Stochastic Behavior of a Two-Unit Cold Standby Redundant System Under Poisson Shocks

El-Sherbeny, Mohamed Salah

doi:10.1007/s13369-017-2515-1

Cited by 8 publications

(3 citation statements)

References 15 publications

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“…Again, different methods of solution can be adopted. These approximates of the quantile functions obtained will be useful in the reliability analysis of engineering systems in general and queuing systems in particular [36,37].…”

Section: Discussionmentioning

confidence: 99%

Closed Form Expressions for the Quantile Function of the Erlang Distribution Used in Engineering Models

Okagbue

Adamu

Anake

2018

Wireless Pers Commun

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Quantile function is heavily utilized in modeling, simulation, reliability analysis and random number generation. The use is often limited if the inversion method fails to estimate it from the cumulative distribution function (CDF). As a result, approximation becomes the other option. The failure of the inversion method is often due to the intractable nature of the CDF of the distribution. Erlang distribution belongs to those classes of distributions. The distribution is a particular case of the gamma distribution. Little is known about the quantile approximation of the Erlang distribution. This is due to the fact that researchers prefer to work with the gamma distribution of which the Erlang is a particular case. This work applied the quantile mechanics approach, power series method and cubic spline interpolation to obtain the approximate of the quantile function of the Erlang distribution for degrees of freedom from one to two. The approximate values compares favorably with the exact ones. Consequently, the result in this paper improved the existing results on the extreme tails of the distribution. The closed form expression for the quantile function obtained here is very useful in modeling physical and engineering systems that are completely described by or fitted with the Erlang distribution.

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Section: Discussionmentioning

confidence: 99%

Closed Form Expressions for the Quantile Function of the Erlang Distribution Used in Engineering Models

Okagbue

Adamu

Anake

2018

Wireless Pers Commun

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“…units with the δ-shock model. Recently, El-Sherbeny [6] studied the behavior of the repairable cold standby system under the effect of Poisson shocks. In discussing the above research, we have found that the failed device is repaired immediately, but, in reality, the failed device may not be repaired immediately for various reasons.…”

Section: Introductionmentioning

confidence: 99%

Reliability Analysis of a Two Nonidentical Unit Parallel System with Optional Vacations under Poisson Shocks

Hussien

2022

Mathematical Problems in Engineering

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In this article, we study the impact of some system parameters on an industrial system consisting of two nonidentical parallel units with one repairer. The active unit may fail due to essential factors such as aging or deterioration, or due to external phenomena such as Poisson shocks occurring at different time periods. Whenever the value of a shock is greater than the specified threshold of the active unit, the active unit fails. The article assumes that the repairman can make one of two decisions at the beginning of system operation: either he takes a vacation when the two units are operating normally, or he remains in the system to monitor it until the first failure of the system. If a failure occurs in either unit during the repairman’s absence, the failed unit must wait until the repairman is called back to work. We assume that the value of each shock is i.i.d. with a known distribution. The length of the repairman’s vacation, the repair time, and the recall time are arbitrary distributions. Various reliability measures were calculated using the supplementary variable technique and the theory of Markov vector processes. Sensitivity and relative sensitivity analyses were also performed for the system parameters. Finally, numerical calculations and graphical analyses were performed to validate the derived indices.

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“…Most contemporary researchers focused on repairable systems under the effect of Poisson shocks. For example, [13] discussed the effect of Poisson Shocks on the behavior of a repairable system which consists of two units, one of them is working and the other is cold standby with a single repairman. [14] analyzed the reliability of the repairable system under the influence of two types of failure.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Behavior of a Two-Unit Parallel System with Dissimilar Units and Optional Vacations under Poisson Shocks

Hussien¹

2021

Preprint

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This article examines the impact of some system parameters on an industrial system composed of two dissimilar parallel units with one repairman. The active unit may fail due to essential factors like aging or deteriorating, or exterior phenomena such as Poisson shocks that occur at various time periods. Whenever the value of a shock is larger than the specified threshold of the active unit, the active unit will fail. The article assumes that the repairman has the right to take any of two decisions at the beginning of the system operation: either a takes a vacation if the two units work in a normal way, or stay in the system to monitor the system until the first system failure. In case of having a failure in any of the two units during the absence of the repairman, the failing unit will have to wait until the repairman is called back to work. We suppose that the value of every shock is assumed to be i.i.d. with some known distribution. The length of the repairman’s vacation, repair time, and recall time are arbitrary distributions. Various reliability measures have been calculated by the supplementary variable technique and the Markov’s vector process theory. At last, numerical computation and graphical analysis have been given for a particular case to validate the derived indices.

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Stochastic Behavior of a Two-Unit Cold Standby Redundant System Under Poisson Shocks

Cited by 8 publications

References 15 publications

Closed Form Expressions for the Quantile Function of the Erlang Distribution Used in Engineering Models

Closed Form Expressions for the Quantile Function of the Erlang Distribution Used in Engineering Models

Reliability Analysis of a Two Nonidentical Unit Parallel System with Optional Vacations under Poisson Shocks

Stochastic Behavior of a Two-Unit Parallel System with Dissimilar Units and Optional Vacations under Poisson Shocks

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