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.

a. Calculate the mean and range for the above samples. (Round "Mean" to 2 decimal places and "Range" to the nearest whole number.)

d. Determine the UCL and LCL for R-chart. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 3 decimal places.)

e. What comments can you make about the process?

SAMPLE NUMBER READINGS (IN OHMS) 1 1092 1099 1016 979 2 1011 978 1023 976 3 974 1003 996 998 4 981 988 1001 1007 5 992 976 978 1001 6 988 1030 1030 1014 7 1022 1010 1021 990 8 1010 998 981 975 9 997 1018 983 1024 10 1028 974 989 989 11 972 1010 1007 992 12 1013 981 1002 1009 13 1005 1021 996 1014 14 995 973 971 975 15 1011 1001 987 1015

Explanation / Answer

a. Mean = sum of values of 4 units in each sample / 4

Range = Highest value in a sample - lowest value in a sample

b. Xbar bar = Mean of averages = 1001.48

Rbar = Mean of range values =39.86

c. UCL for Xbar chart = Xbarbar + A2Rbar

LCL for Xbar chart = Xbarbar - A2 Rbar

Value of A2 for sample of 4 units is 0.729 ( from standard table)

Hence

UCL = 1001.48 + 0.729x 39.86 = 1030.53

LCL = 1001.48 - 0.729 x39.86 = 972.42

d.

UCL for R chart = D4Rbar = 2.282 x39.86 = 90.96

LCL for R chart = D3 Rbar = 0

e. It can be seen from the table that there are X and R values beyond the limit ( in sample 1) so the process is out of control.

S.No. Xbar R 1 1046.5 120 2 997 47 3 992.75 29 4 994.25 26 5 986.75 25 6 1015.5 42 7 1010.5 32 8 991 35 9 1005.5 41 10 995 54 11 995.25 38 12 1001.25 32 13 1009 25 14 978.5 24 15 1003.5 28

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