Economic Design of a Single CUSUM Chart with Combined One-sided Monitoring of Process Mean

Abstract

A single, two-sided CUSUM chart utilizing continuously variable sampling intervals and continuously variable sample sizes monitors a process mean and is optimized through an economic design metric. The combined CUSUM statistic is capable of detecting positive and negative shifts simultaneously in one chart, which relies on consecutive indications of either an increase or decrease in mean. A family of polynomial shapes define the rate at which the minimum sample size/maximum sampling interval sweeps to the maximum sample size/minimum sampling interval as the combined CUSUM statistic approaches the boundary. All possible transition probabilities are derived and nine parameters are optimized by minimizing a long-run hourly cost function using 16 different scenarios, varying costs and times spent in/out of control.