Phase II synthetic exponential charts and effect of parameter estimation

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.

Keywords:

• Synthetic chart
• average run length
• process mean
• time-between-events

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.

Additional information

Funding

The work of Cheng was supported by a grant from City University of Hong Kong [Project number 9380058]; the National Natural Science Foundation of China [number 71371163]; University Grants Council of Hong Kong [GRF 9042327]. The work of Sun is sponsored by the Zhejiang Provincial Natural Science Foundation of China [grant number LY16G020003]; Foundation of Ministry of Education of China [grant number 13YJC910005], [grant number 13YJC910010]; Philosophy and Social Science Research Project in Zhejiang Province of China [grant number 13NDJC055YB]; National Statistical Research Plan Project [grant number 2015LZ50]; Research Foundation of Education Bureau of Zhejiang Province of China [grant number Y201329882]; Zhejiang Provincial Key Research Base for Humanities and Social Science Research (Statistics). The work of Guo is sponsored by the National Social Science Foundation of China [grant number 14BTJ030].