Cycle Time Approximations for the G/G/m Queue Subject to Server Failures and Cycle Time Offsets with Applications

Approximate queueing formulae are often employed for the practical evaluation of manufacturing system performance. Common approximations do not fully address practical issues such as idle tools with work in queue, travel time between stages of production, removal of lots from queue pending process issue resolution and the tendency of lots to defect from a failed server in favor of an equivalent available server. In this paper, approximate queueing formulae are proposed which extend popular existing formulae. To test the quality of the proposed approximations, data from production toolsets in IBM's 200mm semiconductor manufacturing fabricator is considered. It is demonstrated that the approximations perform well on the toolsets studied