Statistical design of ATS-unbiased charts with runs rules for monitoring exponential time between events

Abstract

Time between events (TBE) control charts play an important role in monitoring high-yield processes. In this article, Phase II Shewhart-type $t_r$-charts, with various runs rules, are considered for monitoring TBE exponential data with a known rate parameter and the charts’ performance is examined in terms of the average time to signal (ATS). The ATS metric is more suitable due to the possibly unequal times arising between the events. The $t_r$-charts with runs rules are designed so that they are ATS-unbiased for a nominal ATS value. The performance of the proposed charts is compared with that of existing ATS-unbiased $t_r$-charts without runs rules. The proposed charts are found to be more sensitive in detecting small downward and upward shifts. An illustration is provided based on real data, as well as conclusions and some topics for future research.

Keywords:

• Average time to signal
• control chart
• exponential distribution
• high-yield processes
• time between events

Acknowledgement

The authors thank the anonymous reviewers for their comments. The second author would like to express his gratitude to the University of the Aegean, where this research was completed, when he was affiliated with it.

Additional information

Funding

First author’s work was supported by Science and Engineering Research Board (SERB), Government of India (grant number-EMR/2017/002281) and Banaras Hindu University, India under the IoE Scheme (Grant Number 6031).