Copula Approach for Reliability and Performance Estimation of Manufacturing System

Subject Areas : Reliability Engineering

Ibrahim Yusuf ¹ , Abdullahi Sanusi ²

1 - Department of Mathematical Sciences Bayero University, Kano
2 - Bayero University, Kano

Received: 2022-01-05 Accepted : 2023-01-03 Published : 2022-06-01

Keywords: reliability, profit, Availability, mean time to failure, manufacturing system,

Abstract :

This study focuses on an investigation into the analysis of reliability measures used to determine the strength of a serial manufacturing system comprising of three subsystems A, B, and C in the form of units, conveyors, and processors. Subsystem A has three parallel active units, whereas subsystems B and C each have two units. The system is analyzed using the linear differential difference equation, supplementary variable technique and Gumbel-Hougaard family of copula to obtain expressions of reliability measures for determining system strength such as availability, reliability, mean time to failure (MTTF), and profit function. Numerical examples are provided to illustrate the obtained results and analyze the effects of various system parameters. The current study may assist manufacturing, industries, reliability engineers, maintenance managers, system designers and their repairers in alleviating some of the challenges faced by repairers in certain manufacturing and industrial systems operating in harsh environments or under unfavorable weather conditions.

References:

[1] Abubakar, M.I. and Singh, V.V. (2019) ‘Performance assessment of an industrial system (African Textile Manufactures Ltd.) through copula linguistic approach’, Operation Research and Decisions, 29(4),1–18.

[2] Chang, P.C., Lin, Y.K and Chen, J.C. (2017). System reliability for a multi-state manufacturing network with joint buffer stations, J Manuf Syst; 42: 170–178

[3] Chen Z., He Y., Zhao Y., Han X., He Z., Xu Y and Zhang A. (2019) Mission reliability evaluation based on operational quality data for multistate manufacturing systems, International Journal of Production Research, 57:6, 1840-1856, DOI: 10.1080/00207543.2018.1508906

[4] Chen, Y and Jin, J. (2005). Quality-reliability chain modeling for system-reliability analysis of complex manufacturing processes. IEEE Trans. Reliab. ;54:475–488. doi: 10.1109/TR.2005.853441.

[5] 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 Vol. 4, No. 1, 116–130. DOI: 10.33889/IJMEMS.2019.4.1-011

[6] Duan, J., Xie, N and Li, L. (2019). Modelling and evaluation of multi-state reliability of repairable non-series manufacturing system with finite buffers, Advances in Mechanical Engineering, Vol. 11(6) 1–13.DOI: 10.1177/1687814019855483
[7] Farahani, A., Tohidi, H., (2020). Integrated optimization of quality and maintenance: A literature review, Computers & Industrial Engineering, doi: https://doi.org/10.1016/j.cie.2020.106924
[8] Farahani, A., Tohidi, H., and Shoja, A. (2019). An integrated optimization of quality control chart parameters and preventive maintenance using Markov chain. Advances in Production Engineering & Management. 14(1), 5-14, https://doi.org/10.14743/apem2019.1.307
[9] Gahlot, M., Singh, V.V., Ayagi, H.I. and Goel, C.K. (2018) ‘Performance assessment of repairable system in series configuration under different types of failure and repair policies using copula linguistics’, International Journal of Reliability and Safety, 12(4),348–374.
[10] Garg, S., Singh, J and Singh, D. V. (2010). Availability analysis of crank-case manufacturing in a two-wheeler automobile industry. Applied Mathematical Modelling, 34, 1672–1683
[11] Gulati, J., Singh, V.V., 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, Vol. 23, No. 2, pp.812–832.
[12] Han X., Wang Z., He Y., Zhao Y., Chen Z., Zhou D. A Mission Reliability-Driven Manufacturing System Health State Evaluation Method Based on Fusion of Operational Data. Sensors. 2019;19:442. doi: 10.3390/s19030442
[13] He,Y., He,Z., Wang, L and Gu, C.(2015). Reliability modeling and optimization strategy for manufacturing system based on RQR chain. Mathematical Problems in Engineering, 2015:1-13.
[14] He, Y., Han, X., Gu, C and Chen, Z. (2018). Cost-oriented predictive maintenance based on mission reliability state for cyber manufacturing systems. Adv Mech Eng; 10(1),1–15.
[15] He, Y., Gu, C., Han, X., Cui, J and Chen, Z. (2017). Mission reliability modeling for multi-station manufacturing system based on Quality State Task Network. Proc. Inst. Mech. Eng. Part O J. Risk Reliab. ;231:701–715. doi: 10.1177/1748006X17728599
[16] Kumar, K and Kumar, P. (2010). Mathematical Modeling and Analysis of Stainless-Steel Utensil Manufacturing Unit Using Fuzzy Reliability, International Journal of Engineering Science and Technology, Vol. 2(6), 2370-2376.
[17] Lado, A and Singh, V.V. (2019), Cost assessment of complex repairable system consisting of two subsystems in the series configuration using Gumbel–Hougaard family copula, International Journal of Quality and Reliability Management, 36(10), 1683–1698.
[18] Lin, L and Jun, N. (2008). Reliability estimation based on operational data of manufacturing systems. Quality and Reliability Engineering International, 24:843-854.
[19] Li, G.D., Masuda,S., Yamaguchi, D and Nagai, M. (2010). A New Reliability Prediction Model in Manufacturing Systems. IEEE Transactions on Reliability, 59:170-177.
[20] Li, L and Ni, J. (2008). Reliability estimation based on operational data of manufacturing systems. Quality and Reliability Engineering International, 24, 843–854
[21] Lu., B and Zhou., X. ( 2019). Quality and reliability oriented maintenance for multistage manufacturing systems subject to condition monitoring. J. Manuf. Syst.;52:76–85. doi: 10.1016/j.jmsy.2019.04.003
[22] Maihulla, A. S., Yusuf, I., and Bala, S. I. (2021). Reliability and Performance Analysis of a Series-Parallel System using Gumbel–Hougaard Family Copula. Journal of Computational and Cognitive Engineering, 01–10, doi: https://doi.org/10.47852/bonviewJCCE2022010101
[23] Nelson, R.B. (2006) An Introduction to Copulas, 2nd ed., Springer Publisher, New York.
Abubakar and Singh (2019)
[24] Patton, A.J. (2009). Copula–based models for financial time series. In Handbook of Financial Time Series (pp. 767-785). Springer, Berlin, Heidelberg.
[25] 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.
[26] Ram, M and Singh, S. B. (2010). Availability, MTTF and cost analysis of complex system under preemptive-repeat repair discipline using Gumbel-Hougaard family copula. International Journal of Quality & Reliability Management, 27(5), 576-595.
[27] Rodriguez, J.C. (2007). Measuring financial contagion: a copula approach. Journal of Empirical Finance, 14(3), 401-423.
[28] Sha, N. (2021). A Copula Approach of Reliability Analysis for Hybrid Systems. Reliability: Theory & Applications, 16(1), 231-242.
[29] Savsar, M. (2000). Reliability analysis of a flexible manufacturing cell. Reliability Engineering & System Safety, 67(2), 147-152.

