The Changepoint Model for Statistical Process Control

Abstract

Statistical process control (SPC) requires statistical methodologies that detect changes in the pattern of data over time. The common methodologies, such as Shewhart, cumulative sum (cusum), and exponentially weighted moving average (EWMA) charting, require the in-control values of the process parameters, but these are rarely known accurately. Using estimated parameters, the run length behavior changes randomly from one realization to another, making it impossible to control the run length behavior of any particular chart. A suitable methodology for detecting and diagnosing step changes based on imperfect process knowledge is the unknown-parameter changepoint formulation. Long recognized as a Phase I analysis tool, we argue that it is also highly effective in allowing the user to progress seamlessly from the start of Phase I data gathering through Phase II SPC monitoring. Despite not requiring specification of the post-change process parameter values, its performance is never far short of that of the optimal cusum chart which requires this knowledge, and it is far superior for shifts away from the cusum shift for which the cusum chart is optimal. As another benefit, while changepoint methods are designed for step changes that persist, they are also competitive with the Shewhart chart, the chart of choice for isolated non-sustained special causes.

• Cumulative Sum Control Charts
• Exponentially Weighted Moving Average Control Charts
• Shewhart Control Charts

Additional information

Notes on contributors

Douglas M. Hawkins

Dr. Hawkins is a Professor in the School of Statistics. He is a Fellow of ASQ. His email address is [email protected].

Peihua Qiu

Dr. Peihua Qiu is an Associate Professor in the School of Statistics. His email address is [email protected].

Chang Wook Kang

Dr. Chang Wook Kang is an Associate Professor in the Department of Industrial Engineering. His email address is [email protected].