Question

In order to establish a control chart for the mean of a process, 20 samples each of size 4 are collected. We note that 7: = 4000 and = 500. The value of the lower controllimit of the chart for the mean is approximately equal to 195.5. True False

Answer 1

Here we have 20 x = Z x 4000 20 200 20 I=1 20 s = Z si= 500 25 - ! 20 20 Now we know when standards are are not given lower control limit of mean is given as X - Az lower control limit = X - A35 200 - (1.628 x 25) 159.3 wher (A3 = 1.628 from table of control chart constants) for sample size 4 = A3 = 1.628 Hence lower control limit is 1593 and not 195.5 Hence it is false CS Scanned with CamScannen

Table of Control Chart Constants R Chart Constants S Chart Constants X-bar Chart Constants for sigma estimate A2 A3 d2 D3 D4 B3 B4 0 Sample Size = m 2 3 4 5 0 0 0 0 6 0 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1.880 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 0.285 0.266 0.249 0.235 0.223 0.212 0.203 0.194 0.187 0.180 0.173 0.167 0.162 0.157 0.153 2.659 1.954 1.628 1.427 1.287 1.182 1.099 1.032 0.975 0.927 0.886 0.850 0.817 0.789 0.763 0.739 0.718 0.698 0.680 0.663 0.647 0.633 0.619 0.606 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078 3.173 3.258 3.336 3.407 3.472 3.532 3.588 3.640 3.689 3.735 3.778 3.819 3.858 3.895 3.931 0.076 0.136 0.184 0.223 0.256 0.283 0.307 0.328 0.347 0.363 0.378 0.391 0.403 0.415 0.425 0.434 0.443 0.451 0.459 3.267 2.574 2.282 2.114 2.004 1.924 1.864 1.816 1.777 1.744 1.717 1.693 1.672 1.653 1.637 1.622 1.608 1.597 1.585 1.575 1.566 1.557 1.548 1.541 0 0 0 0.030 0.118 0.185 0.239 0.284 0.321 0.354 0.382 0.406 0.428 0.448 0.466 0.482 0.497 0.510 0.523 0.534 0.545 0.555 0.565 3.267 2.568 2.266 2.089 1.970 1.882 1.815 1.761 1.716 1.679 1.646 1.618 1.594 1.572 1.552 1.534 1.518 1.503 1.490 1.477 1.466 1.455 1.445 1.435