非对称极差控制图研究

Study on Asymmetrical Range Charts

  • 摘要: 本文针对现有的国家标准极差控制图的一些问题,在极差的统计性质的基础上,提出了非对称极差控制图的想法,并构造了三种不同的非对称极差控制图,分别给出了报警率达到0.27%时的上、下控制限系数,使得它们的控制限计算非常简便易行.本文给出了这三种非对称极差控制图的含义和各自的侧重点,并将它们与国家标准的极差控制图在对应检验的势函数以及平均运行长度两个方面进行了比较.使用这三种非对称极差控制图可以使真实报警率达到0.27%,远小于现有的国家标准极差控制图的真实报警率.无偏控制图由于具有了"无偏"这一优良性质,成为三张非对称控制图中最具吸引力的.

     

    Abstract: The range chart of National Standard is symmetrical and based on "3σ" principle of normal distribution. We proposed the idea of asymmetrical range chart based on the statistical characteristics of range in this article, constructed three types of asymmetrical range charts and worked out their coefficients of upper and lower control limits at the alert rate of 0.27%. In practice, engineers can use these results very easily. These three types of asymmetrical range charts have their own characters, which were introduced in this article. We also compared them with the range chart of National Standard in the respects of power function and Average Run Length (ARL). We can make the alert rate of the three types of asymmetrical range charts reach 0.27%, which is much lower than the one of range chart of National Standard. Unbiased control chart is the most attractive because of the good characteristic of unbias.

     

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