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Abstract
The tr chart is a Shewhart-type control chart used to monitor the time between events, especially in high-quality processes. It has been shown to be more efficient than classical attribute control charts based on count data. In practical applications, the in-control process parameters are often unknown and need to be estimated from a Phase I reference sample. When the available Phase I data are small and the chart parameters have to be estimated, a popular approach is to adjust the control chart limits from a conditional perspective to avoid frequent false alarms using the exceedance probability criterion. However, this approach ignores the practitioner-to-practitioner (p-to-p) variation caused by the random Phase I reference samples, which results in getting different control limits and chart performance for each practitioner Large p-to-p variation makes practitioners to have a limited confidence on using their own estimated charts. Hence, in this article, we propose to optimize the tr chart via an exact method so that it has a minimum p-to-p variation. Comparisons between the optimal and conventionally adjusted charts are made in both the in- and out-of-control cases. The most important results are that the optimal chart has a far smaller p-to-p variation and its unconditional average run length values are closer to the desired ones compared to the conventional approach regardless of the in- or out-of-control cases. Finally, two real examples are presented to illustrate the implementation of the proposed chart.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Notes on contributors
Baocai Guo
Baocai Guo currently holds a professorship in the School of Statistics and Mathematics at Zhejiang Gongshang University in Hangzhou, China. His academic journey began with a Bachelor’s degree in Mathematics from Qufu Normal University in 2000, followed by a Masters degree in Mathematics from Hohai University in 2003. He then achieved his PhD in Statistics from Zhejiang Gongshang University in 2013. His professional focus is primarily on the field of statistical process control.
Yufei Yang
Yufei Yang is presently a Masters student majored in Statistical Science at the School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, China. Her academic journey began at the same institution where she was awarded a Bachelor of Applied Statistics in 2021. Her research focus is on the field of statistical process control.
Philippe Castagliola
Philippe Castagliola is graduated (PhD 1991) from the UTC (Universit’e de Technologie de Compìegne, France). He is currently full professor at Nantes Universit’e, Nantes, France, and he is also a member of the LS2N (Laboratoire des Sciences du Num’erique de Nantes), UMR CNRS 6004. He is an associate editor for Quality Engineering (QE), Communications in Statistics (LSTA, LSSP, UCAS), the International Journal of Reliability, Quality and Safety Engineering (IJRQSE) and Quality Technology & Quantitative Management (QTQM). His research activity includes developments of new Statistical Process Monitoring techniques.