The economically designed CUSUM chart for monitoring short production runs

This paper proposes a model for the design of a CUSUM chart for monitoring the process mean in short production runs. The model allows the determination of the scheme parameters that minimize the relevant expected cost of the procedure as well as the calculation of several measures of statistical performance. To evaluate the economic effectiveness of the proposed scheme, we compare its optimal expected cost against the expected cost corresponding to implementation of a CUSUM chart optimized for continuous operation (infinite horizon). The numerical results indicate that the potential savings from using the CUSUM scheme designed specifically for short runs are substantial in cases of unreliable processes with high costs of sampling, searching, and removing assignable causes. The results also show that because of the short duration of the run, in many cases it is optimal not to monitor the process at all; the use of the infinite-horizon CUSUM chart in those cases typically leads to significant cost penalties.