Detecting a change in a scale parameter – a combination of SPC and change point procedures

Abstract

The primary objective is to compare between statistical and SPC methods for monitoring process variance via an extensive simulation. The statistical methods are Cumulative Sum (CUSUM) and Likelihood Ratio Test (LRT), and the SPC methods are Moving Range (MR) and Exponentially Weighted Mean Squared deviation (EWMS). In addition, we examined a combination of both statistical and SPC methods, denoted by “Schechtman on S²”. Random series were generated from three distributions: normal, Poisson and lognormal. The parameters of interest were: series length, size of the change, and location. The criteria for comparison were: rates of false alarms, powers and Mean Absolute Deviation (MAD). The main outcomes and results of our simulations show that when the distribution is normal, all procedures are slightly conservative. However, when the distribution is not normal, the rates of false alarm go up to around 0.8 for all but Schechtman on S². Assuming normal distribution, EWMS and CUSUM are powerful for detecting changes, and LRT is capable of estimating the time of change. Therefore, it is worthwhile to complement SPC methods by adding LRT, which provides a good estimate of the point of change. If there are n observations per time point, Schechtman on S² performs well for all distributions under study.

Keywords:

• Monitoring of a process
• Cumulative sum
• Likelihood ratio test
• Non-parametric test

Acknowledgments

The first author was partially supported by the BGU Paul Ivanier Center for Robotics Research and Production Management.