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1. Obs 1 Obs 2 Obs 3 Obs 4 Average Range Sample1 63 58 58 58 59.25 5 Sample2 60

ID: 3224727 • Letter: 1

Question

1.

Obs 1

Obs 2

Obs 3

Obs 4

Average

Range

Sample1

63

58

58

58

59.25

5

Sample2

60

59

60

61

60

2

Sample3

60

58

62

63

60.75

5

Sample4

59

59

59

62

59.75

3

Sample5

60

62

59

57

59.5

5

Sample6

58

58

58

60

?

?


Using this data to establish an SPC chart, what is the LOWER control limit for the x-bar chart? (Note that the size of a sample is 4.)

n

A2

2

1.88

3

1.023

4

0.729

5

0.577

6

0.483

7

0.419

8

0.373

9

0.337

10

0.308

a.

56.95

b.

58.90

c.

62.30

d.

55.96

2.         A customer specifies that she needs her daily deliveries made between 4 pm and 9 pm. Your truck leaves the factory at noon, and the time taken to reach the customer is normally distributed with an average of 6.5 hours and a standard deviation of 1 hour. What is the sigma capability of this delivery process?

a.

1.5

b.

3

c.

2

d.

5

e.

2.5

3.

Obs 1

Obs 2

Obs 3

Obs 4

Obs 5

Average

Range

Sample1

311

304

302

314

323

310.8

21

Sample2

316

308

300

301

306

306.2

16

Sample3

319

314

312

302

323

?

?

Sample4

322

320

316

313

318

317.8

9

Sample5

329

327

321

316

325

323.6

13

Sample6

314

326

322

311

329

320.4

18


Using the above data, what is the value for the center line of the X-bar chart?

a.

314.00

b.

15.40

c.

16.33

d.

315.76

e.

315.47

4.             Checkout time at a supermarket is going to be monitored using mean and range charts. To establish the control charts, the store manager collected a group of samples using a sample size of ten, and then calculated the mean and range for each sample. What is the UPPER control limit for the R chart?

Mean

Range

Sample 1

9

1.0

Sample 2

8

0.7

Sample 3

9

1.0

Sample 4

5

0.8

Sample 5

6

0.5

Sample 6

5

1.0

Sample 7

5

0.6

Sample 8

6

1.3

n

A2

D3

D4

2

1.88

0

3.267

3

1.023

0

2.575

4

0.729

0

2.282

5

0.577

0

2.115

6

0.483

0

2.004

7

0.419

0.076

1.924

8

0.373

0.136

1.864

9

0.337

0.184

1.816

10

0.308

0.223

1.777

a.

8.16

b.

0.19

c.

0.27

d.

6.82

e.

1.54

Obs 1

Obs 2

Obs 3

Obs 4

Average

Range

Sample1

63

58

58

58

59.25

5

Sample2

60

59

60

61

60

2

Sample3

60

58

62

63

60.75

5

Sample4

59

59

59

62

59.75

3

Sample5

60

62

59

57

59.5

5

Sample6

58

58

58

60

?

?

Explanation / Answer

1)

X=Exi/k

=59.25+….+58.5/6

=59.625

R=ERi/k

=5+….+2/6

=3.67

LCL=X-A2(R)=59.625-0.729(3.67)=59.625-2.675=56.95

Correct answer is a.56.95