91影视

The\(p\)chart for the fraction of defective items has lower and upper control limits given by

\(\begin{aligned}{*{20}{r}}{LCL = \bar p - 3\sqrt {\frac{{\bar p(1 - \bar p)}}{n}} }\\{UCL = \bar p + 3\sqrt {\frac{{\bar p(1 - \bar p)}}{n}} ,}\end{aligned}\)

and the center line is\(\bar p\). When\(LCL \le 0\)it is set to zero.

The center line, from the fact that

\(\sum\limits_{i = 1}^k {{{\hat p}_i}} = \frac{{{x_1} + {x_2} + \ldots + {x_k}}}{n} = \frac{{567}}{{200}} = 2.835,\)

is given by

\(\bar p = \frac{{2.835}}{{30}} = 0.0945.\)

0The\(LCL\)is

\(\begin{aligned}{l}LCL = \bar p - 3\sqrt {\frac{{\bar p(1 - \bar p)}}{n}} = 0.0945 - 3 \cdot \sqrt {\frac{{0.0945 \cdot (1 - 0.0945)}}{{200}}} \\ = 0.0325.\end{aligned}\)

The\(UCL\)is

\(\begin{aligned}{l}UCL = \bar p + 3\sqrt {\frac{{\bar p(1 - \bar p)}}{n}} = 0.0945 + 3 \cdot \sqrt {\frac{{0.0945 \cdot (1 - 0.0945)}}{{200}}} \\ = 0.1565\end{aligned}\)

There is one out-of-control point, on the fifth day, because

\(\frac{{37}}{{200}} > 0.1565 = UCL\)