<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">% &lt;html&gt;&lt;head&gt;&lt;title&gt;Factors for Control Charts&lt;/title&gt;

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