An analytical formula for variance of output from a series-parallel production system with no interstation buffers and time-dependent failures

Authors:
B. Tan
Affiliations:
Graduate School of Business, Koç University Çayir Cad. Istinye, Istanbul, 80860, Turkey
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
1998

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Abstract

This paper presents a method to determine the mean and the variance of the amount of materials produced in a fixed time interval by a continuous materials flow production system with N stations in series and M stations in parallel and no interstation buffers. Unreliable stations with exponential failure and repair times, time dependent failures, and deterministic processing times are considered. Closed-form expressions for the asymptotic mean and variance of the amount of materials produced per unit time are given for series, parallel, and series-parallel production systems with identical stations. It is shown that the distribution of the amount of materials produced in a fixed time is asymptotically normal. By using this property, effects of variability on the due-date performance are investigated by considering the probability of meeting a customer order on time. Numerical experiments that explore some relationships among performance measures and production system parameters are also presented.