On inactivity times of failed components of coherent system under double monitoring

Guo, Zhouxia; Zhang, Jiandong; Yan, Rongfang

doi:10.1017/s0269964821000152

Cited by 8 publications

(4 citation statements)

References 44 publications

(78 reference statements)

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“…The lower bound in (7) in Theorem 1 can take negative values for some t ≥ 0. If the lower bound is negative for a given t ≥ 0, the result of Theorem 1 becomes trivial.…”

Section: Resultsmentioning

confidence: 99%

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Stochastic Orderings of the Idle time of Inactive Standby Systems

Shrahili¹,

Kayid²

2023

Preprint

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In this paper we consider a failed cold standby systems and obtain some stochastic bounds on the idle time of such systems. It is assumed that, at a time t the failure of a cold standby system is observed, but the actual time of the failure is a time before t. The idle time of the inactive cold standby system is measured as the time between the exact time of failure, which is a random variable, and time t. We use the idle times of the components of the system to obtain lower and upper bounds on the lifetime of the standby system to which they are assembled. We bring some examples to show that the results and the conditions imposed to get them are achievable.

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“…The lower bound in (7) in Theorem 1 can take negative values for some t ≥ 0. If the lower bound is negative for a given t ≥ 0, the result of Theorem 1 becomes trivial.…”

Section: Resultsmentioning

confidence: 99%

“…have been studied during the past decades (see, for instance, Bayramoglu and Ozkut [3], Zhang and Balakrishnan [24], Navarro et al [17], Kayid et al [10], Navarro and Calì [18], Salehi and Tavangar [20], Toomaj and Di Crescenzo [22], Amini-Seresht et al [2], Guo et al [7] and Kayid and Shrahili [11]).…”

Section: Of 15mentioning

confidence: 99%

Stochastic Orderings of the Idle time of Inactive Standby Systems

Shrahili¹,

Kayid²

2023

Preprint

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“…The idle time is sometimes called the inactivity time or reversed residual lifetime. In view of the idle time, the stochastic properties of coherent systems, a large and well-known class of systems in reliability, have been widely studied during the past decades (see, for instance, Bayramoglu and Ozkut [21], Zhang and Balakrishnan [22], Navarro et al [23], Kayid et al [24], Navarro and Calì [25], Salehi and Tavangar [26], Toomaj and Di Crescenzo [27], Amini-Seresht et al [28], Guo et al [29], and Kayid and Shrahili [30]). However, the study of stochastic comparisons between idle (or inactive) time of cold standby systems has not been conducted in literature to date.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Orderings of the Idle Time of Inactive Standby Systems

Shrahili,

Kayid

2023

Mathematics

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In this paper, we consider a failed cold standby system and obtain stochastic bounds on the idle time of such systems. We state and prove that if the last spare in the system is exponentially distributed and if the components have log-concave lifetime distributions, then the idle time of a failed cold standby system is smaller than the sum of the idle times of the components in the system according to the likelihood ratio order. In order to compare the idle time of two cold standby systems with different numbers of spares and different observation times of the failure in terms of the likelihood ratio order, an additional result is presented. Finally, we establish sufficient conditions for the usual stochastic ordering between the idle time of a cold standby system of size two and the sum of the idle times of the components in the system. We provide several examples to show that the results are achievable.

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“…As two important system structures in reliability theory and engineering, the parallel and series systems have been studied comprehensively, interested readers may refer to Boland et al [6], Singh and Misra [41], Hu and Wang [25], Da et al [11], Navarro and Spizzichino [38], Yan et al [47], Yan and Luo [45], Chen et al [7], Fang and Wang [20], Kundu et al [29], Yan and Wang [46], Majumder et al [36] and the reference therein. Some researchers also focus on the optimal allocation of components for -out-of- systems and the general coherent systems, refer to Bhattacharya and Samaniego [5], Li and Ding [32], Ding and Li [15], You et al [50], Zhang [51], Ding et al [16], Ling and Wei [34], Guo et al [23], Torrado [44] and Yan et al [49].…”

Section: Introductionmentioning

confidence: 99%

Optimal allocation of a coherent system with statistical dependent subsystems

Lü¹,

Zhang²,

Yan³

2021

Prob. Eng. Inf. Sci.

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This paper studies the optimal allocation policy of a coherent system with independent heterogeneous components and dependent subsystems, the systems are assumed to consist of two groups of components whose lifetimes follow proportional hazard (PH) or proportional reversed hazard (PRH) models. We investigate the optimal allocation strategy by finding out the number $k$ of components coming from Group A in the up-series system. First, some sufficient conditions are provided in the sense of the usual stochastic order to compare the lifetimes of two-parallel–series systems with dependent subsystems, and we obtain the hazard rate and reversed hazard rate orders when two subsystems have independent lifetimes. Second, similar results are also obtained for two-series–parallel systems under certain conditions. Finally, we generalize the corresponding results to parallel–series and series–parallel systems with multiple subsystems in the viewpoint of the minimal path and the minimal cut sets, respectively. Some numerical examples are presented to illustrate the theoretical findings.

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On inactivity times of failed components of coherent system under double monitoring

Cited by 8 publications

References 44 publications

Stochastic Orderings of the Idle time of Inactive Standby Systems

Stochastic Orderings of the Idle time of Inactive Standby Systems

Stochastic Orderings of the Idle Time of Inactive Standby Systems

Optimal allocation of a coherent system with statistical dependent subsystems

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