Predecessor-set technique for reliability evaluation of a stochastic manufacturing system

Abstract

This paper studies the reliability evaluation of a stochastic manufacturing system with multiple production lines in parallel. Multiple repairs and different failure rates, never simultaneously addressed in earlier works, are taken into account. First, a revised graphical methodology integrating transformation and decomposition is utilized to construct the stochastic manufacturing system as a multi-state manufacturing network (MSMN). In particular, a “predecessor-set” technique is proposed to deal with multiple repairs. An algorithm is proposed to generate the lowest capacity vectors (LCVs) that stations should provide to satisfy the workloads. Subsequently, the system reliability of the MSMN, which is defined as the probability of demand satisfaction, is calculated in terms of the LCVs. A real case of a printed circuit board manufacturing system is utilized to demonstrate how the system reliability can be evaluated. A further decision making issue is addressed based on the derived system reliability.

Keywords

Multi-state manufacturing network (MSMN) / predecessor-set / lowest capacity vector (LCV) / different failure rates / multiple repairs / system reliability

References

[1] Alexopoulos C. A note on state-space decomposition methods for analyzing stochastic flow networks. IEEE Transactions on Reliability, 1995, 44: 354-357.

[2] Aven T. Reliability evaluation of multistate systems with multistate components. IEEE Transactions on Reliability, 1985, 34: 473-479.

[3] Buscher U, Lindner G. Optimizing a production system with rework and equal sized batch shipments. Computers and Operations Research, 2007, 34: 515-535.

[4] Chen TH, Bao CP. Applying cost-reliability analysis to improve system reliability. Journal of Industrial and Production Engineering, 2013, 30: 467-472.

[5] Chen MS, Lan CH. The maximal profit flow model in designing multiple-production-line system with obtainable resource capacity. International Journal of Production Economics, 2001, 70: 175-184.

[6] Chen SG, Lin YK. Search for all minimal paths in a general large flow network. IEEE Transactions on Reliability, 2012, 61: 949-956.

[7] Ford LR, Fulkerson DR. Flows in Networks, 1962, NJ: Princeton University Press.

[8] Hudson JC, Kapur KC. Reliability bounds for multistate systems with multistate components. Operations Research., 1985, 33: 153-160.

[9] Kazemia MR, Hassanzadeha R, Mahdavia I, Pargar F. Applying fuzzy stochastic programming for multi-product multi-time period production planning. Journal of Industrial and Production Engineering, 2013, 30: 132-147.

[10] Lan CH. The design of multiple production lines under deadline constraint. International Journal of Production Economics, 2007, 106: 191-203.

[11] Lin YK. Two-commodity reliability evaluation of a stochastic-flow network with varying capacity weight in terms of minimal paths. Computers and Operations Research, 2009, 36: 1050-1063.

[12] Lin YK, Chang PC. Evaluate the system reliability for a manufacturing network with reworking actions. Reliability Engineering and System Safety, 2012, 106: 127-137.

[13] Lin YK, Chang PC. System reliability of a manufacturing network with reworking action and different failure rates. International Journal of Production Research, 2012, 50: 6930-6944.

[14] Lin YK, Chang PC. Graphical-based reliability evaluation of multiple distinct production lines. Journal of Systems Science and Systems Engineering, 2013, 22: 73-92.

[15] Lin YK, Chang PC. A novel reliability evaluation technique for stochastic flow manufacturing networks with multiple production lines. IEEE Transactions on Reliability, 2013, 61: 92-104.

[16] Lin YK, Chang PC, Chen JC. Reliability evaluation for a waste-reduction parallel-line manufacturing system. Journal of Cleaner Production, 2012, 35: 93-101.

[17] Listeş O. A generic stochastic model for supply-and-return network design. Computers and Operations Research, 2007, 34: 417-442.

[18] Liu N, Kim Y, Hwang H. An optimal operating policy for the production system with rework. Computers and Industrial Engineering, 2009, 56: 874-887.

[19] Paquet M, Martel A, Montreuil B. A manufacturing network design model based on processor and worker capabilities. International Journal of Production Research, 2008, 46: 2009-2030.

[20] Pillai VM, Chandrasekharan MP. An absorbing Markov chain model for production systems with rework and scrapping. Computers and Industrial Engineering, 2008, 55: 695-706.

[21] Stevenson WJ. Operation Management: International Student Edition with Global Readings, 2007

[22] Teunter R, Kaparis K, Tang O. Multi-product economic lot scheduling problem with separate production lines for manufacturing and remanufacturing. European Journal of Operational Research, 2008, 191: 1241-1253.

[23] Xue J. On multistate system analysis. IEEE Transactions Reliability, 1985, 34: 329-337.

[24] Yang WS, Lim DE, Chae KC. Maintenance of multi-state production systems deteriorated by random shocks and production. Journal of Systems Science and Systems Engineering, 2011, 20: 110-118.

[25] Yarlagadda R, Hershey J. Fast algorithm for computing the reliability of communication network. International Journal of Electronics, 1991, 70: 549-564.

[26] Zuo MJ, Tian Z, Huang HZ. An efficient method for reliability evaluation of multistate networks given all minimal path vectors. IIE Transactions, 2007, 39: 811-817.