Reliability Analysis and ANFIS Computation for Multi-server Redundant Machining System with the Generalized Triadic Policy

Authors

  • Chahal Parmeet Kaur Central University of Jammu, Bagla, Samba, Jammu & Kashmir, India
  • Kamlesh Kumar Central University of Jammu, Bagla, Samba, Jammu & Kashmir, India
  • Bhavneet Singh Soodan Chandigarh University, Kharar, Mohali, Punjab, India

DOI:

https://doi.org/10.2298/YJOR230915030C

Keywords:

Redundant machine repair system, multiple working vacation, Runge-Kutta’s method, generalized triadic policy, pearson correlation coefficient and ANFIS

Abstract

The intent of this research is to have discussions about the transient behavior of a multi-server redundant machining system with a generalized Triadic control policy. Furthermore, the system facilitates a multiple working vacation policy for servers. The relevant rates of the associated birth-death process are chosen in order to frame the differential-difference equations for the system. Using the fourth order Runge-Kutta technique, time-dependent probabilities of the states are derived. Some performance metrics of system such as the average number of failed machines, average waiting time of failed machines, and reliability function are established using the states probabilities. Graphical and tabular representations demonstrate the behavior of these metrics with respect to a variety of system characteristics. Statistical hypothesis testing has been employed to compare the outcomes presented in tabular format. Beside these, numerical findings of the Runge-Kutta method are compared to those delivered by an adaptive neuro-fuzzy inference system (ANFIS) technique.

References

Y. Yadin and P. Naor, “Queueing systems with a removable service station,” Journal of the Operational Research Society, vol. 14, no. 4, pp. 393-405, 1963. doi: 10.2307/3006802

P. K. Chahal and K. Kumar, “Queueing models of machine repair problems with control policies: a survey and analysis,” International Journal of Operational Research, vol. In press, 2023. doi: 10.1504/IJOR.2023.10060548

C. E. Bell, “Optimal operation of an M/M/2 queue with removable servers,” Operations Research, vol. 28, no. 5, pp. 1189-1204, 1980. doi: 10.1287/opre.28.5.1189

H. K. Rhee and B. D. Sivazlian, “Distribution of the busy period in a controllable M / M / 2 queue operating under the triadic ( 0 , K , N , M ) policy,” Journal of Applied Probability, vol. 27, no. 2, pp. 425-432, 2015. doi: 10.2307/3214662

K. H.Wang and C. L. Chang, “Reliability of a controllable M/M/2 system with warm standbys operating under the triadic (0, Q, N, M) policy,” Computers and Industrial Engineering, vol. 28, no. 1, pp. 163-178, 1995. doi: 10.1016/0360-8352(94)00035-L

H. I. Huang, P. C. Hsu, and J. C. Ke, “Controlling arrival and service of a two-removableserver system using genetic algorithm,” Expert Systems with Applications, vol. 38, no. 8, pp. 10 054-10 059, 2011. doi: 10.1016/j.eswa.2011.02.011

C. D. Liou, K. H. Wang, and M. W. Liou, “Genetic algorithm to the machine repair problem with two removable servers operating under the triadic (0, Q, N, M) policy,” Applied Mathematical Modelling, vol. 37, no. 18, pp. 8419-8430, 2013. doi: 10.1016/j.apm.2013.03.036

V. Goswami and P. V. Laxmi, “Analysis of discrete-time machine repair problem with two removable servers under triadic policy,” International Journal of Mathematical Modelling & Computations, vol. 5, no. 1, pp. 29-40, 2015. doi: 10.1504/IJOR.2023.10060548

T. Ketema, S. Demie, and M. T. Belachew, “Controllable M/M/2 machine repair problem with multiple working vacations and triadic (0,Q,N,M) policy,” International Journal of Management Science and Engineering Management, vol. 16, no. 3, pp. 184-196, 2021. doi: 10.1080/17509653.2021.1935358

J. Taylor and R. R. P. Jackson, “An application of the birth and death process to the provision of spare machines,” Journal of the Operational Research Society, vol. 5, no. 4, pp. 95-108, 1954. doi: 10.2307/3007087

D. Gross, H. D. Kahn, and J. D. Marsh, “Queueing models for spares provisioning,” Naval Research Logistics, vol. 24, no. 4, pp. 521-536, 1977. doi: 10.1002/nav.3800240402

K. H. Wang, “Cost analysis of the M/M/R machine-repair problem with mixed standby spares,” Microelectronics Reliability, vol. 33, no. 9, pp. 1293-1301, 1993. doi: 10.1016/0026- 2714(93)90131-H

S. Kolledath, K. Kumar, and P. Pippal, “Survey on queueing models with standbys support,” Yugoslav Journal of Operations Research, vol. 28, no. 1, pp. 3-20, 2018. doi: 10.2298/YJOR170621024K

