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

Question

Resistors for electronic circuits 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 NUMBER READINGS (IN OHMS) 972 997 1000 994 1005 996 994 972 994 1025 999 994 1004 993 1009 1016 986 973 1003 987 982977988 998 985 982 1021 1013 1027 1010 1003 989 1028 9971002 978 990 1029 1022 1028 10 1013 1029 1011 12 13 975 1029 1026 979 985 1003 987 980 1022 986 1028 983 998 1023 1027 1021 15 a. Calculate the mean and range for the above samples. (Round "Mean" to 2 decimal places and "Range" to the nearest whole number.) Sample Number Mean 6 10 12 13 15 b. Determine X and R. (Round your answers to 3 decimal places.)

Explanation / Answer

a) Mean = Average of 4 sampel values and Range = Max sample value - Min sample value

b) X-bar-bar = Average of all mean values and R-bar = Average of all Range values

X-bar-bar = (989.75+997.25+.....................+1017.25)/15 = 1001.100

R-bar = (28+11+.....................+29)/15 = 33.933

Sample Readings Mean Range 1 972 990 997 1000 989.75 28 2 994 1005 996 994 997.25 11 3 1029 1022 1028 972 1012.75 57 4 994 1025 999 994 1003 31 5 1004 993 1009 1016 1005.5 23 6 986 973 1003 987 987.25 30 7 982 977 988 998 986.25 21 8 985 982 1021 1013 1000.25 39 9 1027 1010 1003 989 1007.25 38 10 1028 997 1002 978 1001.25 50 11 1013 1029 1011 999 1013 30 12 975 1029 1026 979 1002.25 54 13 985 1003 987 980 988.75 23 14 1022 986 1028 983 1004.75 45 15 998 1023 1027 1021 1017.25 29

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