The design and analysis of 2-CUSUM procedure

Abstract

The 2-CUSUM procedure which is a simple modification or the standard CUSUM chart is described and evaluated asymptotically and in a small average run lengths setting. A Markov chain representation to determine approximate expressions for the run length distribution, its moments and its percentage points is given for thts procedure. A simple design of three 2-CUSUM procedures for detecting small, moderate and large shifts in the mean of a normal distribution is proposed. A comparative analysis with the CUSUM envelope and standard CUSUM charts is given showing Lhat quick detection is attainable simultaneously for a wide range of deviations from the targct mean.

Keywords:

• Average Run Length
• Change Point Problem
• 2-CUSUM Procedure
• Combined Shewhart-CUSUM Chart
• CUSUM Envelope
• CUSUM Chart
• Generalized CUSUM Chart