A single CUSUM chart using a single observation to monitor a variable

Abstract

When Statistical Process Control (SPC) deals with a quality characteristic that is a variable, it is usually necessary to monitor both the mean value and the variability. A CUSUM scheme comprising g cooperative CUSUM charts (called the g-CUSUM scheme) is more effective than the traditional Shewhart &S chart for this purpose. This article proposes a single CUSUM chart (the 1-CUSUM scheme) that detects both mean shift and increasing variance shift by taking a single observation in each sampling (i.e. sample size n = 1). The 1-CUSUM scheme is easier to be generalized to a multi-variate procedure and simpler for implementation and design compared to the g-CUSUM scheme using more than one CUSUM chart. Moreover, according to our studies and those of Reynolds and Stoumbos, the 1-CUSUM scheme generally outperforms many other control charts and schemes for detecting two-sided mean shifts and increasing variance shift.

Keywords:

• Quality control
• Statistical process control
• Quality control chart
• Cumulative sum chart
• Average Time to Signal
• Loss function