分位数控制图中分位数的估计与选择的研究与改进

Improved Design on Nonparametric Quantile-based Control Charts

针对分位数控制图应用中分位点的估计和分位点个数的选取进行了研究和改进,引入非参数平稳估计并进行窗宽调整、研究适合小样本条件分布未知时分位数点的有效估计;此外,提出构造分位数控制图新的准则,选取最优的分位点和分位点个数构造卡方检验统计量。通过模拟计算和比较,改进的分位数控制图方案更加有效和灵敏.最后通过MC模拟编制小样本情形的控制限表,为分位数控制图的应用提供参考依据。

It is about investigating and improving the design of quantile-based control charts. Firstly, it is a smooth nonparametric estimator of a quantile function that is introduced and the window width should be adjusted to obtain the effective estimation of quantiles in the case of small sample size when the distribution is free. Secondly, it is a new criterion of test power that is proposed in order to make optimal choice of the quantiles. Simulation results confirm the high efficiency of the improved nonparametric quantile-based control chart. To provide guidance for application, the control limits table also is calculated in the small sample size by Monte Carlo simulation.