uality Control -- Assignment Problems. A. Note that there are three sets of data. Use the following data to construct one mean (x-bar) chart and one range chart (R-chart). Is the process in control? Sample # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 a 19.47 21.43 20.11 20.90 21.24 20.75 20.50 21.34 20.01 20.90 21.12 20.72 21.49 21.50 20.46 20.37 20.28 20.45 21.29 20.33 21.22 22.00 b 21.21 21.05 21.37 20.88 20.41 20.81 21.41 21.50 19.90 20.12 21.10 21.33 21.34 21.19 20.19 20.08 21.10 20.52 21.35 21.20 21.00 19.52 (Ounces, oz) c d e 20.51 21.19 21.21 21.46 21.48 21.05 19.89 20.18 21.37 20.59 21.10 20.88 20.15 21.50 20.41 21.43 21.34 20.81 21.12 20.10 21.41 21.75 21.45 21.50 20.67 20.90 19.90 20.82 20.73 20.12 20.13 20.71 21.10 22.04 21.39 21.33 21.18 21.50 21.34 21.34 20.19 21.19 20.57 21.03 20.19 21.00 20.87 20.08 20.47 20.59 21.10 21.47 21.41 20.52 21.29 21.28 21.35 20.25 20.98 21.20 20.56 20.54 21.00 20.76 21.38 19.52 f 22.00 21.07 19.98 20.22 19.52 20.97 19.67 21.84 20.76 21.33 20.86 19.65 21.38 20.54 21.01 20.67 20.46 20.37 20.28 20.45 21.29 20.33 B. After a number of complaints about its directory assistance, a telephone company examined samples of calls to determine the frequency of wrong numbers given to callers. Each sample conisted of 100 samples. Is the process stable (i.e, in control)? Determine 2-sigma control limits. Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Errors 5 3 5 7 4 6 8 4 5 9 3 4 5 6 6 7 5 4 8 2 C Given the following data for the number of defects per spool of cable, using three-sigma limit, is the process in control? Compute UCL and LCL. Observation No. of errors 1 2 2 4 3 1 4 0 5 1 6 3 7 2 8 0 9 2 10 1 11 3 12 3 13 2 14 1 15 5 X Bar Chart 1.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 3.06 3.04 3.06 3.00 3.00 3.06 3.00 3.00 3.10 3.00 3.00 3.06 3.06 3.06 3.00 2.00 3.00 3.06 3.09 3.06 3.00 3.00 3.09 3.00 3.00 3.04 3.00 3.00 3.06 3.06 3.06 3.00 3.06 3.06 3.00 3.06 3.00 3.00 3.06 3.00 3.00 3.04 3.05 3.06 3.06 3.06 3.00 4.00 3.06 3.05 3.06 3.06 3.00 3.00 3.06 3.00 3.10 3.00 3.07 3.09 3.06 3.06 3.06 5.00 3.00 3.05 3.00 3.06 3.06 3.00 3.00 3.00 3.05 3.05 3.00 3.06 3.06 3.13 3.16 x barbar 3.05 3.06 3.04 3.04 3.01 3.03 3.02 3.00 3.06 3.02 3.02 3.07 3.06 3.07 3.04 3.04 UCL X 3.04 + .58(.06) UCL = 3.075 LCL X 3.04 - (.58)(.06) LCL = 3 UCL R 2.11 X .06 UCL R 0.129 LCL R 0 X .06 LCL R 0 3.04 3.04 3.04 3.04 3.04 3.04 3.04 3.04 3.04 3.04 3.04 3.04 3.04 3.04 3.04 UCL X 3.07 3.07 3.07 3.07 3.07 3.07 3.07 3.07 3.07 3.07 3.07 3.07 3.07 3.07 3.07 3.07 R Bar Chart LCL X 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 Ranges 0.06 0.05 0.06 0.06 0.06 0.09 0.06 0.00 0.10 0.05 0.07 0.03 0.00 0.07 0.16 0.06 R Bar 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 UCL R 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 LCL R 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Q-Tip X Bar Chart The process is out of control. 3.10 3.08 Inches 3.06 X Bar X Bar Bar UCL LCL 3.04 3.02 3.00 2.98 2.96 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample Number Inches Q-Tip R Bar Chart The process is out of control. 0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 Ranges R Bar UCL LCL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample Number