An SPC Model for Short Production Runs: Minimizing Expected Cost

Abstract

In some manufacturing situations, the assumption of a long production run may not be appropriate. For example, job shops typically will not have the benefit of large production runs. Much of the literature on the economic design of control charts, however, assumes an effectively infinite production run. A finite-horizon or short-production-run version of an economic-process-control model of Bather and Box and Jenkins is considered here. An algorithm is derived that allows implementation of this model and adjustment strategy for the short-production-run case. The solution to the control problem is consistent with traditional statistical process control philosophy in that process adjustment is called for only when the process mean is substantially off target. The control or adjustment limits for this model are time-varying and depend on the break-even points between quadratic cost for being off target and fixed adjustment cost. It is shown that the length of the production run can greatly influence the control or adjustment strategy. Use of control limits based on the assumption of an infinite-run process can significantly increase total expected cost.

KEY WORDS:

• Dynamic programming
• Economic design
• Finite horizon
• Steady model