Production systems with cycle overrun: modelling, analysis, improvability and bottlenecks

Production systems literature usually attributes throughput losses to two reasons: unreliable equipment and random part processing time (also referred to as machine cycle time). In practice, however, one more reason for throughput losses is observed: cycle overrun. The specificity of cycle overrun is that not all parts may require more time than allotted by a fixed cycle time and, if the overrun does occur, its duration is coupled with the part processing time: typically, it is a fraction or a small multiple of the cycle time. This paper is indented to develop methods for analysis and improvement of production systems with unreliable machines and cycle overrun. Specifically, it introduces a mathematical model of an unreliable machine with cycle overrun, develops its simplified version, explores the efficacy of machines' improvability by reducing either downtime or cycle overrun, and discusses the issue of bottleneck identification. These results are obtained under the exponential assumption on machine reliability and overruns and then extended to the non-exponential case. Finally, the methods developed are illustrated by a case study based on an automotive transmission case machining line.