IJE TRANSACTIONS B: Applications Vol. 17, No. 2 (July 2004) 171-182   

downloaded Downloaded: 180   viewed Viewed: 2366

Madhu Jain, Rakhee and Sandhya Maheshwari

Department of Mathematics, Institute of Basic Science
Khandari, Agra-282002, India, madhujain@sancharnet.in
madhuj_2001@yahoo.com - chaya-rakhee@yahoo.com - imsandya2001@yahoo.com
( Received: October 25, 2002 – Accepted in Revised Form: June 10, 2004 )

Abstract    This investigation deals with the transient analysis of the machine repair system consisting of M-operating units operating under the care of single repairman. To improve the system reliability/availability, Y warm standby and S cold standby units are provided to replace the failed units. In case when all spares are being used, the failure of units occurs in degraded fashion. In such situation there is a facility of one additional repairman to speed up the repair. The lifetime and repair time of units are exponentially distributed. We use matrix method to solve the governing Chapman-Kolmogorov equations. Expressions for the system reliability, availability, mean time to system failure, etc. are established in terms of transient probability. Computational scheme is discussed to facilitate the numerical results. Sensitivity analysis is also carried out to depict the effect of various parameters on the system reliability.


Keywords    Machine Repair, Warm Standby, Cold Standby, Degraded, Additional Repairman, Mean Time to Failure (MTTF), Reliability, Availability



1. Kumagai, M., “Reliability Analysis of an n-Spare System with a Single Repair Facility”, Oper. Res. Quart., Vol. 26, No. 3, (1975), 629-640.

2. Kalpakam, S. and Hameed, M. A. S., “Availability and Reliability of an n-Unit Warm Standby Redundant System”, Math. Phys. Sci., Vol. 18, (1984), 41-50.

3. Sivazlian, B. D. and Wang, K. H., “Economic Analysis of the M/M/R Machine Repair Problem with the Warm Standbys”, Microelectron. Reliab., Vol. 29, No. 1,(1989), 25-35.

4. Shao, J. and Lamberson, L. R., “Reliability of Series System with Spares”, IJPAM, Vol. 21, No. 3, (1991), 285-289.

5. Goel, L. R. and Srivastava, P., “Transient Analysis of a Multiple-Unit Redundant System”, Microelectron. Reliab., Vol. 32, No. 10, (1992), 1361-1365.

6. Jain, M., “(m, M) Machine Repair Problem with Spares and State Dependent Rates, a Diffusion Process Approach”, Microelectron. Reliab., Vol. 37, No. 6, (1997), 929-933.

7. Jain, M. and Dhyani, I., “Transient Analysis of M/M/C Machine Repair Problem with Spares”, Agra UniversityJ. of Sci., Vol. 2, (1999), 16-42.

8. Jain, M., Singh, M. and Baghel, K. P. S., “M/M/C/K/N Machine Repair Problem with Balking, Reneging”, Spares and Additional Repairman, J. GSR, Vol. 26-27,(2000), 49-60.

9. Jain, M., Sharma, G. C. and Singh, M., “N-Policy for Degraded Machining System with Spares and Server Breakdowns”, Int. J. Manag. and Syst., India, (In print:2003).

10. Chandre, K. J. and Shanti Kumar, J. G., “On a Machine Interference Problem with Several Types of Machines Attended by a Single Repairman”, Int. J. Prod. Res., Vol. 21, No. 4, (1983), 529-547.

11. Jain, M., “Reliability Analysis for M/M/C Repairable System with Spares and Additional Repairmen”, Proc. Conf. on Mathematics and Its Applications in Engineering and Industry, Roorkee, 16-18 (Dec. 1996), 18-30.

12. Jain, M., “M/M/R Machine Repair Problem with Spares and Additional Repairman”, Ind. J. Pure App. Maths, Vol. 29, No. 5, (1998), 517-524.

13. Jain, M., Singh, M. and Baghel, K. P. S., “Machine Repair Problem with Spares, Reneging, Additional Repairman and Two Modes of Failure”, J. MACT, Vol. 33, (2000), 69-79.

14. Jain, M. and Maheshwari, S. “Transient Analysis of Redundant Repairable System with Additional Repairmen”, American J. Math. and Manag. Sci., USA, (In press: 2003).

15. Goyal, A. and Tantawi, A. N., “Evaluation of Performability for Degraded Computer Systems”, IEEE Trans. Computers, Vol. 29, (1987), 738-744.

16. Meyer, J. F. “On Evaluating the Performance for Degraded Computer Systems”, IEEE Trans. Computers, Vol. 29, (1980), 720-731.

17. Najjar, W. A. and Gaudiot, J. L. “Scalability Analysis in Gracefully Degraded Large Systems”, IEEE Trans. Reliability, Vol. 40, No. 2, (1991), 189-197.

18. Pham, H., Suprasad, A. and Misra, R. B., “Availability and Mean Lifetime Prediction of Multistage Degraded System with Partial Repairs”, Reliab. Eng. Syst. Safety, Vol. 56, (1997), 169-173.

19. Jain, M., Baghel, K. P. S. and Shekhar, C., “Reliability Analysis of Gracefully Degradable Multiprocessor System”, Proc. of Int. Conf. on Operations Research Development and XXXV Annual Convention of ORSI, (Dec. 27-30, 2000), CP-16.

20. Jain, M. and Singh, C. J., “Reliability of Repairable Multi-Component Redundant System”, Int. J. Eng., Vol. 3, (2000), 107-114.

International Journal of Engineering
E-mail: office@ije.ir
Web Site: http://www.ije.ir