Simulation Study on Reliability Estimates of a Repairable System with Lethal and Non-Lethal Common Cause Shock Failures

In order to solve the reliability assessment of repairable systems, this article, based on two-component system, provides the maximum likelihood estimation. The system can be restored through proper repairing even from Common Cause Shock (CCS) failure. We derived M L estimates of availability for series and parallel systems. The approach used is empirical one with Monte Carlo simulation. © 2019 Elixir All rights reserved. Elixir Statistics 126 (2019) 52481-52484 Statistics Available online at www.elixirpublishers.com (Elixir International Journal) G. Y. Sagar et al./Elixir Statistics 126 (2019) 52481-52484 52482 : Availability of the series system : Availability of the parallel system : Steady-state availability of the series system : Steady-state availability of the parallel system ̂ : M L Estimate of steady-state availability of series system ̂ : M L Estimate of steady-state availability of parallel system ̅ ̅ ̅ : Sample means of the occurrence of individual, NCCS and LCCS failures respectively. ̅: Sample mean of service time of the components ̂̅ ̂̅ ̂̅: Sample estimates of individual, NCCS and LCCS failure rates respectively. ̂̅ : Sample estimate of service time of the components n : Sample size N: Number of simulated samples M S E: Mean square error 4. Markov model for state transition The Markov diagram is shown in Fig.1. The numerical in Fig.1 denote the system state. The probability equations associated with the system states are given by