Kolmogorov equations based approximate analysis and sizing of constant work in process unreliable manufacturing system loops

CONWIP or constant work in process is an important manufacturing systems production discipline whereby within a CONWIP loop, there is a cap on the maximum amount of work in process that is permitted at any time. This allows for some mobile storage within the loop, albeit a bounded amount. Enforcement of the discipline is carried out at the entrance of the loop. The presence of a loop wide constraint creates indirectly a significant degree of solidarity among the machines within the loop. This property is exploited to develop a model of storage dynamics involving a number of (virtual) macro machines having some common states and interacting through some unknown parameters which are then estimated. Numerical results are presented and an application in minimal CONWIP loop storage sizing for a given demand rate and service level requirement is reported.