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Optimal (N, F) policy for queue-dependent and time-sharing machining redundant system

Chandra Shekhar (Department of Mathematics, Birla Institute of Technology and Science, Pilani, India)
Madhu Jain (Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India)
Ather Aziz Raina (Department of Mathematical Sciences, Baba Ghulam Shah Badshah University, Jammu, India)
Javid Iqbal (Department of Mathematical Sciences, Baba Ghulam Shah Badshah University, Jammu, India)

International Journal of Quality & Reliability Management

ISSN: 0265-671X

Article publication date: 5 June 2017



The purpose of this paper is to study the performance metrics of redundant repairable machining system which is applicable in various systems like computer and communication system, manufacturing and production system, etc.


In the present investigation, the authors develop Markov model for the system consisting of identical active operating machines which are prone to breakdown. The operating machines are under the care of one permanent repair facility that provides time-sharing basis repair services. The maintenance is facilitated with the provision of standby machines of mixed type and permanent as well as additional repair facility. From the economic point of view, F-policy and N-policy to control the service and arrival of failed machines effectively are included.


For the performance analysis of the system in long run, the authors compute steady-state probabilities using product-type solution method recursively. Sensitivity analysis is performed numerically for various parameters by developing code in MATLAB.

Social implications

The performance prediction done may be helpful for the system designers and decision makers for the improvement of the existing machining systems in various industries.


Markovian model for the performance prediction of fault tolerant multi-identical operating and standby machines redundant system is developed in generic frameworks by incorporating many noble features which were not all taken together by other researchers working on the same lines. The key concepts incorporated for the modeling of the concerned system is: F-policy, N-policy, time-sharing, and sensitivity analysis of availability and cost function.



The authors would like to thank the editor in chief and anonymous referees for their valuable suggestions and critical comments which help a lot in improving the quality and clarity of the paper. The first author is also thankful to DST-FIST for financial grant (SR/FST/MSI-090/2013 (C)).

Conflicts of interest: the authors declare that there is no conflict of interests regarding the publication of this paper.


Shekhar, C., Jain, M., Raina, A.A. and Iqbal, J. (2017), "Optimal (N, F) policy for queue-dependent and time-sharing machining redundant system", International Journal of Quality & Reliability Management, Vol. 34 No. 6, pp. 798-816.



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