Quantitative Techniques to Evaluate Process Stability

ABSTRACT

There have been numerous measures proposed to quantify the capability of a process using statistics such as C _p , C _pk , and C _pm . There are even tests of hypothesis to see if the calculated C _p or C _pk exceeds some constant. However, there are few quantitative summaries to use as a starting point to assess the overall in-control performance of a process. In this article, we propose three measures that can be used to assess the stability of a process and classify the process parameter as stable or unstable. Test criteria for each of the three measures are suggested, and their overall performance under certain conditions are studied. These concepts are demonstrated using three case studies that are detailed throughout the article.

Keywords:

• Statistical process control
• ANOVA
• Stability ratio
• Western Electric rules.

ACKNOWLEDGMENTS

The authors want to acknowledge Dr. José Ramírez and Dr. Donald Wheeler for providing useful ideas and meaningful discussions about how to measure and respond to process stability and capability.

Additional information

Notes on contributors

B. Ramirez

Brenda S. Ramírez is a senior statistician with W.L. Gore & Associates, Inc., where she exploits the use of statistical tools and techniques to aid scientific exploration and process improvements. Prior to coming to Gore, Brenda spent 10 years in the semiconductor industry driving quality programs, such as Six Sigma, and developing statistical solutions for challenging problems. She has an M.S. degree in Applied Statistics from Worcester Polytechnic Institute and an M.S. in Industrial and Management Engineering from Rensselaer Polytechnic Institute.

G. Runger

George C. Runger, Ph.D., is a Professor in the department of Industrial Engineering at Arizona State University. His research is on real-time monitoring and control, data mining, and other data analysis methods with a focus on large, complex, multivariate data streams. He has more than 100 research publications in these areas. His work is funded by grants from the National Science Foundation and corporations. In addition to academic work, he was a senior engineer at IBM. He holds degrees in industrial engineering and statistics.