In: Statistics and Probability
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. *ONLY ANSWER b,c,d, e please. Thank you!*
SAMPLE NUMBER | READINGS (IN OHMS) | |||
1 | 992 | 992 | 1000 | 1027 |
2 | 978 | 994 | 985 | 1018 |
3 | 1021 | 998 | 1018 | 994 |
4 | 974 | 1022 | 999 | 1026 |
5 | 1000 | 1012 | 1030 | 991 |
6 | 974 | 987 | 985 | 987 |
7 | 1005 | 973 | 1011 | 1001 |
8 | 983 | 1024 | 1012 | 977 |
9 | 990 | 1004 | 973 | 999 |
10 | 990 | 1018 | 1024 | 1001 |
11 | 998 | 976 | 1029 | 980 |
12 | 1024 | 1020 | 1020 | 976 |
13 | 1026 | 1018 | 1029 | 971 |
14 | 982 | 979 | 982 | 989 |
15 | 991 | 988 | 980 | 994 |
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 | 1002.75 | 35 |
2 | 933.75 | 40 |
3 | 1007.75 | 27 |
4 | 1005.25 | 52 |
5 | 1008.25 | 39 |
6 | 983.25 | 13 |
7 | 997.50 | 38 |
8 | 999 | 47 |
9 | 991.50 | 31 |
10 | 1008.25 | 34 |
11 | 995.75 | 53 |
12 | 1010 | 48 |
13 | 1011 | 58 |
14 | 983 | 10 |
15 | 988.25 | 14 |
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. |
Solution(a)
Sample Number |
Xbar |
Range |
||||
1 |
992 |
992 |
1000 |
1027 |
1002.75 |
35 |
2 |
978 |
994 |
985 |
1018 |
993.75 |
40 |
3 |
1021 |
998 |
1018 |
994 |
1007.75 |
27 |
4 |
974 |
1022 |
999 |
1026 |
1005.25 |
52 |
5 |
1000 |
1012 |
1030 |
991 |
1008.25 |
39 |
6 |
974 |
987 |
985 |
987 |
983.25 |
13 |
7 |
1005 |
973 |
1011 |
1001 |
997.5 |
38 |
8 |
983 |
1024 |
1012 |
977 |
999 |
47 |
9 |
990 |
1004 |
973 |
999 |
991.5 |
31 |
10 |
990 |
1018 |
1024 |
1001 |
1008.25 |
34 |
11 |
998 |
976 |
1029 |
980 |
995.75 |
53 |
12 |
1024 |
1020 |
1020 |
976 |
1010 |
48 |
13 |
1026 |
1018 |
1029 |
971 |
1011 |
58 |
14 |
982 |
979 |
982 |
989 |
983 |
10 |
15 |
991 |
988 |
980 |
994 |
988.25 |
14 |
Solution(b)
Xdoublebar =
(1002.75+993.75+1007.75+1005.25+1008.25+983.25+997.5+999+991.5+1008.25+999.75+1010+1011+983+988.25)/15
= 999.012
Rbar = (35+40+27+52+39+13+ 38+47+31+34+53+48+58+10+14)/15 =
35.933
Solution(c)
LCL = Xdoublebar - A2*Rbar = 999.02 - 0.729*35.93 = 972.827
UCL = Xdoublebar + A2*Rbar = 999.02 + 0.729*35.93 =
1025.213
Solution(d)
LCL = D3*Rbar = 0*35.93 = 0
UCL = D4*Rbar = 2.282*35.93 = 81.992
Solution(e)
From the LCL and UCL limits of Range and Mean, we can say that the
process is in statistical control.