A novel representation of tandem systems with inter-stage storage applied to on-line system monitoring

One of the goals of operating a tandem manufacturing system with finite inter-stage storage and asynchronous operations is to meet the demand without over-producing, under-producing or carrying large quantities of material in storage. We believe that analysing the operation of such a system on a real-time basis helps achieve this goal. The first step in this real-time analysis would be to quantitatively associate the causes and effects of over-production or under-production as they occur. This requires determining the cumulative effect that the performance that any stage has on the system, based on its history, the current system state and the interrelationships between the stages. This paper proposes a method which first “represents” uniquely and completely each stage and surrounding storage as an “element”. While this system, which consists only of this simple type of “element” functions in exactly the same way as the original one, each “element” is put into an “ideal world” for decoupled measurement. Though an element behaves in exactly the same way whether it is in the “ideal world” or in the “real world”, the elapsed times in the two worlds since the beginning of production can be different, since the responses (occurrences and durations of the blockings and starvations) of the two worlds can be different. A “phase parameter” is introduced for each element to represent this difference. Once the formation of the “phase parameter” of the output element is formulated, quantitative relationships between causes and effects of over-producing or under-producing can be “explained” as they occur.