% <html><head><title>Factors for Control Charts</title>

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  \begin{tabular}{|r|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
    \multicolumn{16}{c}
    {\textbf{Factors useful in the Construction of Control Charts}} \\
    \multicolumn{16}{c}{\ } \\
    \hline
    & \multicolumn{3}{c|}{\textit{Chart for}}
    & \multicolumn{5}{c|}{\textit{Chart for standard deviations}} 
    & \multicolumn{7}{c|}{\textit{Chart for Ranges}} \\
    & \multicolumn{3}{c|}{\textit{Averages}} 
    & \multicolumn{5}{c|}{\ } & \multicolumn{7}{c|}{\ } \\ \hline
    & \multicolumn{3}{c|}{\ } & \multicolumn{5}{c|}{\textit{Factors for:}} 
    & \multicolumn{2}{c|}{\ } & \multicolumn{5}{c|}{\ } \\
      \cline{5-9}
    & \multicolumn{3}{c|}{\textit{Factors for}} & \textit{Central}
    & \multicolumn{4}{c|}{\textit{Control Limits}} 
    & \multicolumn{2}{c|}{\textit{Factors for}}
    & \multicolumn{5}{c|}{\textit{Factors for Control Limits}} \\
    & \multicolumn{3}{c|}{\textit{Control Limits}} & \textit{Line} 
    & \multicolumn{4}{c|}{\ } 
    & \multicolumn{2}{c|}{\textit{Central Line}} 
    & \multicolumn{5}{c|}{\ } \\ \hline
       &       &        &       &       &       &       &       &
       &       &        &       &       &       &       &       \\
    n & A & A$_2$ & A$_3$ & c$_4$ & B$_3$ & B$_4$ & B$_5$ & B$_6$ 
      & d$_2$ & 1/d$_2$ & d$_3$ & D$_1$ & D$_2$ & D$_3$ & D$_4$ \\
       &       &        &       &       &       &       &       &
       &       &        &       &       &       &       &       \\
     2 & 2.121 & 1.880 & 2.659 & 0.7979 &   0   & 3.267 &   0   & 2.606
       & 1.128 & 0.8862 & 0.852 &   0   & 3.686 &   0   & 3.266 \\
     3 & 1.732 & 1.023 & 1.954 & 0.8862 &   0   & 2.568 &   0   & 2.276
       & 1.693 & 0.5908 & 0.888 &   0   & 4.357 &   0   & 2.574 \\
     4 & 1.500 & 0.729 & 1.628 & 0.9213 &   0   & 2.266 &   0   & 2.088
       & 2.059 & 0.4857 & 0.879 &   0   & 4.697 &   0   & 2.281 \\
     5 & 1.342 & 0.577 & 1.427 & 0.9400 &   0   & 2.089 &   0   & 1.964
       & 2.326 & 0.4299 & 0.864 &   0   & 4.918 &   0   & 2.114 \\
       &       &        &       &       &       &       &       &
       &       &        &       &       &       &       &       \\
     6 & 1.225 & 0.483 & 1.287 & 0.9515 & 0.030 & 1.970 & 0.029 & 1.874
       & 2.534 & 0.3946 & 0.848 &   0   & 5.078 &   0   & 2.003 \\
     7 & 1.134 & 0.419 & 1.182 & 0.9594 & 0.118 & 1.882 & 0.113 & 1.806
       & 2.704 & 0.3698 & 0.833 & 0.206 & 5.203 & 0.076 & 1.924 \\
     8 & 1.061 & 0.373 & 1.099 & 0.9650 & 0.185 & 1.815 & 0.179 & 1.751
       & 2.847 & 0.3512 & 0.819 & 0.389 & 5.306 & 0.137 & 1.863 \\
     9 & 1.000 & 0.337 & 1.032 & 0.9693 & 0.239 & 1.761 & 0.232 & 1.707
       & 2.970 & 0.3367 & 0.807 & 0.548 & 5.392 & 0.184 & 1.816 \\
    10 & 0.949 & 0.308 & 0.975 & 0.9727 & 0.284 & 1.716 & 0.276 & 1.669
       & 3.078 & 0.3249 & 0.797 & 0.688 & 5.467 & 0.223 & 1.777 \\
