P chart

Statistics

我的想法

中文名叫做属性控制图，思路跟 x chart 类似的。比较大的区别是 P chart 讨论的是 proportion

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Step

First, calculate their average, whether the sample is fail or not?

$$\overline{p}=\frac{{\sum }_{j=1}^k{\hat{p}}_j}{k}$$

Equations

The center line is $\overline{p}$

Lower control limit = $\overline{p}-3\sqrt{\frac{\overline{p}(1-\overline{p})}{n}}$

Upper control limit = $\overline{p}+3\sqrt{\frac{\overline{p}(1-\overline{p})}{n}}$

If the lower control limit is negative (seems to be very familiar) set it to be 0.

Pattern test

Like the one in the x chart, we also have pattern test to test whether we can say the fail rate.

Reference