Statistical Quality Control Problem Set - 7

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Part 1 of 2

 

This part of the question is based on the following information.

 

 

 

When set at the standard position, Autopitch can throw hard balls toward a batter at an average speed of 60mph. Autopitch devices are made for both major- and minor-league teams to help them improve their batting averages. Autopitch executives take samples of 10 Autopitch devices at a time to monitor these devices and to maintain the highest quality. The average range is 3mph. Using control chart techniques, determine control-chart limits for averages and ranges for Autopitch.

 

 

 

Sample Size, n

Mean Factor, A_2

Upper Range, D_4

Lower Range, D_3

2

1.88

3.268

0

3

1.023

2.574

0

4

0.729

2.282

0

5

0.577

2.114

0

6

0.483

2.004

0

7

0.419

1.924

0.076

8

0.373

1.864

0.136

9

0.337

1.816

0.184

10

0.308

1.777

0.223

12

0.266

1.716

0.284

14

0.235

1.671

0.329

16

0.212

1.636

0.364

18

0.194

1.608

0.392

20

0.18

1.586

0.414

25

0.153

1.541

0.459

 

 

 

  1. Based on the table, the upper control limit for averages is __________________ (round two decimal points and include no units)

  2. Based on the table, the lower control limit for  averages is __________________ (round two decimal points and include no limits).

  3. Based on the table, the upper control limit for ranges is ______________ (round two decimal points and include no units)

  4. Based on the table, the lower control limit for ranges is ___________________ (round two decimal points and include no units.

 

 

 

Part 2 of 2

 

 

 

This part of the question is based on the following information.

 

Colonel Electric is a large company that produces light bulbs and other electrical products.  One particular light bulb is supposed to have an average life of about 1,000 hours before it burns out. Periodically the company will test 5 of these and measure the average time before these burn out. The following table gives the results of 10 such samples.

 

 

 

 

 

Sample

1

2

3

4

5

6

7

8

9

10

Mean

979

1087

1080

934

1072

1007

952

986

1063

958

Range

50

94

57

65

135

134

101

98

145

84

 

 

 

  1. The overall average of these means is ________________, and the overall average range is _______________. (round it to one decimal point and include no units)

  2. Based on the result in Question 5 and the table for part 1, the upper control limit for a 99.7% control chart for the mean/average is _______________. (Round it to two decimal points and include no units)

  3. Based on the results in Question 5 and the table in part 1, the lower control limit for a 99.7% control chart for the mean/average is __________________. (round it to two decimal points and include no units).

  4. Does this process appear to be in control in terms of the mean? Yes or No

  5. Based on the results in Question 5 and the table for Part 1, the upper control limit for a 99.7% control chart for the range is _________________ and the lower control limit is ________________. (Round it to two decimal points and include no units)

  6.  Does this process appear to be in control in terms of the range? Yes or No.

 

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