Production variability of production lines

Production variability of a production line with M machines and M−1 buffers of finite size is addressed. All the processing times by these machines are assumed to be exponential. Based on Markovian arrival process (MAP), an approximate approach is proposed to determine production variability, which includes the variance of the number of parts produced in a given time period and the variance of the time to produce a given number of products. Through numerical experiments this approach is shown to have many advantages in the study of production variability of a more complicated production line that has been an important topic in this area up to now. Also, numerical experiments indicate basic relationships between the system parameter and the production variability.