Question

Problem 1 A restaurant wants to control kitchen preparation time of dinner meals using an X chart. The process standard deviation is unknown. Each evening a manager takes a random sample of 14 dinner orders and measures and records their kitchen preparation time. Create an X Chart using data in the table below with recorded times in minutes) for the last 18 evening samples. (Note- a sample spreadsheet layout is attached at the end of this document] Evening X-Bar LOL UCL 1 109 2 2 18.9 9.8 15.8 16.9 4 5 6 7 8 16.B 18.3 19.B 13.7 10.7 23.1 18.6 15.6 17.1 12.9 13.2 9.2 15.8 22.4 20.8 16.3 14.7 20.5 11.6 17.3 12.8 14.8 23.4 16.3 18.6 13.6 15.1 28.4 26.5 15.6 17.2 16.2 17 19.5 17.6 20.3 17.1 16.9 12.4 12 17.2 15 20.2 14.4 19.3 20 20.1 18.1 15.3 20.4 25.3 16.8 24.8 17.1 16.9 18.8 20,6 16.5 18.1 19 17.1 13.7 17.2 18.7 13.3 21.9 13.3 17.9 18.1 15.9 13.2 17.6 16.2 27.4 21.6 Dinner Meal Preparation Time (minutes) 19.7 17.7 13.7 14.4 17.7 18.91 11.4 18.8 14.B 16.1 14.5 17.2 13.9 18.4 19.9 13.9 24.4 19.7 20.3 20.9 19.6 20.4 19.2 14.5 18.7 13.8 19,8 18.9 12.8 18 25 16.9 12.2 13.1 14.3 16.5 16.5 16.4 19.3 14.4 19.3 24 18.7 18 15.4 14.8 13.5 24.2 20.2 15.6 20.3 18.5 10.4 16.1 17.6 16.5 19.7 21.7 21.4 20 19.1 11 24.2 17.5 22 24.4 16.2 19.a 23.6 26 25.9 23.5 9 10 11 12 13 14 15 16 14.3 13.B 9.6 12.6 13 121 15.8 11.2 12.7 20.4 18.4 17.4 18.1 16.1 20.7 12.6 22.7 22.6 16.3 19.9 21 15.7 9.8 20.5 16.8 14.2 14.2 17.2 14.7 24.7 12.4 13.6 20.6 16.9 17.9 21.4 20.2 19.2 23.3 12.9 24.6 16.1 14.6 13.41 17.1 12.4 12.6 24.6 16.5 15.6 19.4 19.3 15.4 18.3 20.5 10.2 18.3 12 11.2 15.1 15.5 11.8 12.9 14.1 11.3 18.2 R 15.62 17.26 17.40 16.23 17.49 17.65 17.41 15.54 16.15 15.39 16.16 15.4 19 16.4 18.4 15.1 16.3 17.1 15.6 20.2 19.9 23.3 25.3 24.6 24.8 20.5 25 21.9 20.6 24 24.7 25.5 23.4 21.7 24.2 28.4 26.5 17.60 18.4 25.5 17 15.9 15.5 25.5 18.7 13.5 13.9 10.1 23.4 13.1 17.2 19.6 23.8 16.52 16.78 17.25 16.21 21.71 13.8 12.5 22 24.7 17 18 11.6 20.2 17.9 18.4 24.11 22.89 a.) why shoushould an X chart be use? N AZ X-Dbl Bar R- Bar LCL UCL 17.29 23.58

can u clearly show me how to find a sample size (N) , A2, and can you also tell me why we are using an X Chart?

Answer 1

For measuring continuous data like weight,size,any other measurement which need to be continuous monitored to address the performance of the manufacturing process and thus to reduce the variability and defect in the manufacturing system.

solution as attached Below

UCL and LCL are the Upper and lower limits were the X double bar is the mean of all the observations.

UCL = X Double Bar + (A2 x R-bar) = 17.29 + (0.194 * 23.58) = 21.86 Number of Observations Sample (N) = 18 LCL = X Double bar -(A2 x R-bar) = 17.29 - (0.194 * 23.58) = 12.72 Sample 1 2 3 K double bar =17.29 R bar = 23.58 Given Here A2 is the constant with respect to N number of samples 4 From Attached Table value of A2 (N-18) = 0.194 5 6 N A2 A, d2 D D4 B3 B4 8 9 10 11 12 13 14 15 2 3 4 5 6 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 0 0 O O 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 O 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 16 17 18