Statistics for Process Control Engineers

15CUSUM

CUSUM, or cumulative sum, is a simple mathematical technique that separates any underlying trend in data from random behaviour. For the process control engineer its applications include the detection of bias error in a measurement and determining whether a process has memory.

Measurements are subject to two forms of error – random and bias. A common requirement is to determine into which category falls an error that has been detected in an inferential property (or on‐stream analyser) when it is compared to a laboratory sample. A random error may result from instrument repeatability, poor time‐stamping and mistakes. A bias error may result from change in feed composition or degradation of catalyst activity. In practice, a recorded error is likely to comprise both. Applying a correction term to the inferential in response to a random error will reduce the accuracy of the inferential. Overlooking a bias error will result in off‐grade production.

CUSUM, in this case, is calculated as the cumulative sum of disagreements between two measurements of the same property. Using the example of C₃ in butane, we have 1,152 sequential measurements from an on‐stream analyser collected every 30 minutes. We also have the corresponding measurements from the inferential. We define the error as the inferential measurement minus that of the analyser. Figure 15.1 plots this error over time. Visually it would appear to be randomly distributed either side of zero. However, Figure 15.2 plots ...