Linking EWMA p Charts and the Risk Adjustment Control Charts

This paper develops an adaptive exponentially weighted moving average (EWMA) chart that can be used as either a p chart for monitoring significant departures from in‐control non‐homogenous probabilities of failure or success or a risk‐adjusted control chart for success or failure of an event. An example of a risk adjustment process is monitoring the performance of a particular surgery over time where we need to adjust for the temporal changes in patient case mix. If the magnitude of this shift is known in advance, as would be the case in some hypothesis testing applications, then the paper offers a way of selecting the appropriate exponential weights to be efficient at detecting such a variable shift. The adaptive EWMA p chart is tested using extensive simulations. Processes for its efficient design are offered. The example application offers practitioners a means of evaluating a trial in real time rather than the traditional approach of evaluating the trial at the end of the study period. This is helpful in deciding how long the trial should run as well as potentially adapting the design over time as more is understood about the trial uncertainties. This may be particularly useful in evaluating expensive trials.