Reliability Analysis of Distributed System for Enhancing Data Replication using Gumbel-Hougaard Family Copula Approach Joint Probability Distribution

Journal of Industrial Engineering International

دوره 17، شماره 3، آبان 2021، صفحه 59-78   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/jiei.2021.1944531.1177

نویسندگان

Ibrahim Yusuf^{* 1}؛ Abdulkareem Lado Ismail²؛ Nasir Ahmad Sufi³؛ Faruku Umar Ambursa⁴؛ Abdullahi Sanusi⁵؛ Muhammad Salihu Isa⁶

¹Department of Mathematical Sciences, Bayero University, Kano

²Department of Mathematics, Kano State College of Education and Preliminary Studies

³Department of Computer Science, Federal University Dutse, Nigeria

⁴Bayero Univrsity, Kano

⁵Bayero University, Kano

⁶Department of Mathematics, Federal University Dutse Nigeria

چکیده

In today’s world of technology, it is impossible to see where computer system does not play an important role. The application of distributed systems is gradually becoming broad and diverse, and as a result of this, reliability prediction is a key concern. This paper, considered a distributed system with five standby subsystems A (the clients), B (two load balancers), C (two distributed database servers), D (two mirrored distributed database serves) and E (centralized database server) is considered arranged as series-parallel system. Exponential failure and repair are susceptible for all the components of this system. Each component’s failure rates are constant and considered to obey an exponential distribution, and they are repaired using general repair or copula repair. The system is evaluated using first-order partial differential equations and the supplementary variable technique, Gumbel-Hougaard family of Copula, to find expressions for reliability metrics of system strength such as availability, reliability, MTTF, sensitivity, and profit function. These reliability metrics have been validated for different parametric values and the results are presented in tables and figures.

کلیدواژه‌ها

Availability؛ Analysis؛ Distributed system؛ Reliability؛ Replication

مراجع

- Abubakar MI, Singh VV, (2019). Performance assessment of African textile manufacturers, LTD, in
Kano state, Nigeria, through Multi failure and repair using copula. Operation Research Decision. 29(4):1–18.      

- Attar, A., Raissi, S and Khalili-Damghani, K. (2016). A simulation-based optimization approach for free distributed repairable multi-state availabilityredundancy allocation problems, Reliability
Engineering & System Safety 157, 177-191, https://doi.org/10.1016/j.ress.2016.09.006

- Chen, L.; Wang, J.; Xu, X. (2019). An energy client single machine scheduling problem with machine reliability constraints. Comput. Ind. Eng., 137. 

-  Chopra, G and Ram, M. (2019). Reliability Measures of Two Dissimilar Units Parallel System Using Gumbel-Hougaard Family Copula, International Journal of Mathematical, Engineering and
Management Sciences 4(1), 116–130. DOI: 10.33889/IJMEMS.2019.4.1-011

- Goyal, D., Kumar, A., Saini, M., and Joshi. H. (2019). “Reliability, maintainability and sensitivity analysis of physical processing unit of sewage treatment plant.” SN Appl. Sci. 1:1507, https://doi.org/10.1007/ s42452-019-1544-7.

- Gahlot, Monika, V. V. Singh H. Ismail Ayagi and C.K. Goel, “Performance assessment of repairable system in the series configuration under different types of failure and repair policies using Copula Linguistics," International Journal of Reliability and Safety, 2018, Vol.12 (4), pp.367-374.

