ENBIS-17 in Naples

9 – 14 September 2017; Naples (Italy) Abstract submission: 21 November 2016 – 10 May 2017

Self-Starting Control Charts and their Accurate Run-Length Distributions

13 September 2017, 10:10 – 10:30


Submitted by
Seiichi Yasui
Yoshiaki Kunikawa (Tokyo University of Science), Seiichi Yasui (Tokyo University of Science)
When monitoring processes by control charts, it is necessary to estimate control limits. However, in small-lot production, it is difficult to obtain sufficient data so as to obtain accurate estimates of control limits because it is required to start monitoring quickly. Thus, self-starting control charts have been proposed. Many have proposed as Shewhart, CUSUM, and EWMA types. The plotted values in these charts are constructed by the inverse cumulative normal distribution function of the probability integral transformation of the standardized residuals that are obtained from the accumulated data which have judged as in-control. We propose new two self-starting control charts in which the statistics for subgroups are directly plotted without any transformation as well as the conventional control charts. However, the control limits in our charts are obtained by weighted average of previous control limits.
In general, occurance of the out-of-control signal for a certain plot is not independent of those for any other previous plot in self-staring control charts. This is the reason why the data judged as in-control is incorporated with the last control limits to judge the next plot. As a result, though simulation is used to determine appropriate control limits, we are able to analytically calculate control limits of proposed charts and Q type control charts.
In this paper, it is demonstrated to derive exact run length distributions for proposed control charts and Q type control charts (Start-up Shewhart Xbar charts) which allow for proper control for the desired in-control ARL, and the performance is evaluated.
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