Economic cost models of integrated APC controlled SPC charts

In this paper, an economic cost model is proposed for processes integrating both automatic process control (APC) and statistical process control (SPC) for quality monitoring and control. Both the special cause and common cause variations are reduced by applying integrated APC and SPC. Traditionally, the integrated processes using APC and SPC are evaluated by the average run length (ARL). However, ARL may not be appropriate as a measurement of the economic design since it does not take into consideration the run length variation. Also, there are few studies that compare the cost models of such an integrated control system and the effect of cost parameters using different APC controllers. Therefore, we develop an economic cost model using non-homogenous Poisson process to describe the occurrence of an APC adjustment and develop a long run expected cost to investigate the use of different controllers in such integrated systems. Numerical examples are presented to demonstrate the applicability of the proposed model.