التفاصيل البيبلوغرافية
| العنوان: |
Distribution-free multivariate time-series monitoring with analytically determined control limits. |
| المؤلفون: |
Liu, Di, Kim, Heeseon, Kim, Seong-Hee, Kim, Taeheung, Lee, Dongki, Xie, Yao |
| المصدر: |
International Journal of Production Research; Oct2023, Vol. 61 Issue 20, p6960-6977, 18p, 6 Charts, 6 Graphs |
| مصطلحات موضوعية: |
CUSUM technique, QUALITY control charts, MARGINAL distributions, BROWNIAN motion, STATISTICAL process control |
| مستخلص: |
We consider the problem of detecting a shift in the mean of a multivariate time-series process with general marginal distributions and general cross- and auto-correlation structures. We propose a distribution-free monitoring procedure that does not need model fitting or trial-and-error calibration for control limits, which makes the procedure convenient to be implemented when a facility consists of many processes to be monitored. The main idea is to convert each observation vector into a one-dimensional T 2 quantity that captures cross-correlation. The T 2 quantities form a univariate auto-correlated process, and CUSUM statistics are constructed on the T 2 quantities. Then using the fact that the CUSUM statistics on the auto-correlated process behave as a reflected Brownian motion asymptotically under some conditions, the control limits of the CUSUM procedure are analytically determined by setting the first-passage time of the Brownian motion equal to a target in-control average run length. We compare the performance of our procedure with three competing procedures on simulated data with various cross- and auto-correlation and real data from a wafer etching process. The proposed procedure delivers actual in-control average run lengths close to the target and shows comparable or better performance in detecting a shift in mean than the competitors. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
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