91影视

The \(c\) chart for the number of defectives in a unit has lower and upper control limits given by

\(\begin{aligned}{l}LCL = \bar x - 3\sqrt {\bar x} \\UCL = \bar x + 3\sqrt {\bar x} ,\end{aligned}\)

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

The center line, from the fact that

\(\sum\limits_{i = 1}^k {{{\hat x}_i}} = \frac{{{x_1} + {x_2} + \ldots + {x_k}}}{n} = \frac{{587}}{{100}} = 102\)

is given by

\(\bar x = \frac{{102}}{{25}} = 4.08\)

The \(LCL\) is

\(\begin{aligned}{l}LCL = \bar x - 3\sqrt {\bar x} = 4.08 - 3 \cdot \sqrt {4.08} \\ = - 2\end{aligned}\)

so set it to zero\(LCL = 0\).

The\(UCL\) is

\(UCL = \bar x + 3\sqrt {\bar x} = 4.08 + 3 \cdot \sqrt {4.08} \)

\( = 10.1\)

From the \(c\) chart one can notice that the process is in-control - no data exceeds \(LCL\) and \(UCL\).