Resistors for electronic cirouits are manufactured on a high-speed automated mac

Question

Resistors for electronic cirouits are manufactured on a high-speed automated machine. The machine is set up to produce a large run of resistors of 1,000 ohms each, Use Exhibit 10.13 To set up the machine and to create a control chart to be used throughout the run, 15 samples were taken with four resistors in each sample. The complete list of samples and their measured values are as follows: Use three-sigma control limits SAMPLE READINGS (IN NUMBER 11013 986 994 977 2 977 1027 962 1024 3 1027 990 998 1017 4 1023 1025 1016 1006 5 1005 1026 975 991 6 983 998 990 988 7 991 999 1001 985 8 1025 1023 1014 1023 9 1019 1004 982 979 10 999 995 991 1010 11 970 992 1008 1012 12 1010 985 983 1030 13 1030 1002 1016 982 14 979 986 1016 988 5 1028 1006 1019 1002 a. Caloulate the mean and range for the above samples. (Round "Mean" to 2 decimal places and "Range" to the nearest whole number.) Number Mean Range 10 12 13 14 15 b. Determine and-(Round your answers to 3 decimal places.) c. Determine the UCL and LCL for a chart. (Round your answers to 3 decimal places.) d. Determine the UCL and LCL for R-chart. (Leave no cells blank-be certain to enter " wherever required. Round your answers to 3 decimal places.)

Explanation / Answer

Mean = Average of 4 readings
Range = Highest reading - Lowest reading

1. Mean = (1013+986+994+977)/4 = 992.5 Range = 1013 - 977 = 36

2. Mean = (977+1027+982+1024)/4= 1002.5 Range = 1027-977= 50

3. Mean=(1027+990+998+1017)/4= 1008 Range = 1027-990= 37

4. Mean = (1023+1025+975+991)/4= 1003.5 Range= 1025-975 = 50

5.Mean = (1005+1026+975+991)/4 = 999.25 Range= 1026-975= 51

6. Mean = (983+998+990+988)/4 = 989.75 Range= 998-983=15

7. Mean = (991+999+1001+985)/4 = 994 Range=1001-985=16

8. Mean = (1025+1023+1014+1023)/4= 1021.25 Range= 1025-1014 = 11

9. Mean = (1019+1004+982+979)/4= 996 Range=1019-979 =40

10. Mean = (999+995+991+1010)/4= 998.75 Range= 1010-991 = 19

11. Mean=(970+992+1006+1012)/4=995 range=1012-970 = 42

12 Mean = (1010+985+983+1030)/4= 1002 range= 1030-983= 47

13 Mean=(1030+1002+1016+982)/4 = 1007.5 range=1030-982= 48

14 Mean=(979+986+1016+988)/4= 992.25 range=1016-979= 37

15 Mean=(1028+1006+1019+1002)/4= 1013.75 range= 1028-1002= 26

X bar = Mean of all 15 samples mean = 1001.07

R bar = Mean of all 15 samples range= 35

X chart (A2=0.73)

UCL= 1001.07+0.73*35= 1026.62
LCL= 1001.07-0.73*35= 975.52

R chart

UCL=2.28*35= 79.8
LCL=0*35=0

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