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. To set up me 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, Refer Exhibit 10.13. Calculate the mean and range for the above samples (Round "Mean" to 2 decimal places and "Range" to the nearest whole number.) Determine X and. (Round your answers to 3 decimal places.) Determine the UCL and LCL for a chart (Round your answers to 3 decimal places.) Ootorrr.no the UCL and LCL for R-chart (Leave no cells blank. be certain to enter "0" where ever required Round your answers to 3 decimal places.)

Explanation / Answer

a)

Mean is Sum of observations / Number of observations and Range is Highest - Lowest

So, the mean and range are shown in below table

b)

Mean of mean = Sum of observations / Number of observations

= 15,058.75 / 15 = 1003.91

Mean of Range = 486 / 15 = 32.4

c)

UCL and LCL of X chart

UCL = Mean + 3 x Square root of mean

= 1003.91 + 3 x 31.68

= 1098.95

LCL = Mean - 3 x Square root of mean

= 1003.91 - 3 x 31.68

= 908.87

d)

UCL and LCL of R chart

UCL = Mean + 3 x Square root of mean

= 32.4 + 3 x 5.69

= 49.47

LCL = Mean - 3 x Square root of mean

= 32.4 - 3 x 5.69

= 15.33

Sample no. Reading 1 Reading 2 Reading 3 Reading 4 Mean Range 1 1,016 995 991 1028 1007.5 37 2 1024 981 991 1,001 999.25 43 3 990 1,015 1025 1012 1010.5 35 4 1018 1,002 972 995 996.75 46 5 1030 1,007 1013 1,002 1013 28 6 1,016 1017 985 1,002 1005 32 7 992 1005 1011 1013 1005.25 21 8 1028 991 1002 995 1004 37 9 1030 1,014 987 1023 1013.5 43 10 986 975 980 968 977.25 18 11 1006 975 1,008 1020 1002.25 45 12 1,016 1004 1020 1019 1014.75 16 13 1,015 1003 1005 998 1005.25 17 14 986 1013 1,004 1020 1005.75 34 15 981 1014 1015 985 998.75 34

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