91影视

There could be four total relevant charts\( - S\)chart,\(R\)chart,\(\bar X\)chart based on\(\bar s\)and\(\bar X\)chart based on\(\bar r\). See the definition of corresponding charts in the book.

\(S\)chart:

\(LCL = 15.4615 - \frac{{3 \times 15.4615\sqrt {1 - 0.95{2^2}} }}{{0.962}} = 15.4615 - 14.9141 = 0.55\)\(UCL = 15.4615 + \frac{{3 \times 15.4615\sqrt {1 - 0.95{2^2}} }}{{0.962}} = 15.4615 + 14.9141 = 30.37\)

\(R\)chart:

\(\begin{array}{l}LCL = 41.31 - \frac{{3 \times 0.848 \times 41.31}}{{2.536}} = 41.31 - 41.44\mathop = \limits^{(1)} 0\\UCL = 41.31 + \frac{{3 \times 0.848 \times 41.31}}{{2.536}} = 41.31 + 41.44 = 82.75\end{array}\)

\(\bar X\)chart based on\(\bar s\):

\(\begin{array}{l}LCL = 422.31 - \frac{{3 \cdot 15.4615}}{{0.952 \cdot \sqrt 6 }} = 402.42\\UCL = 422.31 + \frac{{3 \cdot 15.4615}}{{0.952 \cdot \sqrt 6 }} = 442.20\end{array}\)

\(\bar X\)chart based on\(\bar r\):

\(\begin{array}{l}LCL = 422.31 - \frac{{3 \cdot 41.3077}}{{2.536 \cdot \sqrt 6 }} = 402.36\\UCL = 422.31 + \frac{{3 \cdot 41.3077}}{{2.536 \cdot \sqrt 6 }} = 442.26.\end{array}\)

(1): when \( \le 0\) set it to zero.

Compute \(LCL\)and \(UCL\) for four different charts.