ON THE USE OF BUFFER INVENTORIES TO MINIMIZE COSTS WITH AN UNRELIABLE MACHINE

In this paper, we discuss the problem of quality control with an unreliable machine which produces defects at a rate of Λ₀, per unit when in-control and a rate of Lambda; ₁, when out-of-control (where Λ₁ Λ ₀). Every h time periods, we sample n units, count the number of defects, and (using a process based on a Shewart c-chart) test the hypothesis that the machine is in control by comparing the total number of defects to an upper control limit (UCL). More important, we introduce the concept that a buffer inventory which immediately follows the unreliable machine may reduce expected total costs. This buffer serves to delay the movement of items from the unreliable machine to the next stage of the production process. In this way, we can isolate and repair most defective items before they are embedded in a product downstream or sold to customers where repair is more costly. To search for the optimal control policy, we find bounds for n, h, and UCL; given values for these variables, we show how the optimal buffer size can be determined directly. Numerical results illustrate the magnitude of potential savings.