Mathematical Analysis of Machine repair problem with common cause failure, hot spares and multiple repairmen

Purushottam Jharotia

Abstract


We study the machine repairable system comprising M operating machines, H spares and more than one repairman where “the partial server vacation” is applied on some of the repairmen. In this system, the first repairman never takes vacation and always available for servicing of failed machines while other repairmen goes to random length vacation whenever the number of failed machines are less than N, N +1 respectively. Machines may breakdown individually or due to common cause according to Poisson process. Vacation time and service time of repairmen is follows the exponential distribution. Recursive approach is used to obtain the steady state probabilities. A cost model is developed to determine the optimum value of failed machine maintaining the system availability. Sensitivity analysis is investigated for optimal conditions and also analyzes the reliability characteristics of the system.

We study the machine repairable system comprising M operating machines, H spares and more than one repairman where “the partial server vacation” is applied on some of the repairmen. In this system, the first repairman never takes vacation and always available for servicing of failed machines while other repairmen goes to random length vacation whenever the number of failed machines are less than N, N +1 respectively. Machines may breakdown individually or due to common cause according to Poisson process. Vacation time and service time of repairmen is follows the exponential distribution. Recursive approach is used to obtain the steady state probabilities. A cost model is developed to determine the optimum value of failed machine maintaining the system availability. Sensitivity analysis is investigated for optimal conditions and also analyzes the reliability characteristics of the system.


Keywords


Repairable system; Spares; Partial server vacation; Common cause failure; Sensitivity analysis.

Full Text:

pdf

References


Chien, Y. H. (2010). Optimal number of minimal repairs before ordering spares for preventive replacement, Applied Mathematical Modeling, 34(11), 3439-3450.

Dai, Y. S., Levitin, G., & Wang, X. (2007). Optimal task partition and distribution in grid service system with common cause failure, Future Generation Computer Systems, 23(2), 209-218.

Dequan, Yue, Wuyi, Yue & Hongjuan, Qi (2012). Performance analysis and optimization of a Machine Repair System with Warm Spares and two heterogeneous repairmen, Optim. Eng., 13(4), 545-562.

Doshi, B. T. (1986). Single server queues with vacations: A survey, Queueing System, 1(1), 29-66.

Gupta, S. M. (1997). Machine interface problem with warm spare, server vacation and exhaustive service, performance evaluation, 29(3), 195-211.

Hughes, R. P. (1987). A new approach to common cause failure, Reliability engineering & System Safety, 17(3), 211-236.

Jain, M., & Mishra, A. (2006). Multistage degraded machining system with common cause shock failure and state dependent rates, Journal of Rajasthan Academy of Physical Sciences, 5(3), 251-262.

Jharotia, P., & Sharma, D. C. (2015). Mathematical Analysis of Machining System with Warm Spares and Variable Service Rate, Int. J. Process Management and Benchmarking, (In Press).

Ke, J. C. (2006). Vacation policies for machine interference problem with unreliable server and state dependent service rate, Journal of the Chinese Institute of Industrial engineers, 23(2), 100-114.

Ke, J. C., & Wang, K. H. (2007). Vacation policies for machine repair problem with two type spares. Applied Mathematical Modeling, 31(5), 880-894.

Ke, J. C., & Wu, C. H. (2012). Multi-server machine repair model with standbys and synchronous multiple vacation, Computer & Industrial Engineering, 62(1), 296-305.

Kvam, P. H., & Miller, J. G. (2002). Common cause failure predication using data mapping, Reliability engineering & System Safety, 76(3), 273-278.

Longshree, Singh, P., Sharma, D. C. & Jharotia, P. (2015). Mathematical modelling and performance analysis of machine repair problem with hot spares, Proceedings of the National Academic of sciences, India Section A: Physical Science, 85(1), 127-135.

Sharma, D. C. (2011). Non-perfect M/M/R machine repair problem with spares and two modes of failure, International Journal of Scientific and Engineering Research, 2, 1-5.

Sharma, D. C. (2012). Machine Repair Problem with Spares and N-Policy vacation, Research Journal of Recent Sciences, 1(4), 72-78.

Wang, K. H., & Sivazlian, B. D. (1992). Cost analysis of the M/M/R machine repair problem with spares operating under variable service rates, microelectronics and reliability, 32(8), 1171-1183.

Wang, K. H., & Ke, J. C. (2003). Probabilistic analysis of a repairable system with warm standby plus balking and reneging. Applied Mathematical Modeling, 27(4), 327-336

Tian, N. S., & Zhang, Z. G. (2006). Vacation Queuing Models-Theory and applications, New York: Springer.


Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.