Question

In: Statistics and Probability

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. *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.

Solutions

Expert Solution

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.


Related Solutions

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 READINGS (IN OHMS) 1 1000...
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 READINGS (IN OHMS) 1 986...
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 READINGS (IN OHMS) 1 1092...
Problem 13-9 Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is...
Problem 13-9 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)...
Problem 10-25 Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is...
Problem 10-25 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)...
A random sample of 300 electronic components manufactured by a new machine is tested and 9...
A random sample of 300 electronic components manufactured by a new machine is tested and 9 are found to be defective. The parts using the old machine have a true defective proportion of four percent. Does this sample provide evidence that the true defective proportion for the new machine is less than the old machine’s at the 5% significance level? Justify using a hypothesis test! Be sure to state you Ho and Ha, your test statistic and p-value, your decision...
A new printed circuit board design for a high speed electronic oscillator seems to fail at...
A new printed circuit board design for a high speed electronic oscillator seems to fail at high frequencies. Your job is to double check the design. One part of the circuit consists of two rectangular loops, the smaller one centered inside the larger one. Both rectangles have their long sides in the same direction. The smaller rectangle has long sides of length ℓ and short sides of length w. It is centered inside the larger rectangle whose long sides are...
(First successful high-speed electronic digital computer) OR (Apple Macintosh) OR ( Artificial intelligence) OR ( cybersecurity...
(First successful high-speed electronic digital computer) OR (Apple Macintosh) OR ( Artificial intelligence) OR ( cybersecurity ) Please chose (one) thing from the above about Personal Computers that you are curious to know more about? Research that topic on the web and locate an article about it. Post the URL to the article and write a paragraph synopsis and how it adds to the information. IF you can’t post the URL. Please include the article information so I can find...
Heartland Paper Company is considering the purchase of a new high-speed cutting machine. Two cutting machine...
Heartland Paper Company is considering the purchase of a new high-speed cutting machine. Two cutting machine manufacturers have approached Heartland with proposals: (1) Toledo Tools and (2) Akron Industries. Regardless of which vendor Heartland chooses, the following incremental cash flows are expected to be realized. Year Incremental Cash Inflows Incremental Cash Outflows 1 $ 27,000 $ 22,000 2 28,000 23,000 3 33,000 28,000 4 36,000 31,000 5 35,000 30,000 6 34,000 29,000 a. If the machine manufactured by Toledo Tools...
Jus de Fruit Co. has set up for automated production of its new bottled Triple Berry...
Jus de Fruit Co. has set up for automated production of its new bottled Triple Berry Colada. Five samples were taken during the first week of production. The OM team wants to monitor the dispersion of the process. What chart should they use? Is the process in control? Sample Bottle 1 Bottle 2 Bottle 3 1 20.1 20.1 19.8 2 20.0 19.1 20.0 3 19.9 20.1 19.4 4 18.0 21.8 20.5 5 20.0 19.7 20.0 Sample Size x-bar-Charts (A2) R-Charts...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT