Lean buffering in serial production lines with non-exponential machines

In this paper, lean buffering (i.e., the smallest level of buffering necessary and sufficient to ensure the desired production rate of a manufacturing system) is analyzed for the case of serial lines with machines having Weibull, gamma, and log-normal distributions of upand downtime. The results obtained show that: (1) the lean level of buffering is not very sensitive to the type of upand downtime distributions and dependsmainly on their coefficients of variation,CVup andCVdown; (2) the lean level of buffering is more sensitive to CVdown than to CVup but the difference in sensitivities is not too large (typically, within 20%). Based on these observations, an empirical law for calculating the lean level of buffering as a function of machine efficiency, line efficiency, the number of machines in the system, and CVup and CVdown is introduced. It leads to a reduction of lean buffering by a factor of up to 4, as compared with that calculated using the exponential assumption. It is conjectured that this empirical law holds for any unimodal distribution of upand downtime, provided that CVup and CVdown are less than 1.