Reliability of an (M, M) Machining System with Spares
|International Journal of Engineering Trends and Technology (IJETT)||
|© 2014 by IJETT Journal|
|Year of Publication : 2014|
|Authors : Rashmita Sharma
|DOI : 10.14445/22315381/IJETT-V18P278|
Rashmita Sharma"Reliability of an (M, M) Machining System with Spares", International Journal of Engineering Trends and Technology (IJETT), V18(8),393-400 Dec 2014. ISSN:2231-5381. www.ijettjournal.org. published by seventh sense research group
This paper studies the reliability characteristics of a repairable system with M operating machines, S spare machines. The diffusion approximation technique has been used for multirepairman problem having spares with Poisson interfailure time distribution and exponential repair time distribution. The repair is assumed to be statedependent. We present derivations for the approximate formulae of the average number of failed components and the expected number of components operating in the system.
1. Bunday, B.D. and Scraton, E. (1982) : The G/M/r machine
interference model, Eur, Jr, Opns. Res. , Vol. 4, 399-402.
2. Bunday, B.D. and Khorram, E. (1990) : A note on : A closed form solution for the G/G/r machine interference model, I.J.P.R. (India), Vol. 23, No. 6, 1215-1183.
3. Cherian, J. ; Jain, M. and Sharma, G.C. (1988) : A diffusion approximation for a multi component systems with repair providing spare components, Jr. M.A.C.T. , Vol. 21, 79-90.
4. Feller, W. (1967) : An introduction to probability theory and applications. 3rd Edition Vol. I, John Wiley & sons, New York.
5. Hsieh, Y.C. and Wang, K. (1995): Reliability of a Repairable system with spares and a removable repairman, Micr. Reli. , 35(2) 197-208.
6. Jain, M. and Sharma, G.C. (1986) : A diffusion approximation for the GI/G/r machine interference problem with spare machines. Indian Journal of Technology, Vol. 24, 568-572.
7. Jain, M. (1996): Reliability analysis for M/M/C repairable system with spares and additional repairable, in: Proc.Conf. of Mathematics and its Applications in Engineering and Industry, Roorkee Univ.December.
8. Jain, M. (1997): ( m,M) machine repair problem with spares and state-dependent rates:a diffusion approximation approach, Microelectron Reliab.,37(6), 929-933.
9. Jain, M and Ghimire, R.P. (1997): Machine repair queueing system with non-reliable server and heterogeneous services discipline, J. MACT, 30, 105-115.
10. Jain,M., Singh, M. and Beghel, K.P.S.(2000): Machine repair problem with balking, reneging,spares and two modes of failure, J. MACT, 33, 69-79.
11. Jain, M., Sharma, G.C. ,Singh, M.(2003): M/M/R machine interference model with balking, reneging, spares and two modes of failure, OPSEARCH, 40(1), 24-41.
12. Jain, M.,Beghel, KP.S., Jadown, M. (2004): Performance prediction of machine interference model with spare and two modes of failure, Oper. Res. Inf.Tech. and industry S.R.S. Pub. Agra (2004), 197-208.
13. Jain, M., Sharma, G.C., Pundir,(2007): Reliability analysis of K-out-of N: G machining systems with mixed spares and multiple modes of failure, Int. J. Eng.Trans.B: Applications 20(3), 243-250.
14. Kalpakam, S.,Hameed, M.A.S.(1984): Avalaibility and reliability of an n-unit warm standby redundant system, J. Math. Phys. Sci.,18, 41-50.
15. Ke, JC, Lee, SL, Liou, CH (2009): Machine repair problem in production systems with spares and server vacations, RAIRO Oper. Res., 43(1), 35-54.
16. Kimura, T.(2004) : Diffusion Models for Computer / Communication Systems, Econ. J. of Hokkaiodo Univ.,Vol. 33, 37-52.
17. Kumar, B., Jain, M. (2012): / G/ 1 queueing model with state –dependent arrival and Second optional Vacation, Int.J. Math. In Oper.Res.
18. Muhammed, Masdi; Hussin, H.; Ainul Akmar; Majid, Mohd. A. A. (2012).: Reliability Assesment of Repairable System Based on Performance Data,J. Appl. Sci.,12(24), 25-68.
19. Maheshwari, S.; Sharma, P.; Jain, M. (2010): Machine repair problem with k type warm spares, multiple vacations for repairmen and reneging, Int. J.Eng. Tech. 2(4), 252-258.
20. Nararajan, R. and SubbaRao, S. (1970) : Reliability of a repairable system deterioration in storage, CORS Journal, 8(3),154.
21. Sharma, D. C. (2012) : Machine repair problem with spares and N-policy vacation, Res. J. Recent Sci. 1(4) , 72-78.
22. Shawky, A. L. (1997) : Single server machine interference model with balking, reneging and an additional server for longer queues, Microelectron Reliab. 37(2), 355-357.
23. Shawky, A. L. (2000) : The machine interference model: M / M / C / K / N with balking, reneging and spares, OPSEARCH , 37(1),25-35.
24. Sivazlian, B.D. and Wang, K.H. (1989) : System characteristics and economic analysis of the G/G/R machine repair problem with warm standby using diffusion approximation, Microelect. and Raliab. , Vol. 29. No. 5, 9829-9848.
25. Sivazlian, B.D. and Wang, K.H.(1990) : Diffusion approximation to the G/G/R machine repair problem with warm standby spares, Naval Research Logistics, 37,753-772.
26. Subramanian, R. ; Venkatakrishnan, K. S. and Kistner, K. P.(1976): Reliability of a repairable system with standby failure, Oper. Res. 24(1), 169-176.
27. Sunaga, J. ; Biswas, S.K. and Nishida, N. (1982) : An approximation method using continuous models for queueing problems II (multi-server finite queue), Jr. Opns. Res. Japan, Vol. 25, 113-117.
28. Wang, K.N. and Sivazlian, B.D. (1989) : Reliability of a system with warm standbys and repairmen, Microelectron reliab., 29 (5), 849-860.
29. Wang, K.N. and Sivazlian, B.D. (1992) : Cost analysis of the M/M/R machine repair problem with spares operating under variable service rates, Micrielect. and Reliab., Vol. 32, No. 8, 1171-1183.
30. Yao, D.D. and Buzacott, J.A. (1985) : Queueing models manufacturing station part I : The diffusion approximation, Eur. Jr. Opns. Res., Vol. R-35, No. 3, 285-292.
We present derivations for the approximate formulae of the average number of failed components and the expected number of components operating in the system.