Version 1
: Received: 3 February 2021 / Approved: 4 February 2021 / Online: 4 February 2021 (13:07:59 CET)
How to cite:
El-Sherbeny, M.S.; Hussien, Z.M. Stochastic Behavior of a Two-Unit Parallel System with Dissimilar Units and Optional Vacations under Poisson Shocks. Preprints2021, 2021020138. https://doi.org/10.20944/preprints202102.0138.v1
El-Sherbeny, M.S.; Hussien, Z.M. Stochastic Behavior of a Two-Unit Parallel System with Dissimilar Units and Optional Vacations under Poisson Shocks. Preprints 2021, 2021020138. https://doi.org/10.20944/preprints202102.0138.v1
El-Sherbeny, M.S.; Hussien, Z.M. Stochastic Behavior of a Two-Unit Parallel System with Dissimilar Units and Optional Vacations under Poisson Shocks. Preprints2021, 2021020138. https://doi.org/10.20944/preprints202102.0138.v1
APA Style
El-Sherbeny, M.S., & Hussien, Z.M. (2021). Stochastic Behavior of a Two-Unit Parallel System with Dissimilar Units and Optional Vacations under Poisson Shocks. Preprints. https://doi.org/10.20944/preprints202102.0138.v1
Chicago/Turabian Style
El-Sherbeny, M.S. and Zienab M. Hussien. 2021 "Stochastic Behavior of a Two-Unit Parallel System with Dissimilar Units and Optional Vacations under Poisson Shocks" Preprints. https://doi.org/10.20944/preprints202102.0138.v1
Abstract
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.
Keywords
Mean time to failure; Poisson shock; Steady-state availability; Steady-state frequency; Supplementary variable technique.
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
