# Journal of Mathematics and Statistics

## Cost Analysis of Two-Dissimilar-Unit Cold Standby System with three States and Preventive Maintenance Using Linear First Order Differential Equations

M. Y. Haggag

DOI : 10.3844/jmssp.2009.395.400

Journal of Mathematics and Statistics

Volume 5, Issue 4

Pages 395-400

### Abstract

Problem statement: Several researchers have studied the reliability behavior of a three state systems, but no attention was paid to the reliability evaluation due to preventive maintenance. The better maintenance of the system originates better reliability. Also, standby support increases the reliability of the system. Approach: Determine the efficacy of preventive maintenance on the reliability and performance of the system. In this study, the MTSF, steady-state availability and costt analysis of a two-dissimilar-unit cold standby system with preventive maintenance was discussed. The proposed system has been investigated under the assumption that each unit works in three different states: Normal, partial failed ad total failure. The failure and repair time distributions are exponential. Using linear first order differential equations the system characteristics had been obtained. A special case for the proposed system is given in which preventive maintenance was not considered. Results: The results indicated that the system with preventive maintenance is better than the system without preventive maintenance. Conclusion: These results indicated that the better maintenance of parts of the system originated better reliability and performance of the system.