Reliability Analysis of Linear Consecutive-k-out-of-n: F Retrial Systems with Second Optional Repair and Single Vacation  
Author Yan Wang

 
Co-Author(s) Linmin Hu; Bing Zhao; Ruiling Tian

 
Abstract In this paper, a reliability model of linear consecutive-k-out-of-n: F retrial system with second optional repair and single vacation is investigated, where failure may occur to all non-failed components when the system is in a failed state. We assume that the component lifetimes in the working state and failed state of the system follow the exponential distributions with parameter λ and λ‘ (λ > λ‘), respectively. When a component fails, it can be repaired immediately if the repairman is idle. Otherwise, if the repairman is busy repairing another failed component or is on vacation, the failed component will enter the retrial space and attempt repeatedly according to the first in first out principle until it is repaired. The retrial time obeys the exponential distribution with parameter γ. The repairman provides two-phase repair for each failed component, namely the first essential repair and the second optional repair. All failed components must undergo the first essential repair, whereas only some of the failed components are subject to the second optional repair. That is, after the completion of the first essential repair, the failed component either returns to the system directly with probability 1-q, or it chooses to accept the second optional repair by the same repairman with probability q, and then returns to the system after the second optional repair completion. In order to model the practical systems as precisely as possible, it is assumed that the repair time of each phase is governed by the phase-type distribution.

 
Keywords Reliability, Second optional repair, Vacation, Retrial, Phase-type distribution
   
    Article #:  RQD27-43
 

Proceedings of 27th ISSAT International Conference on Reliability & Quality in Design
Virtual Event
August 4-6, 2022