Analysis of a Risky Two Unit System under Marked Process Incorporating Two Repairmen with Vacations

Abstract

In this paper the system considered consists of two subsystems A and B. Subsystem A has only one unit whereas subsystem B consists of two homogeneous units B1 and B2. Here B2 is in hot standby with B1. In the present study we have incorporated two repairmen namely supervisor and novice to repair the failed units of the system. The supervisor is always there whereas the novice remains in vacation. The system is analyzed under “Preemptiveresume- repair discipline”. We have used supplementary variable technique, Laplace transformation and copula to obtain various transition state probabilities, reliability, availability, cost analysis and the steady state behaviour of the system. To make a comparison between the measures obtained using two families of copulas Gumbel-Hougaard family and Bivariate Clayton, the model has been solved with the help of Gumbel-Hougaard family of copula and Bivariate Clayton copula both in two different cases. Also a comparison between two types of repair policies “Head-of-line-repair” and “Preemptive-resume-repair” has been carried out. At last some numerical examples have been taken.

Keywords

• Reliability
• Marked process
• cost analysis
• Gumbel-Hougaard copula
• Bivariate Clayton copula
• supplementary variable technique.