Mathematical Approaches for Reliability Evaluation of a Parallel-Series System of Order (2, 3, 1) with Exponential Failure Laws
Abstract
Some mathematical approaches have been used to determine reliability measures of a parallel-series system of order (2, 3, 1). The system has four units (A, B, C and D) arranged in two parallel paths (called subsystems). In first subsystem, the three units (A, B and C) are connected in series while there is a single unit ‘D’ in the second subsystem. The failure rate of the units is assumed as constant that follow the negative exponential distribution. The expressions for reliability and MTSF have been derived using decomposition method, cut set method and event space method. The values of these reliability measures have also been obtained for particular values of the parameters related to failure rates of the units considering all units identical in nature. The graphical behavior of reliability and MTSF has also been shown for the particular values. The application of the work has been explained in solar panels systems.
References
1. A. Elsayed; Reliability Engineering. Wiley Series in Systems Engineering and Management (2012).
2. A. Shojaeifar; H. Fazlollahtabar and I. Mahdavi; Decomposition versus Minimal Path and Cuts Methods for Reliability Evaluation of an Advanced Robotic Production System. Journal of Automation, Mobile Robotics and Intelligent Systems, 10(3), 52–57 (2016).
3. B. Epstein and M. Sobel; Life Testing. Journal of the American Statistical Association, 48, 486-502 (1953).
4. B. Singh and S. K. Ghosh; Network Reliability Evaluation by Decomposition. Microelectronics
Reliability, 34(5), 925–927 (1994).
5. C. Singh; A Cut Set Method for Reliability Evaluation of Systems having s-Dependent Components. IEEE Transactions on Reliability, R-29(5), 372–375 (1980).
6. E. Balagurusamy; Reliability Engineering. Tata McGraw Hill Publishing Co. Ltd., India (1984).
7. L. S. Srinath; Concept in Reliability Engineering. Affiliated East-West Press (P) Ltd. (1985).
8. P. K. Joshi; H. Thakur and C. Sharma; Analysis of System Reliability of the System with Different Configurations using Event Space Method. Journal of National Academy of Mathematics India, 34(1), 21-35 (2020).
9. R. E. Barlow and P. Prochan; Mathematical Theory of Reliability. John Wiley, New York (1965).
10. S. K. Chauhan and S. C. Malik; Reliability Evaluation of a Series-Parallel and Parallel-Series Systems for Arbitrary Values of the Parameters. International Journal of Statistics and Reliability Engineering, 3(1), 10-19 (2016).
11.S. K. Chauhan and S. C. Malik; Reliability and MTSF Evaluation of a Parallel-Series System using Weibull Failure Laws. International Journal of Computer Applications, 172(2), 11-21 (2017).
Trion Studio
