The Conditional In-Control Performance of Self-Starting Control Charts

ABSTRACT

The recommended size of the Phase I data set used to estimate the in-control parameters has been discussed many times in the process monitoring literature. Collecting baseline data, however, can be difficult or slow in some applications. Such issues have resulted in the development of self-starting control charts that allow charting early, near the start of data collection. In our article, we use the average of the in-control average run length (AARL) and the standard deviation of the in-control average run length (SDARL) to assess the in-control run length performance of self-starting charts conditioned on the preliminary data used. This approach accounts for practitioner-to-practitioner variability in the in-control average run length (ARL) of self-starting charts, which has not been considered previously. We found that there was a significant amount of variation in the in-control ARL values obtained by practitioners due to the sampling variation of the initial estimators of the in-control parameters. The amount of variation was surprisingly low, however, compared to that resulting from the use of standard Phase I sampling and estimation.

KEYWORDS:

• estimation effect
• Shewhart chart
• SPC
• standard deviation of the average run length
• statistical process control

ACKNOWLEDGMENTS

The authors appreciate the helpful comments by two anonymous reviewers and Douglas M. Hawkins of the University of the Minnesota School of Statistics on a previous version of this article. The authors also thank Jens Meuller in the Research Computing Group at Miami University of Ohio for providing computational support in completing the Monte Carlo simulations.

ABOUT THE AUTHORS

Matthew J. Keefe is a PhD student in the Department of Statistics at Virginia Tech. He earned his M.S. degree in Statistics from Virginia Tech in 2013. He is an active collaborator in LISA (Virginia Tech's Laboratory for Interdisciplinary Statistical Analysis), where he closely works with researchers in other fields.

William H. Woodall is a Professor in the Department of Statistics at Virginia Tech. He is a former editor of the Journal of Quality Technology (2001–2003) and associate editor of Technometrics (1987–1995). He is the recipient of the Lloyd S. Nelson Award (2014), Box Medal (2012), Shewhart Medal (2002), Jack Youden Prize (1995, 2003), Brumbaugh Award (2000, 2006), Søren Bisgaard Award (2012), Ellis Ott Foundation Award (1987), and best paper award for IIE Transactions on Quality and Reliability Engineering (1997). He is a Fellow of the American Statistical Association, a Fellow of the American Society for Quality, and an elected member of the International Statistical Institute.

L. Allison Jones-Farmer is the Van Andel Chair of Analytics and a Professor in the Department of Information Systems and Analytics at Miami University in Oxford, Ohio. Her research focuses on developing practical methods for analyzing data in industrial and business settings. She is on the editorial review board of Journal of Quality Technology, a former Associate Editor of Technometrics, and was recently awarded the Lloyd Nelson Award (2014) for the paper in Journal of Quality Technology with the most immediate impact to practitioners. Dr. Jones-Farmer enjoys developing innovative curricula and teaching analytics and statistics to both undergraduate and graduate students. Prior to joining Miami University of Ohio, Dr. Jones-Farmer was on the faculty at University of Miami in Coral Gables, Florida, and at Auburn University in Auburn, Alabama. She has consulted with numerous organizations and enjoys working with companies to improve their analytics capabilities.

Additional information

Funding

The work of William H. Woodall was partially supported by NSF Grant CMMI-1436365.