Metamodels of production line transient behaviour for sudden machine breakdowns

Production controls based on mean value analysis and steady-state conditions are incapable of making on-time decisions that cope with unexpected dynamic events which are due to interruptions in complex work flow characteristic of modern production lines. One of the most significant dynamic events in production situations is a sudden machine/operator breakdown/outage. Computer simulation is known to be a useful tool for modelling the dynamic response of a system to machine breakdown, but it takes too long to perform its analysis to provide the response time necessary for control procedures. Analytical methods provide formulae which are suitable for real-time analysis, but there are no results available for transient behaviour associated with machine breakdown. Metamodelling is the process of summarizing the results of a simulation study in analytical form. In this paper, the authors present their metamodels for the dynamic behaviour of both time in system and number in system for a general arrival time, general service time, multi-station, multi-server production line system. The formulae are exponential in nature and are developed through a study of first-order differential equations from system control theory. The constants used in the present results are determined off-line through discrete-event simulation analysis. The metamodesl themselves are available to on-line users as a predictor of parts that will be delayed because of breakdown(s) as a function of time in the future. The integrated approach of using simulation for modelling system details and analytic method for describing the revealed system transient behaviour is a powerful methodology for analysing large-scale production systems.