Geodesic
N-policy for a repairable redundant machining system with controlled rates
Jain, Madhu1 ; Shekhar, Chandra2 ; Shukla, Shalini3
1 Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667 Uttarakhand, India.
2 Department of Mathematics, Birla Institute of Technology and Science, Pilani, 333031 Rajasthan, India.
3 Department of Mathematics, D.A.V. (PG) College, Dehra Dun, 248001 Uttarakhand, India.
RAIRO - Operations Research - Recherche Opérationnelle, Special issue - Advanced Optimization Approaches and Modern OR-Applications, Tome 50 (2016) no. 4-5, pp. 891-907

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The present investigation deals with a multi-component machining system operating under N-policy. There is a provision of k type of mixed standbys units and maintenance crew consisting of permanent repairman as well as removable additional repairmen. The life time and repair time of the units are exponentially distributed with interdependent rates. The permanent repairman can start the repair only when N failed units are accumulated in the system. As soon as a unit fails, it is replaced by an available standby unit. In case when all the standby units are exhausted, the machining system starts to function in a degraded mode due to overload. Markov model is developed by constructing the governing transient state equations which are solved by using Runge−Kutta method. Various performance measures viz. queue size distribution, expected number of failed units, cost function, etc. are evaluated. By taking numerical illustration, numerical results are computed and also depicted with the help of graphs and figures.

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DOI : 10.1051/ro/2015032
Classification : 90B22, 90B25, 60K25, 60K30, 68M20
Keywords: Markovian machine repair model, N-policy, mixed standbys, additional repairmen, interdependent rates

Jain, Madhu 1 ; Shekhar, Chandra 2 ; Shukla, Shalini 3

1 Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667 Uttarakhand, India.
2 Department of Mathematics, Birla Institute of Technology and Science, Pilani, 333031 Rajasthan, India.
3 Department of Mathematics, D.A.V. (PG) College, Dehra Dun, 248001 Uttarakhand, India. 
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     author = {Jain, Madhu and Shekhar, Chandra and Shukla, Shalini},
     title = {N-policy for a repairable redundant machining system with controlled rates},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {891--907},
     publisher = {EDP-Sciences},
     volume = {50},
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     doi = {10.1051/ro/2015032},
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Jain, Madhu; Shekhar, Chandra; Shukla, Shalini. N-policy for a repairable redundant machining system with controlled rates. RAIRO - Operations Research - Recherche Opérationnelle, Special issue - Advanced Optimization Approaches and Modern OR-Applications, Tome 50 (2016) no. 4-5, pp. 891-907. doi: 10.1051/ro/2015032

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