Resistors for electronic circuits are manufactured on a high-speed automated mac
ID: 2908803 • Letter: R
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) 1 972 990 997 1000 2 994 1005 996 994 3 1029 1022 1028 972 4 994 1025 999 994 5 1004 993 1009 1016 6 986 973 1003 987 7 982 977 988 998 8 985 982 1021 1013 9 1027 1010 1003 989 10 1028 997 1002 978 11 1013 1029 1011 999 12 975 1029 1026 979 13 985 1003 987 980 14 1022 986 1028 983 15 998 1023 1027 1021Explanation / Answer
Part a
Here, we have to find the mean and range for the given 15 samples.
Sample means and sample ranges are given in the following tables:
Sample mean = total / n
Here, n = 4 for each sample
Range = R = maximum – minimum
Calculations by using excel are given below:
SAMPLE NUMBER
READINGS (IN OHMS)
Total
Xbar
R
1
972
990
997
1000
3959
989.75
28
2
994
1005
996
994
3989
997.25
11
3
1029
1022
1028
972
4051
1012.75
57
4
994
1025
999
994
4012
1003
31
5
1004
993
1009
1016
4022
1005.5
23
6
986
973
1003
987
3949
987.25
30
7
982
977
988
998
3945
986.25
21
8
985
982
1021
1013
4001
1000.25
39
9
1027
1010
1003
989
4029
1007.25
38
10
1028
997
1002
978
4005
1001.25
50
11
1013
1029
1011
999
4052
1013
30
12
975
1029
1026
979
4009
1002.25
54
13
985
1003
987
980
3955
988.75
23
14
1022
986
1028
983
4019
1004.75
45
15
998
1023
1027
1021
4069
1017.25
29
SAMPLE NUMBER
Mean
Range
1
989.75
28
2
997.25
11
3
1012.75
57
4
1003.00
31
5
1005.50
23
6
987.25
30
7
986.25
21
8
1000.25
39
9
1007.25
38
10
1001.25
50
11
1013.00
30
12
1002.25
54
13
988.75
23
14
1004.75
45
15
1017.25
29
Part b
Values for X-doublebar and R-bar are given as below:
X-double bar
1001.100
R-bar
33.933
(by using excel)
Part c
We have formulas for UCL and LCL for Xbar chart given as below:
UCL = X-double bar + A2*R-bar
LCL = X-double bar – A2*R-bar
A2 = 0.729 (From table for values of coefficients for control charts, see subgroup size = 4)
UCL = 1001.100 + 0.729*33.933 = 1025.837
UCL = 1025.837
LCL = 1001.100 - 0.729*33.933 = 976.363
LCL = 976.363
Part d
We have formulas for UCL and LCL for R chart given as below:
UCL = D4*R-bar
LCL = D3*R-bar
D4 = 2.282
D3 = 0
(By using coefficient table for control chart, subgroup size =4 )
UCL = 2.282*33.933 = 77.43511
UCL = 77.435
LCL = 0*33.933 = 0.000
LCL = 0.000
Part e
All Xbar observations are lies within Xbar chart UCL and LCL.
All R observations are lies within R chart UCL and LCL.
So, the process is in statistical control.
(We say that the process is in statistical control when all points in the control chart lies between the given upper and lower control limits for the Xbar chart and R chart.)
SAMPLE NUMBER
READINGS (IN OHMS)
Total
Xbar
R
1
972
990
997
1000
3959
989.75
28
2
994
1005
996
994
3989
997.25
11
3
1029
1022
1028
972
4051
1012.75
57
4
994
1025
999
994
4012
1003
31
5
1004
993
1009
1016
4022
1005.5
23
6
986
973
1003
987
3949
987.25
30
7
982
977
988
998
3945
986.25
21
8
985
982
1021
1013
4001
1000.25
39
9
1027
1010
1003
989
4029
1007.25
38
10
1028
997
1002
978
4005
1001.25
50
11
1013
1029
1011
999
4052
1013
30
12
975
1029
1026
979
4009
1002.25
54
13
985
1003
987
980
3955
988.75
23
14
1022
986
1028
983
4019
1004.75
45
15
998
1023
1027
1021
4069
1017.25
29
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.