ISBIS4 Abstract

Contact Author's Name: LIU JIYING
Title of Abstract: A COMPARATIVE STUDY OF TIME BETWEEN EVENTS CHARTS
Author(s): J.Y.Liu; M. Xie; T.N. Goh
Affiliation: National University of Singapore

Time between events (TBE) charts, also being called as conforming run length (CRL) charts, were proposed in order to solve some problems with traditional attribute control charts (e.g. p chart, np chart, c chart or u chart) for monitoring the nonconforming rate of a process especially in high quality environment where the process nonconforming rate decreases up to parts per million (ppm) or even parts per billion (ppb) levels. One type of TBE charts is the Cumulative Quantity Control (CQC) chart and its extension CQC-r chart, which monitors the quantity inspected to observe a fixed number (r) of defects based on Gamma distribution. Another way is to employ exponential CUSUM and exponential EWMA charts, which are designed to monitor the TBE data based on exponential distribution.

Considering the time needed to plot a point in a control chart, the Average Time to Signal (ATS) is used to compare the performance of TBE charts. The comparison analysis was conducted for upper-sided, lower-sided and two-sided charts among the CQC chart, the CQC-r chart, the exponential EWMA chart and the exponential CUSUM chart. Based on the analysis, we recommend that when the process nonconforming rate is relatively high, the users can still use traditional attribute control charts to monitor process nonconforming rate. On the other hand, when monitoring high-quality processes, if the purpose of employing a TBE chart is to monitor process improvements or the users do not know exactly whether the process will be improved or deteriorated, the CQC or CQC-r chart is a better choice as they are easy to design and implement, and have relatively good ATS performance. Besides, if the focus is only on process deteriorations, and the users can predict the intended possible shift ! to a good precision according to past data or other information, the exponential CUSUM or EWMA charts will be a more efficient tool especially when the shift is small. The CQC-r charts can also be employed to detect relatively large deterioration. Although the ATS performance of the CQC and CQC-r charts is not absolutely better than that of the exponential EWMA and CUSUM charts, the flexible and easy design procedures of the CQC and CQC-r charts make them more convenient for practical implement especially for on-line process monitoring.