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 B 1 and B 2 . Here B 2 is in hot standby with B 1 . 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.

Performance evaluation of a hybrid series–parallel system with two human operators using Gumbel–Hougaard family copula

“…Gahlot et al (2018) analysed a system with two subsystems in the series configuration under k-out-of-n: G; working policy under different types of failures and two kinds of repair using a copula linguistic approach. Tiwari and Singh (2015) have evaluated two units' system in a series configuration in which the second unit consists of a standby unit under the different types of failure and two types of repair using copula. Rawal et al (2015) have used a copula linguistics approach to present the study of reliability measures of an area network.…”

Probabilistic Assessment of Two-Unit Parallel System with Correlated Lifetime under Inspection Using Regenerative Point Technique

“…Munday and Malik [10] examined a computer system software redundancy with priority repair to hardware failure over the software failure using semi Markov process and regenerative point technique. Tiwari and Singh [11] have studied two units' system in a series configuration in which the second unit consists of a standby unit under the different types of failure and two types of repair using copula. Lado et al [12] have evaluated the reliability measures (Availability, reliability, and MTTF, sensitivity and profit analysis) of the repairable complex system with two subsystems connected in a series configuration using the supplementary variable and Laplace transforms.…”