Replacing a current measurement system in an inspection scheme: A case study

Abstract

We consider a measurement system replacement case study. We show that with the collected data we can determine a decision rule for the corresponding 100 percent inspection scheme with the new measurement system that gives the same properties as the current system. However, we are unable to assess the misclassification rates for the inspection system nor could we determine the probabilities of discordance (defined later in this article). In addition, had statistical properties of the two measurement systems been substantially different, we could not have found an appropriate decision rule for the new scheme. We show that augmenting the collected data with available baseline information solves all of these problems.

Keywords:

• repeatability
• reproducibility
• bias
• specifications
• bootstrap

About the Authors

Stefan H. Steiner is a Professor/Department Chair in the Department of Statistics and Actuarial Science as well and Director of the Business and Industrial Statistics Research Group at the University of Waterloo. He holds a Ph.D. in Business Administration (Management Science/Systems) from McMaster University. His primary research interests include quality improvement, process monitoring, experimental design and measurement system assessment.

Nathaniel T. Stevens is an assistant professor of statistics at the University of Waterloo and prior to this he was an assistant professor of statistics at the University of San Francisco. Nathaniel received his Ph.D. in Statistics from the University of Waterloo and his research interests include experimental design and A/B testing, process monitoring and network surveillance, reliability and survival analysis, as well as measurement systems analysis. Nathaniel serves on the editorial board of The American Statistician, the Technometrics management committee and he was the 2017 recipient of the Quality Engineering Best Reliability Paper Award.

Willis A. Jensen is part of the HR Analytics team at W. L. Gore & Associates, with a previous role as the Global Statistics Team leader. He holds degrees in Statistics from Brigham Young University and a Ph.D. in Statistics from Virginia Tech University. He previously served as an Associate Editor of Technometrics and currently serves on the editorial board of the Journal of Quality Technology and as a column editor for Quality Engineering. He is an ASQ Fellow, a three time winner of the Shewell award as well as a winner of both the Nelson and Bisgaard awards from ASQ.

R. Jock MacKay is a Professor Emeritus at the University of Waterloo where he had been a faculty member since 1975. He received his B.Sc. from the University of Waterloo, and his Ph.D. in Statistics from the University of Toronto. He has extensive experience consulting and teaching short courses in industry. He is co-author with Stefan Steiner of the 2005 book Statistical Engineering published by ASQ Press He has worked with numerous companies across Canada, in the U.S. and in New Zealand . He has a long-standing involvement with mathematics education and is the co-author of several mathematics textbooks for secondary schools in Ontario. Jock has research interests in statistical methods for manufacturing industries and in the theory of applying statistical methods (Statistical Engineering). Much of his recent work has been on the assessment and monitoring of measurement systems.