Science Journal Of Mathematics and Statistics, Volume
2014 (2014), March 2014
© Author(s) 2014. This work is distributed under the Creative Commons Attribution 3.0 License.
Cost Analysis of K-Out Of-N Repairable System Using a Continuous-Time Discrete-State Markov Process
Author: M.Y. Haggag
Mathematics Department Faculty of Science, Al-Azhar University Nasr City 11884, Cairo, Egypt.
Accepted: February 28, 2014; Available Online 30 March, 2014
Problem statement: This paper deals with a statistical analysis of k-out of-n repairable system with dependent failure and standby support with repair facility. The entire system is working if at least k of its n components are operating. The failure of any working unit of a system results in the reduction of the efficiency of the whole system and as the result, the reliability of the system reduced. The standby unit support increases the reliability of the system. Approach: Determine the effect of repairing failed units on the reliability of the system and determine the profit function. Using a continuous-time discrete-state Markov process, the system characteristics are obtained. To validate the theoretical results, numerical computations are derived. Tables and graphs have also been given in the end. Results: These results indicated that the system characteristics with repairing a failed unit are greater than the system without repairing with respect to the MTSF, steady state availability and the profit. Conclusion: We concluded that the system with repair is better than the system without with respect to the MTSF, steady state availability and the profit.
Keyword:Cost analysis, Repairable system, Dependent failure rates, Markov process, Laplace transform, Mean time to system failure (MTSF), Steady-state availability, Profit function (PF).