Composite stage effects in unbalancing of series production systems

Abstract

Earlier studies on production systems had indicated that the output is optimum when the less variable stages are loaded slightly more than the more variable stages. It is shown in this paper that this guideline is violated in systems consisting of a hyperexponential stage. From a comparative study of several two-stage systems it is shown that the unusual unbalancing behaviour of the hyperexponential distribution is due neither to its negative memory nor to any abnormality in the plot of its higher moments but to the fact that it is a composite distribution.

Considering a general two-stage system, in which each of the stages is composite to an arbitrary degree, it is shown that the mean cycle time of such a system can be written as a linear combination of the mean cycle times of the several sub-systems into which it can be decomposed. The unbalancing pattern of the overall system is shown to violate the conventional guideline because the component subsystems are in general grossly misbalanced when the overall system is notionally balanced.

Exact expressions for the mean cycle time of two three-state systems (I: exponential-gamma-exponential and II: exponential-hyperexponential-exponential) are obtained by solving the integral equation for the distribution function of the residual time. From a comparative study of their unbalancing behaviour it is shown that the ‘composite stage effects play as dominant a role as the ‘bowl phenomenon’ or the ‘variability imbalance‘.