Fast Initial Response for CUSUM Quality-Control Schemes: Give Your CUSUM A Head Start

Abstract

The fast initial response (FIR) feature for cumulative sum (CUSUM) quality-control schemes permits a more rapid response to an initial out-of-control situation than does a standard CUSUM quality-control scheme. This feature is especially valuable at start-up or after a CUSUM has given an out-of-control signal. This article presents the average run length and the distribution of run length for CUSUM schemes with the FIR feature and compares FIR CUSUM schemes to standard CUSUM schemes. The comparisons show that if the process starts out in control, the fast initial response feature has little effect; however, if the process mean is not at the desired level, an out-of-control signal will be given faster when the FIR feature is used.

KEY WORDS:

• Quality control
• Cumulative sum (CUSUM)
• Average run length (ARL)
• V mask
• Markov chain
• FIR feature