D E G H 1. Problem 2. Resistors for electronic circuits are manufactured on a high-speed automated 2 machine. The machine is set up to produce a large run of resistors of 1,000 ohms each. To set 3 up the machine and to create a control chart to be used throughout the run, 15 samples 4 were taken with four resistors in each sample. The complete list of samples and their 5 measured values are as follows: 6 7 Readings (in Ohms) 8 Sample number 1 2 3 9 9 10 11 4 4 5 12 13 5 6 7 8 14 00 15 16 1010 995 990 1015 1013 994 989 1001 1006 992 996 1019 981 999 1013 991 996 1003 1020 1019 1001 992 986 989 1007 1006 996 991 993 1002 985 1009 1015 1009 1005 994 982 996 1005 1006 997 991 989 988 1005 986 994 1008 998 993 1005 1020 996 1007 979 989 1011 1003 984 992 9 17 . 18 19 10 11 12 13 14 15 20 21 22 23 24 25 a. Develop an chart and R-chart and plot the values. Readings in Ohms) Sample number X-bar R 27 28 29 3 5 1010 995 990 1015 1013 994 989 1001 1006 32 33 -Nm 09 AM 7 8 A6%89%888988 991 996 1003 1020 1019 1001 992 986 989 1007 1006 996 991 993 1002 985 1009 1015 1009 1005 994 982 996 1005 1006 997 991 989 988 1005 986 994 1008 998 993 1005 1020 996 1007 979 989 1011 1003 984 992 992 36 37 38 39 10 11 12 13 14 15 996 1019 981 999 1013 R Average of Average of 182 38&$88989898989 44 Exhibit 10.13 45 Factor for R Chart Observation Lower Upper sin Factor for Control Control Subgroup-bar Chart Limit Limit 0, D. 2 0 3.27 3 0 2.57 4 0 2.28 5 0 2.11 6 0 2 7 0.08 8 0.14 186 9 0.18 1.82 10 0.22 1.78 -11 0.26 174 12 0.28 172 13 0.31 169 14 0.33 167 15 0.35 165 16 0.36 164 17 0.38 162 18 0.39 161 19 04 16 20 0.18 0.41 159 CEREREEEEEEEEEEEEEE 68 69 UCL X 70 LCLE R-bar ) 71 Az 72 UCL D. 73 LCLA D 74 75 UCL = x + AR 76 LCL = A2R 77 78 UCLR=DER 79 LCLR=D2R 80 81 82 X-bar Chart 83 84 85 86 87 88 89 90 91 0 92 1 2 3 4 5 93 9 10 11 12 13 14 15 94 95 96 R-chart 97 1 98 99 1 100 1 101 102 1 103 -R-chart 104 105 0 106 107 108 1 2 3 4 6 7 8 9 10 11 12 13 14 15 the b. From the charts, what comments can you make about the process? (Use three-sigma control limits as Exhibit 10.13.) Conclusion Therefore, the process is out of 10 are out of controllimits