Design of exponential control charts based on average time to signal using a sequential sampling scheme

Abstract

Exponential charts based on time-between-events (TBE) data are widely investigated and applied in various fields. The average time to signal (ATS) is used instead of the average run length to evaluate the performance of TBE charts, since the ATS involves both the number and the time of samples inspected until a signal occurs. An ATS-unbiased exponential control chart is proposed when the in-control parameter is known. Considering the need in practice to start monitoring a production process as soon as possible, a sequential sampling scheme is adopted and the in-control parameter is estimated by an unbiased and consistent estimator. Some specific guidelines to stop updating control limits are obtained from the relationship between the phase I sample size and the actual false alarm rate. Finally, two real examples are given to illustrate the implementation and efficiency of the proposed method.

Keywords:

• time between events
• average time to signal (ATS)
• unbiased control chart
• Gamma distribution
• sequential sampling

Acknowledgements

The authors are particularly grateful to the editor and three anonymous reviewers who gave useful suggestions and considerably helped in improving the manuscript.

Additional information

Funding

Funding. This work was supported in part by China NSFC under [grant number 11001005] and the Fundamental Research Funds for the Central Universities under Grant YWF-14-KKX-008.