**Statistical Filter**

This is a procedure for triggering change. It is grounded in a Statistical Process Control (SPC) concept of preventing tampering, of only permitting change when there is adequate statistical evidence. I have used it for both control and coefficient value adjustment in both batch and continuous processes.

“Tampering” is the SPC label for implementing change in response to noise in data. If a process is at set point, then there should be no control action. But, if the vagaries of measurement noise make it appear to be off of target, then a controller will take action, and that action will drive the process away from set point. This is termed tampering. A famous example is W. Edwards Demming’s funnel thought-experiment.

In the method, the statistic is the cumulative sum of deviations from target since the last change. The sum is normalized by the signal variability. When there is 95% statistical confidence that change is justified, make the change, otherwise keep the output unchanged. The method is described here r3eda site SPC Filter 2016-06-29 and demonstrated here with a VBA simulator r3eda SPC Filter 2017-04-23 and user guide r3eda site SPC Filter user Manual 2016-06-29.

The original publication on the method is Rhinehart, R. R., “A CUSUM-Type On-Line Filter,” __Process Control and Quality__, Vol. 2, No. 2, February, 1992, pp. 169-176.

Application publications include: Mahuli, S. K., R. R. Rhinehart, and J. B. Riggs, “pH Control Using a Statistical Technique for Continuous On-Line Model Adaptation,” __Computers & Chemical Engineering__, Vol. 17, No 4, 1993, pp 309-317; Rhinehart, R. R. “A Statistically Based Filter”, __ISA Transactions__, Vol. 41, No. 2, April 2002, pp 167-175; and Muthiah, N., and R. Russell Rhinehart, “Evaluation of a Statistically-Based Controller Override on a Pilot-Scale Flow Loop”, __ISA Transactions__, Vol. 49, No. 2, pp 154-166, 2010. Those are pilot- or lab-scale demonstrations. I have been a part of un-published, but also successful industrial applications.