G. Gao and J. Wang, “Reliability and availability analysis of a retrial system with mixed standbys and an unreliable repair facility,” Reliability Engineering and System Safety, vol. 205, p. 107240, 2021. doi: 10.1016/j.ress.2020.107240

K. Kumar, M. Jain, and S. Chandra, “Machine repair system with threshold recovery policy , unreliable servers and phase repairs,” Quality Technology & Quantitative Management, pp. 1-24, 2023. doi: 10.1080/16843703.2023.2232639

Y. Levy and U. Yechiali, “Utilization of idle time in an M / G / 1 queueing system,” Management Science, vol. 22, no. 2, pp. 202-211, 1975. doi: 10.1287/mnsc.22.2.202

V. M. Chandrasekaran, K. Indhira, M. C. Saravanarajan, and P. Rajadurai, “Queueing models of machine repair problems with control policies: a survey and analysis,” International Journal of Pure and Applied Mathematics, vol. 106, no. 6, pp. 33-41, 2016. doi: 10.12732/ijpam.v106i6.5

D. Y. Yang and C. L. Tsao, “Reliability and availability analysis of standby systems with working vacations and retrial of failed components,” International Journal of Operational Research, vol. 182, pp. 46-55, 2019. doi: 10.1016/j.ress.2018.09.020

A. A. Bouchentouf and L. Yahiaoui, “On feedback queueing system with reneging and retention of reneged customers, multiple working vacations and bernoulli schedule vacation interruption,” Operations Research, vol. 6, no. 1, pp. 1-11, 2017. doi: 10.1007/s40065-016- 0161-1

M. Jain, D. Dhibar, and S. S. Sanga, “Markovian working vacation queue with imperfect service, balking and retrial,” Journal of Ambient Intelligence and Humanized Computing, vol. 13, no. 4, pp. 1907-1923, 2022. doi: 10.1007/s12652-021-02954-y

S. Gupta, P. K. Joshi, and K. N. Rajeshwari, “Optimization of M/M/2 queueing model with working vacations,” Journal of Scientific Research, vol. 15, no. 1, pp. 31-41, 2023. doi: 10.3329/jsr.v15i1.59348

I. Ziad, P. V. Laxmi, A. A. Bouchentouf, and M. Shakir, “A matrix geometric solution of a multi-server queue with waiting servers and customers’ impatience under variant working vacation and vacation interruption,” Yugoslav Journal of Operations Research, vol. 33, no. 3, pp. 389-407, 2023. doi: 10.2298/YJOR220315001Z

Z. C. Lin and C. Y. Liu, “Analysis and application of the adaptive neuro-fuzzy inference system in prediction of CMP machining parameters,” International Journal of Computer Applications in Technology, vol. 17, no. 2, pp. 80-89, 2003. doi: 10.1504/IJCAT.2003.000335

K. Kumar and M. Jain, “Threshold n-policy for (M, m) degraded machining system with K-heterogeneous servers, standby switching failure and multiple vacations,” International Journal of Mathematics in Operational Research, vol. 5, no. 4, pp. 423-445, 2013. doi: 10.1504/IJMOR.2013.054719

M. Jain and R. K. Meena, “Vacation model for markov machine repair problem with two heterogeneous unreliable servers and threshold recovery,” Journal of Industrial Engineering International, vol. 14, no. 1, pp. 143-152, 2018. doi: 10.1007/s40092-017-0214-x

R. Sethi, M. Jain, R. K. Meena, and D. Garg, “Cost optimization and ANFIS computing of an unreliable M/M/1 queueing system with customers’ impatience under N-policy,” International Journal of Applied and Computational Mathematics, vol. 6, no. 2, pp. 1-14, 2020. doi: 10.1007/s40819-020-0802-0

A. Ahuja, A. Jain, and M. Jain, “Transient analysis and ANFIS computing of unreliable single server queueing model with multiple stage service and functioning vacation,” Mathematics and Computers in Simulation, vol. 192, pp. 464-490, 2022. doi: 10.1016/j.matcom.2021.09.011

K. H. Wang and Y. L. Wang, “Optimal control of an M/M/2 queueing system with finite capacity operating under the triadic (0, Q, N, M) policy,” Mathematical Methods of Operations Research, vol. 55, no. 3, pp. 447-460, 2002. doi: 10.1007/s001860200190

K. Kumar and M. Jain, “Bi-level control of degraded machining system with two unreliable servers, multiple standbys, startup and vacation,” International Journal of Operational Research, vol. 21, no. 2, pp. 123-142, 2014. doi: 10.1504/IJOR.2014.064540

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Published

2023-12-02

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Vol. 34 No. 2 (2024)

Section

Research Articles

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