The Run Length Distribution of the CUSUM with Estimated Parameters

L. Allison Jones‐Farmer · Charles W. Champ · Steven E. Rigdon

142 citations0/0 files storedJournal of Quality Technology

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Advanced Statistical Process Monitoring Probability and Statistical Research Fault Detection and Control Systems

Abstract

The 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.

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References

1954CONTINUOUS INSPECTION SCHEMES 1972An Approach to the Probability Distribution of Cusum Run Length 1998Cumulative Sum Charts and Charting for Quality Improvement 1993The Effect of Sample Size on Estimated Limits forXandXControl Charts 1999EWMA Control Charts for Monitoring the Mean of Autocorrelated Processes 2001The Performance of Exponentially Weighted Moving Average Charts With Estimated Parameters 1983The Distribution of the Run Length of One-Sided CUSUM Procedures for Continuous Random Variables

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2010Nonparametric CUSUM and EWMA Control Charts for Detecting Mean Shifts 2009Distribution-free cumulative sum control charts using bootstrap-based control limits 2007A Self-Starting Control Chart for Linear Profiles 2007Nonparametric control chart based on change-point model 2010A CUSUM control chart for monitoring the variance when parameters are estimated 2014Distribution‐free Phase II CUSUM Control Chart for Joint Monitoring of Location and Scale

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