Statistical process control using run sums

Abstract

We develop a novel and effective way to monitor quality using the large volumes of positively autocorrelated data produced by high-frequency sampling of a process. We regard the process as a sequence of runs above and below the mean. The sums of the observations in these runs behave as independent random variables suitable for charting. Using simulated data, we show that the average run length performance of charts based on run sums compares favorably to that of alternative charts based on ARMA residuals, while avoiding the need for ARMA modeling. Furthermore, we obtained the same relative performance results for iid data. Thus, run sum charts provide a powerful and comprehensive method for SPC in data-rich environments.

Keywords:

• Autocorrelation
• ARMA models
• level rossing
• Monte Carlo methods
• run sums
• Shewhart hart
• statistical process control