The use of the Cpm index to monitor processes

Abstract

AbstractThe Cpm index was originally created to measure the ability of the process to produce products meeting specifications but, more recently, the Cpm has also been used to control processes. In this new application, the charting points of the control chart are the estimated values of the Cpm index obtained with the mean and the variance of the samples. The performance of the Cpm chart is not affect by the values of the specification limits, but it is highly affected by d, the distance between the middle point of the specifications and the in‐control mean of the X distribution. Because of that, a search is conducted to find d that optimizes the overall performance of the Cpm chart in signaling the three usual types of changes in process parameters: isolated mean shifts, isolated variance increases, and the two together. Comparing the joint and S2 charts, the Cpk chart and the Cpm chart, the last one is always the most sensitive in detecting all three types of process changes, except when the variance remains unaltered and the mean increases/decreases a lot (one and half standard deviations); in this case, the joint and S2 charts are slightly faster than the Cpm chart.