Linking EWMA p Charts and the Risk Adjustment Control Charts

Abstract

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. Copyright © 2016 John Wiley & Sons, Ltd.

Exponentially weighed moving average charts for monitoring zero-inflated proportions with applications in health care

“…According to Sparks, 36 the EWMA statistic (see equation (9)) can be viewed as a weighted average of all the observed data from the beginning of process monitoring, which are available at time point i. This is the reason why it is able to detect moderate and persistent shifts in the monitoring process.…”

A new p‐control chart with measurement error correction

“…Under the assumption of parametric distributions, the strategies of Shewhart charts have been adopted to construct 𝑝-control charts (e.g., Qiu, 1 Section 3.3). Some relevant extensions have also been explored, such as quasi ARL-unbiased 𝑝-charts based on a heuristic method (e.g., Argoti and Carrión-García 15 ), the risk adjustment control charts for categorical random variables (e.g., Sparks 16 ) and the general framework of distribution free settings (e.g., Yang and Arnold, 17 Aslam et al 18 ). Some applications of 𝑝-control charts have also been discussed.…”

Monitoring multistage multivariate therapeutic processes using risk‐adjusted model‐based group multivariate EWMA control chart

“…Lovegrove et al, 38 Poloniecki et al, 39 and Lovegrove et al 40 first used the concept of risk adjustment for observed-expected (O-E) plots. They were followed by researchers such as Steiner et al, [41][42][43] Alemi and Olivier, 44 Cook et al, 45 Sego et al, 46,47 Cockings et al, 48 Grigg and Spiegelhalter, 49 Steiner and Jones, 50 Cook et al, 51 Chen et al, 52 Szarka and Woodall, 53 Paynabar and Jin, 54 Shojaei and Niaki, 55 Tian et al, 56 Mohammadian et al, 57 Zhang et al, 58 Zhang and Woodall, [59][60][61] and Sparks 62 who developed the risk-adjusted control charts. In recent years, Sachlas et al, 63 Begun et al, 64 Roy et al, 65 Ali et al, 66 Ding et al, 67 Rafiei and Asadzadeh, 68 Keshavarz et al, 69 Keshavarz and Asadzadeh, 70 and Kazemi et al 71 proposed some novel approaches for medical risk-adjustment monitoring.…”