The Run Length Distribution of the CUSUM with Estimated Parameters

Abstract

AbstractThe CUSUM control chart is a popular method used to monitor the performance of production processes. The performance of the CUSUM is generally evaluated with the assumption that the process parameters are known. In practice, the parameters are rarely known and are frequently replaced with estimates from an in-control reference sample. We discuss the run length distribution of the CUSUM with estimated parameters and provide a method for approximating this distribution and moments. We evaluate the performance of the CUSUM with estimated parameters in a variety of practical situations.KeywordsAverage Run LengthControl ChartsCumulative Sum Additional informationNotes on contributorsL. Allison JonesDr. Jones is an Assistant Professor in the Department of Management. She is a Member of ASQ. Her email address is [e-mail] W. ChampDr. Champ is a Professor in the Department of Mathematical Sciences. He is a Member of ASQ. His email address is [e-mail] E. RigdonDr. Rigdon is a Professor in the Department of Mathematics and Statistics. He is a Member of ASQ. His email address is [e-mail].