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X-charts versus X/MR chart combinations: IID cases and non-IID cases

机译:X图表与X / MR图表组合:IID案例和非IID案例

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There has been a lot of discussion regarding these two process monitoring schemes. (Refs. 1, 2) discussed the computation of ARL for complied individual measurement and moving range charts under iid model assumptions. For the iid cases, the following has been observed. The X-chart alone (X-only chart) is better than the X - MR chart combinations in detecting changes in the process mean (Case 1). For cases where the process standard deviation changes (Case 2), the X/MR chart can be slighlty better than the X-chart alone. In the case where both process mean and process standard deviation change (Case 3), the X-only chart is better than the X/MR chart combinations. Although the X-only chart can be better, the improvement in the off-target ARLs for both Cases 2 and 3 is not large (coming in only the third decimalplace or beyqnd. If we round the results to the closest integer value, typically both will be/rounded to the same value. Therefore, in general, it is rounded to the same value. Therefore, in general, we can say the X/MR chart combinations are nearly as efficient as the X-chart alone in detecting changes involving the process standard deviation. (The two monitoring schemes are about equally effective in detecting simultaneous changes in both process mean and process standard deviation. (Ref. 3) discussed several options in designinga Shewhart-type for individual observations and concluded that adding a moving range charge to an individual chart provides no real improvement. For R large, the monitoring scheme is essentially the individual chart alone (Ref. 4).
机译:关于这两个过程监视方案已经进行了很多讨论。 (参考文献1、2)讨论了在iid模型假设下针对已编译的单独测量和移动范围图的ARL的计算。对于iid情况,观察到以下情况。在检测过程平均值的变化方面(案例1),单独使用X图表(仅X图表)要好于X-MR图表组合。对于过程标准偏差发生变化的情况(案例2),X / MR图表的清晰度可能比单独的X图表更好。在过程均值和过程标准偏差都发生变化的情况下(案例3),仅X图表优于X / MR图表组合。尽管仅X的图表可能更好,但是情况2和情况3的脱靶ARL的改善并不大(仅出现在小数点后三位或beyqnd中。如果将结果四舍五入到最接近的整数值,通常情况下都是将被四舍五入为相同的值,因此,通常将其四舍五入为相同的值,因此,通常来说,我们可以说X / MR图组合在检测涉及(过程标准偏差)(这两种监视方案在检测过程均值和过程标准偏差的同时变化方面都具有同等效力。(参考文献3)讨论了设计Shewhart型用于个别观察的几种方法,并得出结论,增加移动范围对单个图表收取费用并没有真正的改善,对于R large而言,监视方案本质上仅是单个图表(参考文献4)。

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