Buffer capacity for accommodating machine downtime in serial production lines

This paper investigates the smallest level of buffering (LB), necessary to ensure the desired production rate in serial lines with unreliable machines. The reliability of machines is assumed to obey either exponential, or Erlang, or Rayleigh models. The LB is measured in units of the average downtime, Tdown. The dependence of LB on the reliability model, the number of machines, M, the average uptime, Tup, and the efficiency, e = Tup /(Tup + Tdown) is analysed. It is shown that reliability models with larger coefficient of variation require larger LB, and an empirical law that connects LB of the exponential model with those for other reliability models is established. It is shown that LB is an increasing function of M, but with an exponentially decreasing rate, saturating at around M = 10. Also, it is shown that LB does not depend explicitly on Tup and is a decreasing function of e. Based on these results, rules-of-thumb are provided for selecting buffer capacity, which guarantee sufficiently high line efficiency.