Article: Threshold N-policy for (M, m) degraded machining system with K-heterogeneous servers, standby switching failure and multiple vacations Journal: International Journal of Mathematics in Operational Research (IJMOR) 2013 Vol.5 No.4 pp.423 - 445 Abstract: This paper is concerned with multi-component machining system having online or operating units along with K-type of standby units under the facility of K-heterogeneous servers. The servers switch on one by one when the number of failed units in the system reaches to a predefined threshold policy (Ni for ith server: i = 1, 2, ..., K). Once server returns from a vacation, he can leave the system and go for another vacation only if no failed unit available in the system for repair. Whenever any unit fails, it is immediately replaced by an available standby unit. In case when all standbys are used, the system works in degraded mode. The standby units have switching failure probability q. The governing equations are constructed by using appropriate birth-death rates. A cost function has also been constructed to calculate the optimal number of standby units for providing the desired efficiency to the system. The SOR method is employed to find the steady state probabilities, mean number of failed units in the system, reliability and throughput. Numerical results obtained by successive over relaxation (SOR) method are matched by the results evaluated using soft computing approach based on adaptive neuro-fuzzy inference system (ANFIS). Inderscience Publishers - linking academia, business and industry through research

Title: Threshold N-policy for (M, m) degraded machining system with K-heterogeneous servers, standby switching failure and multiple vacations

Authors: Kamlesh Kumar; Madhu Jain

Addresses: Department of Mathematics, IIT Roorkee-247667, India ' Department of Mathematics, IIT Roorkee-247667, India

Abstract: This paper is concerned with multi-component machining system having online or operating units along with K-type of standby units under the facility of K-heterogeneous servers. The servers switch on one by one when the number of failed units in the system reaches to a predefined threshold policy (N_i for i^th server: i = 1, 2, ..., K). Once server returns from a vacation, he can leave the system and go for another vacation only if no failed unit available in the system for repair. Whenever any unit fails, it is immediately replaced by an available standby unit. In case when all standbys are used, the system works in degraded mode. The standby units have switching failure probability q. The governing equations are constructed by using appropriate birth-death rates. A cost function has also been constructed to calculate the optimal number of standby units for providing the desired efficiency to the system. The SOR method is employed to find the steady state probabilities, mean number of failed units in the system, reliability and throughput. Numerical results obtained by successive over relaxation (SOR) method are matched by the results evaluated using soft computing approach based on adaptive neuro-fuzzy inference system (ANFIS).

Keywords: redundant systems; degraded failure rate; heterogeneous servers; standby switching failures; threshold N-policy; SOR method; multiple vacations; neuro fuzzy; degraded machining systems; soft computing; adaptive neuro-fuzzy inference system; ANFIS; neural networks; fuzzy logic.

DOI: 10.1504/IJMOR.2013.054719

International Journal of Mathematics in Operational Research, 2013 Vol.5 No.4, pp.423 - 445

Received: 03 Apr 2012
Accepted: 07 Jun 2012
Published online: 31 Mar 2014 *

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Title: Threshold N-policy for (M, m) degraded machining system with K-heterogeneous servers, standby switching failure and multiple vacations

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