Resistors for electronic circuits are manufactured on a high-speed automated mac
ID: 376135 • 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
Please find below table which calculates Mean and Range for each sample of 4 resistors each :
SERIAL NUMBER
SAMPLE
1
2
3
4
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
SUM =
15016.5
509
Following formula may be noted :
Mean for any sample = Sum of sample values / 4
Range for each sample = Maximum value in that sample – Minimum value in that sample
Therefore,
Xbar-bar = Mean of sample means = Sum of all sample means / 15 ( i.e number of samples ) = 15016.5/15 = 1001.10
Rbar = Mean of Range values = Sum of all range values / 15 (i.e number of samples ) = 509/15 = 33.93
Following are the value so constants derived from standard table for Xbar chart and Range chart for sample size, n = 4 :
A2 = 0.729
D4 = 2.282
D3 = 0
Accordingly,
Control Limits for Xbar chart :
Upper Control Limit = UCL = Xbar-bar + A2.Rbar = 1001.10 + 0.729 x 33.93 = 1001.10 + 24.734 = 1025.834
Lower Control Limit = LCL = Xbar-bar – A2.Rbar = 1001.10 – 0.729 x 33.93 = 1001.10 – 24.734 = 976.366
Control Limits for Range chart :
Upper Control Limit -= D4.Rbar = 2.282 x 33.93 = 77.428
Lower Control Limit = D3.Rbar = 0
As per control limits for Xbar chart, for the process to be in control all data must be within control range of 976.366 – 1025.834
However, there are sample data e.g 972, 973,1026, 1027, 1028, 1029 which are outside the above control limits
It therefore can be concluded that the process is out of statistical control
THE PROCESS IS OUT OF STATISTICAL CONTROL
SERIAL NUMBER
SAMPLE
1
2
3
4
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
SUM =
15016.5
509
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