Derivative Estimation for Buffer Capacity of Continuous Transfer Lines Subject to Operation-Dependent Failures

We derive estimators of throughput sensitivity to changes in buffer capacity for continuous flow models of a transfer line comprising two machines separated by a buffer of finite capacity, where machines are subject to operation-dependent failures, i.e., a machine cannot fail when it is idle. Both repair times and failure times may be general, i.e., they need not be exponentially distributed. The system is hybrid in the sense that it has both continuous dynamics – as a result of continuous material flow – and discrete events: failures and repairs. The combination of operation-dependent failures and buffer capacity as the parameter of interest make the derivative estimation problem difficult, in that unlike previous work on continuous flow models, careful use of conditional expectation (i.e., smoothed perturbation analysis) is required to obtain unbiased estimators.