[30] Singh, V.V and Ayagi, H.I. (2018). Stochastic analysis of a complex system under preemptive resume repair policy using Gumbel-Hougaard family copula, International Journal of Mathematics in Operational Research, 12(2), 273-291
[31] Singh, V.V., Gahlot, M., Ayagi, H.I and Goel, C.K. (2018). Performance assessment of repairable system in series configuration under different types of failure and repair policies using copula linguistics, International Journal of Reliability and Safety, 12(4), 348-374.
[32] Singh, V. V and Ayagi, H. I. (2017). Study of reliability measures of system consisting of two subsystems in series configuration using copula. Palestinian Journal of Mathematics, 6(1), 1-10.
[33] 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
[34] Sklar, A. (1973). Random variables, joint distribution functions, and copulas. Kybernetika, 9(6), 449-460.
[35] Sun J., Xi L., Du S., Ju B. (2008). Reliability modeling and analysis of serial-parallel hybrid multi-operational manufacturing system considering dimensional quality, tool degradation and system configuration. Int. J. Prod. Econ. 114:149–164. doi: 10.1016/j.ijpe.2008.01.002
[36] Trivedi, P.K., & Zimmer, D.M. (2007). Copula modeling: an introduction for practitioners. Now Publishers Inc, U.S.A.
[37] Tyagi, V., Arora, R and Ram, M. (2021). Copula based measures of repairable parallel system with fault coverage, International Journal of Mathematical, Engineering and Management Sciences Vol. 6, No. 1, 322-344
[38] Xu, X., Jianlin, L., Gong, J., Deng, H and Wan, L. (2016). Copula-based slope reliability analysis using the failure domain defined by the 𝑔-Line, Mathematical Problems in Engineering Volume 2016, Article ID 6141838. http://dx.doi.org/10.1155/2016/6141838.
[39] Ye, Z., Cai, Z., Si, S., Zhang, S and Yang,H.(2020). Competing Failure Modeling for Performance Analysis of Automated Manufacturing Systems With Serial Structures and Imperfect Quality Inspection, IEEE Transactions on Industrial Informatics, vol. 16, no. 10, pp. 6476-6486, Oct. 2020, doi: 10.1109/TII.2020.2967030.
[40] Ye, Z., Cai, Z., Zhou, F., Zhao, J and Zhang, P. (2019). Reliability analysis for series manufacturing system with imperfect inspection considering the interaction between quality and degradation. Reliab. Eng. Syst. Saf. 189:345–356. doi: 10.1016/j.ress.2019.05.005
[41] Ye, Z., Cai, Z and Yang, H. (2020). "Reliability Analysis of Manufacturing Machine with Degradation and Low-quality Feedstocks," 2020 Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling (APARM), 2020, pp. 1-5, doi: 10.1109/APARM49247.2020.9209452.
[42] Youssef, A.M.A., Mohib, A and Eimaraghy.H.A. (2006). Availability assessment of multi-state manufacturing systems using universal generating function, CIRP annals, 55(1): 445–448.
[43] Youssef, A.M.A., Mohib, A and Eimaraghy.H.A. (2008). Performance analysis of manufacturing systems composed of modular machines using the universal generating function, J Manuf Syst, 27(2), 55–69.
[44] Zhou, X and Lu, B. (2018). Preventive maintenance scheduling for serial multi-station manufacturing systems with interaction between station reliability and product quality. Comput. Ind. Eng. 122:283–291. doi: 10.1016/j.cie.2018.06.009
[45] Zhang, H, Li., A.P and Liu., X.M. (2017). Modeling and performance evaluation of a multistage serial manufacturing system considering rework and product polymorphism. Chin J Mech Eng; 53: 191–201.