Mixed Exponentially Weighted Moving Average–Cumulative Sum Charts for Process Monitoring

The control chart is a very popular tool of statistical process control. It is used to determine the existence of special cause variation to remove it so that the process may be brought in statistical control. Shewhart-type control charts are sensitive for large disturbances in the process, whereas cumulative sum (CUSUM)–type and exponentially weighted moving average (EWMA)–type control charts are intended to spot small and moderate disturbances. In this article, we proposed a mixed EWMA–CUSUM control chart for detecting a shift in the process mean and evaluated its average run lengths. Comparisons of the proposed control chart were made with some representative control charts including the classical CUSUM, classical EWMA, fast initial response CUSUM, fast initial response EWMA, adaptive CUSUM with EWMA-based shift estimator, weighted CUSUM and runs rules–based CUSUM and EWMA. The comparisons revealed that mixing the two charts makes the proposed scheme even more sensitive to the small shifts in the process mean than the other schemes designed for detecting small shifts. Copyright © 2012 John Wiley & Sons, Ltd.

[1]  Muhammad Riaz,et al.  Enhancing the performance of EWMA charts , 2011, Qual. Reliab. Eng. Int..

[2]  Michael B. C. Khoo,et al.  Design of Runs Rules Schemes , 2003 .

[3]  Fred Spiring,et al.  Introduction to Statistical Quality Control , 2007, Technometrics.

[4]  A Frutiger,et al.  Improving time-sensitive processes in the intensive care unit: the example of 'door-to-needle time' in acute myocardial infarction. , 2000, International journal for quality in health care : journal of the International Society for Quality in Health Care.

[5]  Roger M. Sauter,et al.  Introduction to Statistical Quality Control (2nd ed.) , 1992 .

[6]  Athanasios C. Rakitzis,et al.  The Modified r Out of m Control Chart , 2008, Commun. Stat. Simul. Comput..

[7]  E. S. Page.  CONTINUOUS INSPECTION SCHEMES , 1954 .

[8]  James M. Lucas,et al.  Fast Initial Response for CUSUM Quality-Control Schemes: Give Your CUSUM A Head Start , 2000, Technometrics.

[9]  Muhammad Riaz,et al.  Improving the performance of CUSUM charts , 2011, Qual. Reliab. Eng. Int..

[10]  D. Hawkins,et al.  Cumulative Sum Charts and Charting for Quality Improvement , 1998, Statistics for Engineering and Physical Science.

[11]  Authors' Biographies , 2005 .

[12]  S. W. Roberts,et al.  Control Chart Tests Based on Geometric Moving Averages , 2000, Technometrics.

[13]  Giovanna Capizzi,et al.  An Adaptive Exponentially Weighted Moving Average Control Chart , 2003, Technometrics.

[14]  S. Steiner.  EWMA Control Charts with Time-Varying Control Limits and Fast Initial Response , 1999 .

[15]  James M. Lucas,et al.  Exponentially weighted moving average control schemes: Properties and enhancements , 1990 .

[16]  Wei Jiang,et al.  Adaptive CUSUM procedures with EWMA-based shift estimators , 2008 .

[17]  James M. Lucas,et al.  Combined Shewhart-CUSUM Quality Control Schemes , 1982 .

[18]  Emmanuel Yashchin,et al.  Weighted Cumulative Sum Technique , 1989 .