Design of adaptive EWMA control charts using the conditional false alarm rate

The article discusses the design of adaptive control charts, specifically focusing on the adaptive exponentially weighted moving average (AEWMA) control charts using the conditional false alarm rate (CFAR). Dynamic control limits are emphasized as beneficial, especially when factors like sample sizes or risk scores change over time. The CFAR approach, through computer simulation, can control the in-control run length properties. The article demonstrates that the CFAR method can be applied to design AEWMA charts where the smoothing parameter depends on the observed value at a specific time. While AEWMA charts are the primary example, the methodology can be applied to other adaptive charts like the cumulative sum (CUSUM) chart.

The paper delves into applying the CFAR approach in designing adaptive control charts. Adaptive charts have been proposed for monitoring situations where parameters or sample sizes change based on observed data. However, the CFAR approach hasn’t been widely used in designing these adaptive charts. The article applies the CFAR method to design AEWMA charts, ensuring that CFARs are controlled at every monitoring point. The article is structured to define the CFAR, present the AEWMA method, discuss the simulation algorithm for dynamic probability control limits, and evaluate the performance of these charts.

In conclusion, the article showcases how controlling the CFAR can effectively determine AEWMA charts’ control limits. Using dynamic limits is particularly beneficial during the initial monitoring stages. The approach can adapt to varying sample sizes or score functions over time, and the run length performance typically resembles a geometric distribution. One of the significant advantages of this method is that it doesn’t require assumptions about the sample size to design the chart, and it can adapt to sample size changes over time. The methodology presented can also be extended to other adaptive control charts, highlighting its versatility.

Read the full article