基于Cornish-Fisher展开的稳健综合控制图设计

本文根据Cornish-Fisher展开, 对Shewhart $ol X$控制图的上下控制限进行修正并拓展为前四阶矩有关的表达式,使之可以运用到任何分布类型上, 然后构造出基于这种展开的综合控制图,最后通过计算机模拟计算给出了一些具体的包含对称、厚尾、轻尾和偏斜等分布类型下受控和失控的平均运行长度结果,并且与传统的综合控制图(见cite{1})结果做比较,从而得到新控制图更为稳健的结论.

A Synthetic Control Chart Based on Cornish-FisherExpansion

According to Cornish-Fisher expansion, the control limits of Shewhart $ol X$ control chart were constructed with up to the fourth moment (The moments are estimated from the in-control historical samples when the process distribution isunknown, and no further assumptions are made on the distribution). Then we made a synthetic control chart based on the Cornish-Fisher expansion. The in-control ARL's (average run length) and out-of-control ARL's of the new chart builded here were evaluated to compare with synthetic control chart (see cite{1}) when the process distribution is Student-t, Weibull, Lognormal and Burr. Simulation results show that the new control chart is more robust than theother methods.