Variance of the output as a function of time: production line dynamics

Abstract

We consider Markovian models of discrete materials flow production systems. The transient behavior of a production line is investigated. Namely, mean and variance of the number of parts produced in a given time period conditioned on an arbitrary initial condition is determined by using a Markov reward model. Closed-form expression for the variance of the output from a single unreliable station is derived to illustrate the procedure. Then variance of the output from a general two-station production line with a finite buffer is determined by using a set of recursive equations that exploits the special structure of the probability matrix. The relationship between the due-time performance and variability of the line is investigated by determining the probability of meeting a customer order on time and also the time to produce a given order approximately. Numerical experiments that investigate the relationships between the system parameters and production line dynamics are also included.