Efficient control chart calibration by simulated stochastic approximation

ABSTRACT

The accurate determination of control limits is crucial in statistical process control. The usual approach consists in computing the limits so that the in-control run-length distribution has some desired properties; for example, a prescribed mean. However, as a consequence of the increasing complexity of process data, the run-length of many control charts discussed in the recent literature can be studied only through simulation. Furthermore, in some scenarios, such as profile and autocorrelated data monitoring, the limits cannot be tabulated in advance, and when different charts are combined, the control limits depend on a multidimensional vector of parameters. In this article, we propose the use of stochastic approximation methods for control chart calibration and discuss enhancements for their implementation (e.g., the initialization of the algorithm, an adaptive choice of the gain, a suitable stopping rule for the iterative process, and the advantages of using multicore workstations). Examples are used to show that simulated stochastic approximation provides a reliable and fully automatic approach for computing the control limits in complex applications. An R package implementing the algorithm is available in the supplemental materials.

Keywords:

• Stochastic approximation
• statistical process control
• control charts
• multi-chart schemes
• stochastic root finding

Acknowledgement

The authors thank the Department Editor and referees for their timely review and helpful comments that improved the article. This research was partially funded by the UNIPD CPDA128413/12 grant.

Additional information

Notes on contributors

Giovanna Capizzi

Giovanna Capizzi is an Associate Professor of Statistics at the Department of Statistical Sciences, University of Padua, Italy. She holds a Ph.D. in Statistics from Padua University. Her publications have appeared in referred journals including Environmetrics, IIE Transactions, Journal of Quality Technology, Technometrics, Statistics and Computing. She is serving as an Associate Editor of Technometrics and she is on the Editorial Board of Journal of Quality Technology. Her current research is focused on change-point models, statistical process monitoring, and quality control.

Guido Masarotto

Guido Masarotto is a Professor of Statistics at the Department of Statistical Sciences, University of Padua, Italy. His current research includes statistical process monitoring and statistical computing. His research has been published in various scientific journals including Biometrika, Biostatistics, Statistics and Computing, Annals of Applied Statistics, IIE Transactions, Journal of Quality Technology, and Technometrics.