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Variance of the throughput of an \(N\)-station production line with no intermediate buffers and time dependent failures. (English) Zbl 0916.90119
Summary: The variance of the throughput of an \(N\)-station production line with no intermediate buffers and time dependent failures is analytically determined. Time to failure and time to repair distributions are assumed to be exponential. The analytical method yields a closed-form expression for the variance of the throughput. The method is based on determining the limiting variance of the total residence (sojourn) time in a specific state of an irreducible recurrent Markov process from the probability of visiting that state at time \(t\) given an initial state. This probability function is the instantaneous availability of a production system in the reliability context. A production line with no inter-station buffers and time-dependent failures is basically a series system with hot standby. The same procedure can be applied to determine the variance of the throughputs of various arrangements of workstations including series, parallel, series-parallel systems provided that the instantaneous availabilities of these systems can be written explicitly. Numerical experiments show that, although the expected throughput decreases monotonically, the variance of the throughput may increase and then decrease as the number of stations in the line increases depending on the system parameters. Numerical experiments that investigate this phenomenon and also the dependence of the coefficient of variation on the number of stations are also presented in this study.

MSC:
90B25 Reliability, availability, maintenance, inspection in operations research
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[1] Barnes, J.A.; Disney, R.L., Traffic processes in a class of finite Markovian queues, Queuing systems, 6, 311-326, (1990) · Zbl 0696.60090
[2] Dallery, Y.; Gershwin, S.B., Manufacturing flow line systems: A review of models and analytical results, Queuing systems theory and applications, 12, 1+2, 3-94, (1992), Special Issue on Queuing Models of Manufacturing Systems · Zbl 0782.90048
[3] Dallery, Y.; Frein, Y., On decomposition methods for tandem queuing networks with blocking, Operations research, 41, 2, 386-399, (1993) · Zbl 0771.90046
[4] Hatcher, J.M., The effect of internal storage on the throughput of a series of stages having exponential service times, AIIE transactions, 1, 2, 150-156, (1969)
[5] Hendricks, K.B., The output processes of serial production lines of exponential machines with finite buffers, Operations research, 40, 6, 1139-1147, (1992) · Zbl 0825.90522
[6] Hendricks, K.B.; McClain, J.O., The output processes of serial production lines of general machines with finite buffers, Management science, 39, 10, 1194-1201, (1993)
[7] Høyland, A.; Rausand, M., ()
[8] Jacobs, D.; Meerkov, S.M., Due time performance in Lean and mass manufacturing environments, University of michigan department of electrical engineering and computer science report no. CGR-93-5, (1993), February, 1993
[9] Kemeny, J.G.; Snell, J.L., ()
[10] Lavenberg, S.S., The steady-state queuing time distribution for the M/G/1 finite capacity queue, Management science, 21, 5, 501-506, (1975) · Zbl 0302.60058
[11] Matis, J.H.; Wehrly, T.E.; Metzler, C.M., On some stochastic formulations and related statistical moments of pharmokinetic models, Journal of pharmokinetics and biopharmaceutics, 11, 1, 77-92, (1983)
[12] Miltenburg, G.J., Variance of the number of units produced on a transfer line with buffer inventories during a period of length T, Naval research logistics, 34, 811-822, (1987) · Zbl 0648.90034
[13] Papadopoulos, H.T., An analytic formula for the Mean throughput of K-station production lines with no intermediate buffers, European journal of operational research, 91, 481-494, (1994) · Zbl 0924.90086
[14] Papadopoulos, H.T., The throughput rate of multistation reliable production lines with no intermediate buffers, Operations research, 43, 4, 712-715, (1995) · Zbl 0860.90069
[15] Tan, B.; Yeralan, S., A general decomposition method for heterogeneous multistation production lines, Koç university working paper, series 94-13, Istanbul, Turkey, (1994)
[16] Yeralan, S.; Muth, E.J., A general model of a production line with intermediate buffer and station breakdown, IIE transactions, 19, 2, 130-139, (1987)
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