       &       &        &       &       &       &       &       &
       &       &        &       &       &       &       &       \\
    11 & 0.905 & 0.285 & 0.927 & 0.9754 & 0.321 & 1.679 & 0.313 & 1.637
       & 3.173 & 0.3152 & 0.787 & 0.813 & 5.533 & 0.256 & 1.744 \\
    12 & 0.866 & 0.266 & 0.886 & 0.9776 & 0.354 & 1.646 & 0.346 & 1.610
       & 3.258 & 0.3069 & 0.778 & 0.924 & 5.593 & 0.284 & 1.716 \\
    13 & 0.832 & 0.249 & 0.850 & 0.9794 & 0.382 & 1.618 & 0.374 & 1.585
       & 3.336 & 0.2998 & 0.770 & 1.026 & 5.646 & 0.307 & 1.693 \\
    14 & 0.802 & 0.235 & 0.817 & 0.9810 & 0.406 & 1.594 & 0.399 & 1.563
       & 3.407 & 0.2935 & 0.763 & 1.119 & 5.695 & 0.328 & 1.672 \\
    15 & 0.775 & 0.223 & 0.789 & 0.9823 & 0.428 & 1.572 & 0.421 & 1.544
       & 3.472 & 0.2880 & 0.756 & 1.204 & 5.739 & 0.347 & 1.653 \\
       &       &        &       &       &       &       &       &
       &       &        &       &       &       &       &       \\
    16 & 0.750 & 0.212 & 0.763 & 0.9835 & 0.448 & 1.552 & 0.440 & 1.526
       & 3.532 & 0.2831 & 0.750 & 1.283 & 5.781 & 0.363 & 1.637 \\
    17 & 0.728 & 0.203 & 0.739 & 0.9845 & 0.466 & 1.534 & 0.458 & 1.511
       & 3.588 & 0.2787 & 0.744 & 1.357 & 5.819 & 0.378 & 1.622 \\
    18 & 0.707 & 0.194 & 0.718 & 0.9854 & 0.482 & 1.518 & 0.475 & 1.496
       & 3.640 & 0.2747 & 0.738 & 1.425 & 5.855 & 0.392 & 1.608 \\
    19 & 0.688 & 0.187 & 0.698 & 0.9862 & 0.497 & 1.503 & 0.490 & 1.483
       & 3.689 & 0.2711 & 0.733 & 1.490 & 5.888 & 0.404 & 1.596 \\
    20 & 0.671 & 0.180 & 0.680 & 0.9869 & 0.510 & 1.490 & 0.504 & 1.470
       & 3.735 & 0.2677 & 0.728 & 1.550 & 5.920 & 0.415 & 1.585 \\
       &       &        &       &       &       &       &       &
       &       &        &       &       &       &       &       \\
    21 & 0.655 & 0.173 & 0.663 & 0.9876 & 0.523 & 1.477 & 0.516 & 1.459
       & 3.778 & 0.2647 & 0.724 & 1.607 & 5.950 & 0.425 & 1.575 \\
    22 & 0.640 & 0.167 & 0.647 & 0.9882 & 0.534 & 1.466 & 0.528 & 1.448
       & 3.819 & 0.2618 & 0.719 & 1.661 & 5.978 & 0.435 & 1.565 \\
    23 & 0.626 & 0.162 & 0.633 & 0.9887 & 0.545 & 1.455 & 0.539 & 1.438
       & 3.858 & 0.2592 & 0.715 & 1.712 & 6.004 & 0.444 & 1.556 \\
    24 & 0.612 & 0.157 & 0.619 & 0.9892 & 0.555 & 1.445 & 0.549 & 1.429
       & 3.895 & 0.2567 & 0.712 & 1.761 & 6.030 & 0.452 & 1.548 \\
    25 & 0.600 & 0.153 & 0.606 & 0.9896 & 0.565 & 1.435 & 0.559 & 1.420
       & 3.931 & 0.2544 & 0.708 & 1.807 & 6.055 & 0.460 & 1.540 \\
       &       &        &       &       &       &       &       &
       &       &        &       &       &       &       &       \\
    Over 25 & $3/\sqrt{n}$ & $3/d_2\sqrt{n}$ & $\cdots$ & $\cdots$ & * & ** 
       & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ 
       & $\cdots$ & $\cdots$ & $\cdots$ \\ \hline
  \end{tabular}
  \[ *\ 1-\frac{3}{\sqrt{2n}} \qquad\qquad\qquad\qquad
     \text{**}\ 1+\frac{3}{\sqrt{2n}} \]
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