In this study, we analyze Markov model for the performance prediction of failure prone machining device that operates under the fault tolerance measures and admission control policy. The threshold-based admission policy is proposed to examine the functioning of designed fault tolerance system. The stationary queue size distribution of failed machines has been established using a recursive approach. The key output metrics and cost function have been designed to analyze the functional efficiency and cost benefit of the system. The numerical implementation of the performance indices and cost analysis have been done to examine the sensitiveness of the system descriptors. Furthermore, harmony search approach has been used to optimize the total cost associated with different activities.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
Sivazlian BD, Wang KH (1989) Economic analysis of the M/M/R machine repair problem with warm standbys. Microelectron Reliab 29:25–35
Wang KH, Sivazlian BD (1992) Cost analysis of the M/M/R machine repair problem with spars operating under variable service rates. Microelectron Reliab 32:1171–1183
Jain M (2005) Finite capacity M / M / r queueing system with queue-dependent servers. Comput Math with Appl 50:187–199
Jain M, Meena RK (2017) Fault tolerant system with imperfect coverage, reboot and server vacation. J Ind Eng Int 13:171–180
Wang KH, Chiu LW (2006) Cost benefit analysis of availability systems with warm standby units and imperfect coverage. Appl Math Comput 172:1239–1256
Bin KJ, Lee WC, Wang KH (2007) Reliability and sensitivity analysis of a system with multiple unreliable service stations and standby switching failures. Phys A Stat Mech Appl 380:455–469
Hsu YL, Lee SL, Ke JC (2009) A repairable system with imperfect coverage and reboot: Bayesian and asymptotic estimation. Math Comput Simul 79:2227–2239
Wang KH, Su JH, Yang DY (2014) Analysis and optimization of an M/G/1 machine repair problem with multiple imperfect coverage. Appl Math Comput 242:590–600
Ke JC, Liu TH (2014) A repairable system with imperfect coverage and reboot. Appl Math Comput 246:148–158
Jain M (2016) Reliability prediction of repairable redundant system with imperfect switching and repair. Arab J Sci Eng 41:3717–3725
Kuo CC, Ke JC (2017) Modeling and comparison of the series systems with imperfect coverage for an unreliable server. Soft Comput 23:2073–2082
Jain M, Kumar P, Sanga SS (2020) Fuzzy Markovian modeling of machining system with imperfect coverage, spare provisioning and reboot. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-020-02523-9
Gupta SM (1995) Interrelationship between controlling arrival and service in queueing systems. Comput Oper Res 22:1005–1014
Wang KH, Kuo CC, Pearn WL (2008) A recursive method for the F-policy G/M/1/K queueing system with an exponential startup time. Appl Math Model 32:958–970
Tadj L, Choudhury G (2005) Optimal design and control of queues. Top 13:359–412
Yang DY, Wang KH, Wu CH (2010) Optimization and sensitivity analysis of controlling arrivals in the queueing system with single working vacation. J Comput Appl Math 234:545–556
Huang HI, Hsu PC, Ke JC (2011) Controlling arrival and service of a two-removable-server system using genetic algorithm. Expert Syst Appl 38:10054–10059
Shekhar C, Jain M, Raina AA, Iqbal J (2017) Optimal (N, F) policy for queue-dependent and time-sharing machining redundant system. Int J Qual Reliab Manag 34:798–816
Wang KH, Yang DY (2009) Controlling arrivals for a queueing system with an unreliable server: Newton-Quasi method. Appl Math Comput 213:92–101
Jain M, Meena RK (2017) Markovian analysis of unreliable multi-components redundant fault tolerant system with working vacation and F-policy. Cogent Math Stat 4:1306961
Jain M, Sanga SS (2020) State dependent queueing models under admission control F-policy: A survey. J Ambient Intell Humaniz Comput 1–19. https://doi.org/10.1007/s12652-019-01638-
Sethi R, Jain M, Meena RK, Garg D (2020) Cost optimization and ANFIS computing of an unreliable M/M/ 1 queueing system with customers ’ impatience under N-policy. Int J Appl Comput Math 6:1–14
Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76:60–68
Geem ZW, Lee KS, Park Y (2005) Application of harmony search to vehicle routing. Am J Appl Sci 2:1552–1557
Meena RK, Jain M, Sanga SS, Assad A (2019) Fuzzy modeling and harmony search optimization for machining system with general repair, standby support and vacation. Appl Math Comput 361:858–873
Jain M, Kumar P, Meena RK (2020) Fuzzy metrics and cost optimization of a fault-tolerant system with vacationing and unreliable server. J Ambient Intell Humaniz Comput 1–16.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Sethi, R., Jain, M., Meena, R.K. et al. Markov Model for Fault Tolerant Machining System Operating under Admission Control Policy. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. (2021). https://doi.org/10.1007/s40010-021-00734-z
- Markov model
- Recursive approach
- Harmony search (HS)