The Effects to VSSI X Chart When Control Limits Are Estimated

估计控制限对VSSI X控制图的影响

10.6338/JDA.200906_4(3).0001

周茂袁(Mao-Yuan Zhou)；王秀丽(Xiu-Li Wang)；李雪艳(Xue-Yan Li)

平均报警时间 ； 可变样本容量和抽样区间的X控制图 ； 参数估计 ； Average Time to Signal ； Variable Sample Size and Sampling interval X charts ； Parameter Estimation

Journal of Data Analysis

4卷3期（2009 / 06 / 01）

1 - 13

英文

关于VSSI X控制图的理论结果都是在过程统计量的均值和方差已知的前提下考虑的。但是，在实际中过程统计量的均值和方差都是未知的。在这种情况下，一般的处理方法就是利用历史数据对未知参数进行估计。到目前为止，当控制限被估计时，我们对VSSI X控制图的平均报警时间（ATS）会受到怎样的影响还不甚了解。本文将计算VSSI X控制图的控制限被估计时，其ATS的期望值。计算结果表明，参数估计对受控情况下的ATS有显著的影响，而对失控情况下的ATS却影响不大。这些结果将有助于我们选择历史数据的样本数m和样本容量n。

The theoretical results about VSSI X charts are concerned with the case in which the mean and the standard deviation of the given process characteristic are known. However, in practice the mean and standard deviation are unknown. In this case, the common treatment is to estimate the unknown parameters using historical data.Up to now we have no idea about the average time to signal (ATS) of VSSI X charts when the control limits are estimated. This paper will calculate the mean of the ATS for VSSI X charts with estimated limits.The result shows that parameter estimation has significant effect on the in-control ATS of the chart, but has little effect on the out-of-control ATS. These results could show us some good reference idea for choosing adequate number of sample groups m and the sample size n of historical data.

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