The SPRT Control Chart for Standard Deviation Based on Individual Observations

Abstract

When the production rate is low or only one observation is available at each time that a sample is to be taken, the traditional control chart for monitoring the process variation is the moving range chart. In this paper, we propose a chart based on the sequential probability ratio test (SPRT) for detecting increases in process variability, which can have some impact on process capability and product quality. Critical values for the control chart are presented. To demonstrate an application of the SPRT chart, an example using real manufacturing data is presented.

Key Words:

• Integral equation
• operating characteristic
• sequential probability ratio

Additional information

Notes on contributors

Youn-Min Chou

Youn-Min Chou is a Professor of Applied Mathematics at the University of Texas at San Antonio. She received her Ph.D. degree in statistics from Southern Methodist University. She is a Fellow of the American Society for Quality. She has published papers in quality control, statistics, and environmental engineering journals. Dr. Chou was co-inventor of an advanced method for statistical process control in integrated circuit manufacturing (U.S. Patent No. 5,987,398).

Robert L. Mason

Robert L. Mason is an Institute Analyst at Southwest Research Institute in San Antonio. He received his doctorate degree in statistics from Southern Methodist University. He is a Fellow of both the American Statistical Association and the American Society for Quality. He is the author of several textbooks and has published numerous papers in the areas of quality control and statistics. Dr. Mason is a former President of the American Statistical Association.

John C. Young

John C. Young is a Professor of Statistics at McNeese State University, Lake Charles, LA, and is also president of InControl Technologies, Inc. in Houston, Texas. He received his Ph.D. degree in statistics from Southern Methodist University. He is the author of several textbooks and has published numerous papers in the areas of quality control and statistics.