The data shown in Table below are the deviations from nominal diameter for holes drilled in a carbon-fiber composite material used in aerospace manufacturing. The values reported are deviations from nominal in tenthousands of an inch. a) Set up xbar and R charts on the process. Is the process in statistical control? (xbar charts- 15 points and R charts15 points) b) Estimate the process standard deviation using the range method. (10 points) c) If specifications are at nominal +/100, what can you say about the capability of this process? Calculate the PCR Cp. (10 points) Problem 1 - Table Factors for Constructing Variables Control Charts \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \multirow{3}{*}{ObservationsinSample,n} & \multicolumn{5}{|c|}{ Chart for Averages } & \multicolumn{6}{|c|}{ Chart for Standard Deviations } & \multicolumn{5}{|c|}{ Chart for Ranges } \\ \hline & \multicolumn{3}{|c|}{FactorsforControlLimits} & \multicolumn{2}{|c|}{FactorsforCenterLine} & \multicolumn{4}{|c|}{ Factors for Control Limits } & \multicolumn{2}{|c|}{FactorsforCenterLine} & \multicolumn{5}{|c|}{ Factors for Control Limits } \\ \hline & A & A2 & A3 & c4 & 1/c4 & B3 & B4 & B5 & B6 & d2 & 1/d2 & d3 & D1 & D2 & D3 & D4 \\ \hline 2 & 2.121 & 1.880 & 2.659 & 0.7979 & 1.2533 & 0 & 3.267 & 0 & 2.606 & 1.128 & 0.8865 & 0.853 & 0 & 3.686 & 0 & 3.267 \\ \hline 3 & 1.732 & 1.023 & 1.954 & 0.8862 & 1.1284 & 0 & 2.568 & 0 & 2.276 & 1.693 & 0.5907 & 0.888 & 0 & 4.358 & 0 & 2.574 \\ \hline 4 & 1.500 & 0.729 & 1.628 & 0.9213 & 1.0854 & 0 & 2.266 & 0 & 2.088 & 2.059 & 0.4857 & 0.880 & 0 & 4.698 & 0 & 2.282 \\ \hline 5 & 1.342 & 0.577 & 1.427 & 0.9400 & 1.0638 & 0 & 2.089 & 0 & 1.964 & 2.326 & 0.4299 & 0.864 & 0 & 4.918 & 0 & 2.114 \\ \hline 6 & 1.225 & 0.483 & 1.287 & 0.9515 & 1.0510 & 0.030 & 1.970 & 0.029 & 1.874 & 2.534 & 0.3946 & 0.848 & 0 & 5.078 & 0 & 2.004 \\ \hline 7 & 1.134 & 0.419 & 1.182 & 0.9594 & 1.0423 & 0.118 & 1.882 & 0.113 & 1.806 & 2.704 & 0.3698 & 0.833 & 0.204 & 5.204 & 0.076 & 1.924 \\ \hline 8 & 1.061 & 0.373 & 1.099 & 0.9650 & 1.0363 & 0.185 & 1.815 & 0.179 & 1.751 & 2.847 & 0.3512 & 0.820 & 0.388 & 5.306 & 0.136 & 1.864 \\ \hline 9 & 1.000 & 0.337 & 1.032 & 0.9693 & 1.0317 & 0.239 & 1.761 & 0.232 & 1.707 & 2.970 & 0.3367 & 0.808 & 0.547 & 5.393 & 0.184 & 1.816 \\ \hline 10 & 0.949 & 0.308 & 0.975 & 0.9727 & 1.0281 & 0.284 & 1.716 & 0.276 & 1.669 & 3.078 & 0.3249 & 0.797 & 0.687 & 5.469 & 0.223 & 1.777 \\ \hline 11 & 0.905 & 0.285 & 0.927 & 0.9754 & 1.0252 & 0.321 & 1.679 & 0.313 & 1.637 & 3.173 & 0.3152 & 0.787 & 0.811 & 5.535 & 0.256 & 1.744 \\ \hline 12 & 0.866 & 0.266 & 0.886 & 0.9776 & 1.0229 & 0.354 & 1.646 & 0.346 & 1.610 & 3.258 & 0.3069 & 0.778 & 0.922 & 5.594 & 0.283 & 1.717 \\ \hline 13 & 0.832 & 0.249 & 0.850 & 0.9794 & 1.0210 & 0.382 & 1.618 & 0.374 & 1.585 & 3.336 & 0.2998 & 0.770 & 1.025 & 5.647 & 0.307 & 1.693 \\ \hline 14 & 0.802 & 0.235 & 0.817 & 0.9810 & 1.0194 & 0.406 & 1.594 & 0.399 & 1.563 & 3.407 & 0.2935 & 0.763 & 1.118 & 5.696 & 0.328 & 1.672 \\ \hline 15 & 0.775 & 0.223 & 0.789 & 0.9823 & 1.0180 & 0.428 & 1.572 & 0.421 & 1.544 & 3.472 & 0.2880 & 0.756 & 1.203 & 5.741 & 0.347 & 1.653 \\ \hline 16 & 0.750 & 0.212 & 0.763 & 0.9835 & 1.0168 & 0.448 & 1.552 & 0.440 & 1.526 & 3.532 & 0.2831 & 0.750 & 1.282 & 5.782 & 0.363 & 1.637 \\ \hline 17 & 0.728 & 0.203 & 0.739 & 0.9845 & 1.0157 & 0.466 & 1.534 & 0.458 & 1.511 & 3.588 & 0.2787 & 0.744 & 1.356 & 5.820 & 0.378 & 1.622 \\ \hline 18 & 0.707 & 0.194 & 0.718 & 0.9854 & 1.0148 & 0.482 & 1.518 & 0.475 & 1.496 & 3.640 & 0.2747 & 0.739 & 1.424 & 5.856 & 0.391 & 1.608 \\ \hline 19 & 0.688 & 0.187 & 0.698 & 0.9862 & 1.0140 & 0.497 & 1.503 & 0.490 & 1.483 & 3.689 & 0.2711 & 0.734 & 1.487 & 5.891 & 0.403 & 1.597 \\ \hline 20 & 0.671 & 0.180 & 0.680 & 0.9869 & 1.0133 & 0.510 & 1.490 & 0.504 & 1.470 & 3.735 & 0.2677 & 0.729 & 1.549 & 5.921 & 0.415 & 1.585 \\ \hline 21 & 0.655 & 0.173 & 0.663 & 0.9876 & 1.0126 & 0.523 & 1.477 & 0.516 & 1.459 & 3.778 & 0.2647 & 0.724 & 1.605 & 5.951 & 0.425 & 1.575 \\ \hline 22 & 0.640 & 0.167 & 0.647 & 0.9882 & 1.0119 & 0.534 & 1.466 & 0.528 & 1.448 & 3.819 & 0.2618 & 0.720 & 1.659 & 5.979 & 0.434 & 1.566 \\ \hline 23 & 0.626 & 0.162 & 0.633 & 0.9887 & 1.0114 & 0.545 & 1.455 & 0.539 & 1.438 & 3.858 & 0.2592 & 0.716 & 1.710 & 6.006 & 0.443 & 1.557 \\ \hline 24 & 0.612 & 0.157 & 0.619 & 0.9892 & 1.0109 & 0.555 & 1.445 & 0.549 & 1.429 & 3.895 & 0.2567 & 0.712 & 1.759 & 6.031 & 0.451 & 1.548 \\ \hline 25 & 0.600 & 0.153 & 0.606 & 0.9896 & 1.0105 & 0.565 & 1.435 & 0.559 & 1.420 & 3.931 & 0.2544 & 0.708 & 1.806 & 6.056 & 0.459 & 1.541 \\ \hline \end{tabular} A=n3A3=c4n3c44n34(n1)B3=1c42(n1)3B4=1+c42(n1)3