Abstract
Exponential charts for monitoring time-between-events data are widely studied recently as it has shown a wide range in different applications. To improve the sensitivity of the simple exponential chart, this paper develops a synthcontrol chart to monitor the two-sided shifts in the exponential mean. This synthetic chart consists of an exponential sub-chart and a conforming run length (CRL) sub-chart and it is designed from two new perspectives. Previous synthetic charts are constructed based on the optimization program for a specified shift size, which proves to be difficult to predict in practice. In this paper, the synthetic chart is constructed based on a new design method which takes the mean (ARL) and the standard deviation (SDRL) of the run length into consideration. The other improvement is that the exponential sub-chart is designed to ensure that the CRL sub-chart only needs a lower control limit and that the proposed synthetic chart is ARL-unbiased. The effect of parameter estimation on the proposed synthetic chart is also studied in this paper. Performance comparisons show that our proposed chart has a better performance in general.
Acknowledgements
The authors thank the Editor, the Guest Editor and the reviewers for their detailed comments and suggestions, which considerably helped improve the manuscript.
Notes
No potential conflict of interest was reported by the authors.