Evaluation of Reliability and Availability Characteristics of a Repairable System with Active Parallel Units

Ibrahim Yusuf, Fatima Salman Koki

Department of Mathematical Sciences, Bayero University, Kano, Nigeria.
Department of Physics, Bayero University, Kano.

DOI: 10.4236/ojapps.2013.35044                

Abstract

In this paper, we study the reliability and availability characteristics of a repairable system consisting of two subsystems A and B in series. Subsystem A consists of two units A₁ and A₂ operating in active parallel while subsystem B is a single unit. Failure and repair times are assumed exponential. The explicit expressions of reliability and availability characteristics like mean time to system failure (MTSF), system availability, busy period and profit function are derived using Kolmogorov forward equations method. Various cases are analyzed graphically to investigate the impacts of system parameters on MTSF, availability, busy period and profit function.

Keywords

Active Parallel; Reliability; Availability; Mean Time to System Failure

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	K. M. El-Said and M. S. EL-Sherbeny, “Evaluation of Reliability and Availability Characteristics of Two Different Systems by Using Linear First Order Differential Equations,” Journal of Mathematics and Statistics, Vol. 1, No. 2, 2005, pp. 119-123. http://dx.doi.org/10.3844/jmssp.2005.119.123
[2]	I. Yusuf and N. Hussaini, “Evaluation of Reliability and Availability Characteristics of 2-Out of -3 Standby System under a Perfect Repair Condition,” American Journal of Mathematics and Statistics, Vol. 2, No. 5, 2012, pp. 114-119. http://dx.doi.org/10.5923/j.ajms.20120205.03
[3]	S. V. Amari, J. B. Dugan and R. B. Misra, “Optimal Reliability of Systems Subject to Imperfect Fault-Coverage,” IEEE Transactions on Reliability, Vol. 48, No. 3, 1999, pp. 275-284. http://dx.doi.org/10.1109/24.799899
[4]	K.-H. Wang and B. D. Sivazlian, “Reliability of System with Warm Standbys and Repairmen,” Microelectronics and Reliability, Vol. 29, No. 5, 1989, pp. 849-860. http://dx.doi.org/10.1016/0026-2714(89)90184-4
[5]	J.-C. Ke and K.-H. Wang, “The Reliability Analysis of Balking and Reneging in a Repairable System with Warm Standbys,” Quality and Reliability Engineering International, Vol. 18, No. 6, 2002, pp. 467-478. http://dx.doi.org/10.1002/qre.495
[6]	K.-H. Wang and J.-C. Ke, “Probabilistic Analysis of a Repairable System with Warm Standbys Plus Balking and Reneging,” Applied Mathematical Modeling, Vol. 27, No. 4, 2003, pp. 327-336. http://dx.doi.org/10.1016/S0307-904X(02)00133-6
[7]	K.-H. Wang, Y.-J. Lai and J.-B. Ke, “Reliability and Sensitivity Analysis of a System with Warm Standbys and a Repairable Service Station,” International Journal of Operations Research, Vol. 1, No.1, 2004, pp. 61-70
[8]	K. M. El-Said, “Cost Analysis of a System with Preventive Maintenance by Using Kolmogorov’s forward Equations Method”. American Journal of Applied Sciences, Vol.5, No.4, 2008, 405-410.
[9]	M. Y. Haggag. “Cost Analysis of a System Involving Common Cause Failures and Preventive Maintenance”. Journal of Mathematics and Statistics, Vol. 5, No.4, 2009. pp 305-310. http://dx.doi.org/10.3844/jmssp.2009.305.310
[10]	M. Y. Haggag, “Cost Analysis of k-Out-of-n Repairable System with Dependent Failure and Standby Support Using Kolmogorov’s Forward Equations Method,” Journal of Mathematics and Statistics, Vol. 5, No. 4, 2009. pp. 401-407.