the time interval between two consecutive shocks is less than [Formula: see text], and the time interval bigger than [Formula: see text] has no effect on the system activity. In addition, the system fails with a probability of, say, [Formula: see text], when the time interval varies between [Formula: see text] and [Formula: see text]. Therefore, this model can be regarded as an extension of discrete time version of [Formula: see text]-shock model, and such an idea can be also applied in the extension of other shock models. The present study obtains the reliability function and the probability generating function of the system’s lifetime under this model. The present study offers some properties of the system and refers to a generalization of the new model. In addition, the mean time of the system’s failure is obtained under reduced efficiency which is created when the time between two consecutive shocks varies between [Formula: see text] and [Formula: see text] for the first time.

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“…Lam and Zhang (2004) are the pioneers to introduce the d-shock model in which a shock is known as a deadly shock if the interarrival time between two shocks is smaller than a specific threshold d and leads to system failure. From the standpoint of maintenance theory, the following papers contribute a considerable amount of work to the application of d-shock for repairable deteriorating systems (Eryilmaz 2012;Eryilmaz 2017;Eryilmaz and Bayramoglu 2014;Eryilmaz and Kan 2020;Wang and Zhang 2005).…”

Section: Introductionmentioning

confidence: 99%