The sample mean and ranges for 20 samples, each of size n = 10, from a manufacturing process are provided below. Sample Range | Mean Sample Range | Mean 1 2.450 19.256 11 2.098 19.587 2 3.941 19.857 12 3.428 22.777 3 2.686 20.141 13 2.845 20.709 4 1.336 22.819 14 3.253 20.821 5 3.429 19.836 15 2.994 20.654 6 1.706 21.500 16 3.440 20.193 7 3.786 21.252 17 3.239 22.730 8 1.704 19.953 18 4.383 21.152 9 1.724 22.196 19 3.824 20.880 10 1.204 19.760 20 2.391 19.315 Download CSV Table of Control Chart Constants Report answers accurate to 3 decimal places. Do not round intermediate results. a) The lower and upper control limits for the R-chart are: LCL= 0.575 UCL = 4.580 Does it appear that the process range is out of control? Yes. There is at least one point outside the control limits. No. There is no point outside the control limits. Yes. There is no point outside the control limits. No. There is at least one point outside the control limits. b) The lower and upper control limits for the z-chart are: LCL = 20.579 UCL = 22.166 Does it appear that the process mean is out of control? O No. There is no point outside the control limits. O Yes. There is no point outside the control limits. No. There is at least one point outside the control limits. Yes. There is at least one point outside the control limits. 12 0.266 0.283 1.717 13 0.249 0.307 1.693 14 0.235 0.328 1.672 15 0.223 0.347 1.653 16 0.212 0.363 1.637 17 0.203 0.378 1.622 18 0.194 0.391 1.609 19 0.187 0.404 1.596 20 0.180 0.415 1.585 21 0.173 0.425 1.575 22 0.167 0.435 1.565 23 0.162 0.443 1.557 24 0.157 0.452 1.548 25 0.153 0.459 1.541 Report answers accurate to 3 decimal places. Do not round intermediate results. a) The lower and upper control limits for the R-chart are: LCL = 4.955 x UCL = 0.622 Does it appear that the process range is out of control? Yes. There is at least one point outside the control limits. No. There is no point outside the control limits. O Yes. There is no point outside the control limits. No. There is at least one point outside the control limits. b) The lower and upper control limits for the 2-chart are: LCL = 21.628 x UCL 19.911 x Does it appear that the process mean is out of control? No. There is no point outside the control limits. Yes. There is no point outside the control limits. No. There is at least one point outside the control limits. Yes. There is at least one point outside the control limits. Table of Control Chart Constants Sample Size A2 D3 DA 2 1.880 0 3.267 m4 3 1.023 0 2.575 4 0.729 0 2.282 5 0.577 0 2.114 10 6 0.483 0 2.004 7 0.419 0.076 1.924 8 0.373 0.136 1.864 9 0.337 0.184 1.816 10 0.308 0.223 1.777 11 0.285 0.256 1.744 2 12 13 m4 0.266 0.283 1.717 0.249 0.307 1.693 14 0.235 0.328 1.672 15 0.223 0.347 1.653 16 0.212 0.3631.637 17 0.203 0.378 |1.622 18 0.194 0.391 1.609 19 0.187 0.404 1.596 20 0.180 0.415 1.585 21 0.173 0.425 1.575 22 0.167 0.435 1.565 23 0.162 0.443 1.557 24 0.157 0.452 1.548 25 0.153 0.459 1.541