- Harish Garg (2017). Performance analysis of an industrial system using soft computing based
hybridized technique. Journal of Brazilian Society of Mechanical Sciences and Engineering, Springer, 39(4),1441-1451.
- Ibrahim, K.H., Singh, V.V. and Lado, A. (2017), “Reliability assessment of complex system consisting two subsystems connected in series configuration using Gumbel-Hougaard family copula distribution”, Journal of Applied Mathematics and Bioinformatics, Vol. 7 No. 2, pp. 1-27.
- Mehta M., Singh J., and Sharma S. (2018) “Availability Analysis of an Industrial System using
Supplementary Variable Technique,” Jordan journal of mechanical and industrial engineering, vol. 12, no. 4, pp. 245-251, ISSN 1995-6665.
- Nelson, R.B. (2006) An Introduction to Copulas, 2nd ed., Springer Publisher, New York.
- Niwas, R., and Garg, H. (2018), An approach for analyzing the reliability and profit of an industrial system based on the cost-free warranty policy, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40: 265.
- Patton, A.J. (2009). Copula–based models for financial time series. In Handbook of Financial Time Series (pp. 767-785). Springer, Berlin, Heidelberg.
- Pourhassan., M.R., Raissi, S and A Hafezalkotob, A. (2019). Effects of faulty estimate in component reliability on system designing: a simulation approach, Journal of Industrial and Systems Engineering 12 (2), 174-185
- Pourhassan,M.R., Raissi, S and fezalkotob, H. A. (2020) A simulation approach on reliability assessment of complex system subject to stochastic degradation and random shock., Eksploatacja i Niezawodnosc – Maintenance and Reliability, 22 (2): 370–379, http://dx.doi. org/10.17531/ ein.2020.2.20.
- Pourhassan,M.R., Raissi, S and Apornak, A. (2021). Modeling multi-state system reliability analysis in a power station under fatal and nonfatal shocks: a simulation approach, International Journal of Quality and Reliability Management, DOI 10.1108/IJQRM07-2020-0244
- Potapov, V. I., Shafeeva, O. P., Gritsay, A. S., Makarov, V. V., Kuznetsova, O. P., Kondratukova, L.
K. (2019, August). Reliability in the model of an information system with client-server architecture.
Int. Journal of Physics: Conference Series (Vol. 1260, No. 2, p. 022007). IOP Publishing.
- Rahman, P.A. (2018), Analysis of stationary availability factor of two-level backbone computer
networks with arbitrary topology, Journal of Physics: Conf. Series 1015 (2018) 022016. DOI:10.1088/1742- 6596/1015/2/022016.
- Raissi, S and Ebadi, S. (2018). A computer simulation model for reliability estimation of a complex system, Int. J. Res. Ind. Eng., 7(1) 19–31.
- Rajesh, Gulshan T. and Jagdish P. (2018), Reliability and Availability Analysis for a Three Unit Gas Turbine Power Generating System with Seasonal Effect and FcFs Repair Pattern, International Journal of Applied Engineering Research, ISSN 0973-4562 13 (12): 10948-10964
- Ram, M and Singh, S. B. (2008). Availability and cost analysis of a parallel redundant complex system with two types of failure under preemptive-resume repair discipline using Gumbel-Hougaard family copula in repair. International Journal of Reliability, Quality and Safety Engineering, 15(04), 341-365.
- Ram, M and Singh, S. B. (2010). Availability, MTTF and cost analysis of complex system under
preemptive-repeat repair discipline using GumbelHougaard family copula. International Journal of Quality & Reliability Management, 27(5), 576-595.
- Rodriguez, J.C. (2007). Measuring financial contagion: a copula approach. Journal of Empirical
Finance, 14(3), 401-423.
- Sanusi, A and Yusuf, I. (201). Reliability, Availability, Maintainability, and Dependability (RAMD) Analysis of Computer Based Test (CBT) Network System. RT&A, 16(3), 99-114. https//doi.org/10.24412/1932- 2321-2021-363-99-114.
- Sklar, A. (1973). Random variables, joint distribution functions, and copulas. Kybernetika, 9(6), 449-460.
- Singh, V and Lado, A. (2019). Cost assessment of complex repairable system consisting two subsystems in series configuration using Gumbel Hougaard family copula, International Journal of Quality & Reliability Management, 36(10),1683- 1698. https://doi.org/10.1108/IJQRM-12-2018-0322
- Singh, V.V., Gulati, J., Rawal, D.K and Goel, C.K. (2016). Performance analysis of complex system in series configuration under different failure and repair discipline using copula, International Journal of Reliability Quality and Safety Engineering, 23 (2). https://doi.org/10.1142/S0218539316500108
- Singh, V.V., Lado Ismail, A.K., Yusuf, I. and Abdullahi, A.H. (2021). Probabilistic Assessment of ComputerBased Test (CBT) Network System Consists of Four Subsystems in Series Configuration Using Copula Linguistic Approach. Journal of Reliability and Statistical Studies.
- Singh, V.V. and Hamisu, H.I. (2018). “Stochastic analysis of a complex system under preemptive
resume repair policy using Gumbel–Hougaard family copula”, International Journal of Mathematics and Operation Research, Vol. 12 No. 2, pp. 273-291.
- Singh, V. V, Poonia, P. K, Rawal, D. K, (2020), Reliability analysis of repairable network system of
three computer labs connected with a server under 2- out-of- 3: G configuration, Life Cycle Reliability, and Safety Engineering. (DOI: 10.1007/s41872-020- 00129-w)
- Steen, V and Tanenbaum, M. (2016). A brief introduction to distributed system systems, Computing, 98, 967-1009. Doi.org/10.1007/s00607-016-0508-7
- Tsarouhas P, Arvanitoyannis I, Varzakas T (2009) Reliability and maintainability analysis of cheese
(feta) production line in a Greek medium-size company: a case study. J Food Eng 94(34):233–240.
- Trivedi, P.K., & Zimmer, D.M. (2007). Copula modeling: an introduction for practitioners. Now
Publishers Inc, U.S.A.
- Yang L, Guo Y, Wang Q (2019) Reliability assessment of a hierarchical system subjected to inconsistent priors and multilevel data. IEEE Trans Reliab 68(4):277–292
- Yusuf, I., Ismail, A. L., Singh, V. V., Ali, U. A., Sufi, N. A. (2020). Performance Analysis of Multi- Computer System Consisting of Three Subsystems in Series Configuration Using Copula Repair Policy. SN Computer Science, 1(5), 1-11.
- Yusuf, I., Yusuf, B., Babagana, M., Sani, B., Lawan, M. A. (2018). Some reliability characteristics of a linear consecutive 2-out-of-4 system connected to 2-outof-4 supporting device for operation. International Journal of Engineering &Technology, 7(1), 135-139.
- Zhang, F. (2019). Research on reliability analysis of computer network based on intelligent cloud
computing method. International Journal of Computers and Applications, 41:4, 283-288.