Sequential Bayesian assurance tests for degradation data

Abstract

Measuring degradation of items in a reliability context may be all that is feasible. There may simply be neither enough time nor resources to produce a sufficient number of item failures to characterize the underlying time-until-failure distribution. In such contexts, degradation data-based assurance testing can be tuned to strike a compromise between consumer and producer risk when deciding whether to accept or reject a product. A one-stage assurance test counts the number of items in a sample exceeding a fixed degradation threshold at a fixed time and uses this count to make the decision: accept or reject. A general Bayesian framework for extending assurance testing from one-stage to a multi-stage or sequential setting is presented. Our multi-stage assurance tests are shown to compare favorably to their one-stage counterparts by possessing a lower expected time requirement at given sample size and risk constraints. Examples of the methods based on a printhead application are provided and are reproducible with the supplemental R code.

Keywords:

• acceptance sampling
• degradation model
• degradation testing
• Monte Carlo integration
• sequential testing

Supplemental material

R-Code: The R code loads data and basic functions and then reproduces all examples. See the readme.html file in this zipped folder for instructions. (code.zip)

Acknowledgements

We thank two anonymous referees whose insightful comments on an earlier version helped to improve the exposition of this article.

Additional information

Notes on contributors

Kenneth J. Ryan

Kenneth J. Ryan is a professor of Statistics at West Virginia University. He holds a Ph.D. in Statistics from Iowa State University and is a fellow of the American Statistical Association.

Michael S. Hamada

Michael S. Hamada is now retired, but was a statistical scientist at Los Alamos National Laboratory. He holds a Ph.D. in Statistics from the University of Wisconsin-Madison and is a fellow of the American Statistical Association and of the American Society for Quality.

John R. Twist

John R. Twist is a graduate student in Statistics at West Virginia University. He holds a B.S. in Industrial Mathematics and Statistics from West Virginia University.