Closed production lines with arbitrary models of machine reliability

Closed production lines have been analyzed in the literature under the assumption that the machines obey either the Bernoulli or exponential reliability models. Empirical evidence indicates, however, that manufacturing equipment on the factory floor often has the coefficients of variation of up- and downtime less than 1; therefore, the statistics of machine reliability may be neither Bernoulli nor exponential. This paper analyzes the performance, system-theoretic, and improvability properties of closed production lines with machines having up- and downtime distributed according to any unimodal distribution, provided that the coefficients of variation are less than or equal to 1.