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) | ||||
1 | 1000 | 992 | 1014 | 1026 | |
2 | 1006 | 977 | 1027 | 1016 | |
3 | 985 | 1029 | 1018 | 992 | |
4 | 1001 | 1006 | 971 | 1000 | |
5 | 1028 | 970 | 979 | 1025 | |
6 | 997 | 1026 | 1007 | 1003 | |
7 | 1016 | 1003 | 987 | 1006 | |
8 | 995 | 1029 | 978 | 986 | |
9 | 1027 | 995 | 1003 | 1008 | |
10 | 991 | 987 | 981 | 996 | |
11 | 994 | 1000 | 978 | 971 | |
12 | 999 | 983 | 973 | 1005 | |
13 | 1003 | 993 | 974 | 1002 | |
14 | 1005 | 972 | 994 | 1000 | |
15 | 1012 | 1018 | 982 | 1014 | |
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 | Range |
1 | ||
2 | ||
3 | ||
4 | ||
5 | ||
6 | ||
7 | ||
8 | ||
9 | ||
10 | ||
11 | ||
12 | ||
13 | ||
14 | ||
15 | ||
b. Determine X=X= and R−R−. (Round your answers to 3 decimal places.)
X=X= | |
R−R− | |
c. Determine the UCL and LCL for a X−X−chart. (Round your answers to 3 decimal places.)
UCL | |
LCL | |
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.)
UCL | |
LCL | |
e. What comments can you make about the process?
The process is in statistical control. | |
The process is out of statistical control. |
a.
Sample Mean and Sample Range for all the samples are calculated as per the below table:
Sample Readings | ||||||
Number | 1 | 2 | 3 | 4 | Sample Mean | Sample Range |
1 | 1000 | 992 | 1014 | 1026 | 1008 | 34 |
2 | 1006 | 977 | 1027 | 1016 | 1006.5 | 50 |
3 | 985 | 1029 | 1018 | 992 | 1006 | 44 |
4 | 1001 | 1006 | 971 | 1000 | 994.5 | 35 |
5 | 1028 | 970 | 979 | 1025 | 1000.5 | 58 |
6 | 997 | 1026 | 1007 | 1003 | 1008.25 | 29 |
7 | 1016 | 1003 | 987 | 1006 | 1003 | 29 |
8 | 995 | 1029 | 978 | 986 | 997 | 51 |
9 | 1027 | 995 | 1003 | 1008 | 1008.25 | 32 |
10 | 991 | 987 | 981 | 996 | 988.75 | 15 |
11 | 994 | 1000 | 978 | 971 | 985.75 | 29 |
12 | 999 | 983 | 973 | 1005 | 990 | 32 |
13 | 1003 | 993 | 974 | 1002 | 993 | 29 |
14 | 1005 | 972 | 994 | 1000 | 992.75 | 33 |
15 | 1012 | 1018 | 982 | 1014 | 1006.5 | 36 |
b.
X double bar = Mean of Sample Ranges = ( 1008 + 1006.5 + 1006 + 994.5 + 1000.5 + 1008.25 + 1003 + 997 + 1008.25 + 988.75 + 985.75 + 990 + 993 + 992.75 + 1006.5) / 15 = 14988.75 / 15 = 999.25
R bar = Mean of Sample Rnages = ( 34 + 50 + 44 + 35 + 58 + 29 + 29 + 51 + 32 + 15 + 29 + 32 + 29 + 33 + 36) / 15 = 536 / 15 = 35.733
c.
X bar chart:
UCL = X double bar + ( R bar x A2)
LCL = X double bar - ( R bar x A2)
For a sample size of 4, A2 value is 0.729 ( From Control chart constant table)
So,
UCL = 999.25 + ( 35.733 x 0.729) = 999.25 + 26.049 = 1025.299
LCL = 999.25 - ( 35.733 x 0.729) = 999.25 - 26.049 = 973.201
d.
R bar chart:
UCL = R bar x D4
LCL = R bar x D3
For a sample size of 4, D4 value is 2.282 and D3 value is 0 ( From Control chart constant table)
So,
UCL = 35.733 x 2.282 = 81.543
LCL = 35.733 x 0 = 0
e.
All the Sample mean values are within the UCL and LCL values of X bar chart.
All the Sample range values are within the UCL and LCL values of R bar chart.
Therefore,
The process is in statistical control.
Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is set up...
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 NOEM READINGS (IN OHMS) 1000...
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) 1 992...
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