91影视

See the text for the transformation. Mean value of the given transformation

\(Y = h(X) = 2\sqrt X \)

is given by

\(2\sqrt \mu \)

and variance\(1.\)

The values using the transformation\(Y\)are

\(\begin{aligned}{*{20}{c}}i&{2\sqrt {{x_i}} }\\1&{3.46}\\2&{5.29}\\3&{4.47}\\4&{3.46}\\5&{4.00}\\6&{2.83}\\7&{5.66}\\8&{4.00}\\9&{3.46}\\{10}&{3.46}\\{11}&{4.90}\\{12}&{5.29}\\{13}&{2.83}\\{14}&{3.46}\\{15}&{2.83}\\{16}&{4.00}\\{17}&{5.29}\\{18}&{3.46}\\{19}&{2.83}\\{20}&{4.00}\\{21}&{4.00}\\{22}&{2.00}\\{23}&{4.47}\\{24}&{4.00}\\{25}&{4.90}\\{}&{}\end{aligned}\)

The center line, from the fact that

\(\sum\limits_{i = 1}^k {{{\hat y}_i}} = 98.37\)

is given by

\(\bar y = \frac{{98.37}}{{25}} = 3.93\)

The\(LCL\)is

\(\begin{aligned}{l}LCL = \bar y - 3 \cdot 1 = 3.93 - 3 \cdot 1\\ = 0.93\end{aligned}\)

The\(UCL\)is

\(\begin{aligned}{l}UCL = \bar y + 3 \cdot 1 = 3.93 - 3 \cdot 1\\ = 6.93\end{aligned}\)

There are two points out of the limits, first one is \(0.18819\)which is lower than the \(LCL\) and \(0.44462\) which is higher than the \(UCL\).

The process is in-control.