Probabilistic modeling of the states of a buffer in a production flow system

Assembly line manufacturing systems and materials handling systems usually operate through a system of serially linked stages. In a serially dependent system of this type, the failure of any stage either causes a reduction or causes the complete shutdown of the system. The provision of buffers between stages can result in operation of the nonfailed stages even in the event of failure of a stage. The author presents a stochastic analysis of a buffered production system. The probability of the buffer being full is determined as a function of buffer capacity. This, in turn is used to make the decision on buffer size. Results of the analysis indicate that, over the range of buffer capacity from zero to infinity, the probability of the buffer-full-state exhibits monotonically decreasing behavior that approaches zero asymptotically as buffer size approaches infinity. This finding can be used to detect the range over which the probability of the buffer-full-state asymptotically approaches zero, and appropriately select a buffer size beyond which there is no significant gain in system availability to justify the incremental cost of the additional buffer capacity