CUSUM Analyses of Time-Interval Data for Online Radiation Monitoring

Abstract

Three statistical control chart methods were investigated to determine the one with the highest detection probability and the best average run length (ARL). The three control charts include the Shewhart control chart of count data, cumulative sum (CUSUM) analysis of count data (Poisson CUSUM), and CUSUM analysis of time-interval (time difference between two consecutive radiation pulses) data (time-interval CUSUM). The time-interval CUSUM (CUSUMti) control chart was compared with the Poisson CUSUM (CUSUMcnt) and the Shewhart control charts with experimental and simulated data. The experimental data were acquired with a DGF-4C (XIA, Inc.) system in list mode. Simulated data were obtained by using Monte Carlo techniques to obtain a random sampling of a Poisson process. All statistical algorithms were developed using R (R Development Core Team). Detection probabilities and ARLs for the three methods were compared. The time-interval CUSUM control chart resulted in a similar detection probability as that of the Poisson CUSUM control chart but had the shortest ARL at relatively higher radiation levels; e.g., about 40% shorter than the Poisson CUSUM at 10.0 counts per second (cps) (five times above the background count rate). Both CUSUM control charts resulted in a higher detection probability than that of the Shewhart control chart; e.g., 100% greater than the Shewhart control method at 4.0 cps (two times above the background count rate). In addition, when time-interval information was used, the CUSUM control chart coupled with a modified runs rule (mrCUSUMti) showed the ability to further reduce the time needed to respond to changes in radiation levels and keep the false positive rate at a required level.