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ME 406- Manufacturing and Design

Mechanical Engineering Department

 

ME 406- Manufacturing and Design

Project A (Engineering Statistics and Manufacturing)

Title of the Project

Quality Control, Regression Analysis, and Models Fitting

Term 171

Class Section- xx

 

 

Project Team – Group X_X

 

 

xxxxxxxxx Name 1 (Group Coordinator)

xxxxxxxxx Name 2

xxxxxxxxx Name 3

xxxxxxxxx Name 4

 

 

 

 

 

 

 

Assigned on 13th November 2017

Due on 4th January 2018 (Before Exam starts)

 

Note Please Attempt each question as asked using the software where ever mentioned. Full Report generated by STATGRAPHICS Must be included in Problems 1 .All Excel sheets be included in PROBLEMS where Excel has been used such as in Q

Each problem should be started on separate page after pasting the the problem statement at the top of the page. Your Solution will be typewritten.

A hard copy as (WORD +EXCELL SHEETS) be provided along with a Hard copy in PDF format. Plus Software generated reports

A soft copy as a CD (WORD +EXCELL SHEETS) be provided along with a soft copy copy in PDF format. Plus Software generated reports. CD Must have mentioned that it is STSTISTICS PROJECT and it shoulf have All Project students Name and ID mentioned on CD and a on a text file inside the cD.

Project copies both word and PDF will be uploaded on WebCT as will be explained later.

 

PROBLEM # 1 (1.5 point)

 

For alpha distribution

 

Find

a) Plot F(t) versus t/C for =0.05 , 0.1.0.15,0.2 ,0.25 and 0.3 (all curves should be in one Figure for range of t/C varying from (0+=0.05) to 4). Hint use Normal Distribution Function(select True) of Excel subroutine for Z=-

b) Find pdf for t varying from -∞ to +∞ ,(note at t=0 function is undefined). Note

 

 

where

Z=-

 

 

 

 

c) Plot f(t) versus t/C for =0.05 , 0.1.0.15,0.2 ,0.25 and 0.3 .all curves in one Figure for range of t/C varying from (0+=0.05) to 4 . Hint use Normal Distribution Function (select False) of Excel subroutine for Z=-

d) Median value of T, t0.5

e) Quantile, tp which is the solution of F(tp)=p .

f) Mode of T, (value of t where

 

PROBLEM # 2 (1.0 point) Use EXCEL and attach all spreadsheet analysis with solution)

Fifty measurements of the ultimate tensile strength of wire are given in the accompanying table.

a) Group the data and make an appropriate normalized histogram (with total area of histogram be 1 ) to approximate the PDF.

b) Calculate and for the distribution from the ungrouped data.

c) Using and from part b, draw a normal distribution through the normalized histogram .histogram.

Ultimate Tensile Strength

 

 

103,779

102,325

102,325

103,799

102,906

104,651

105,377

100,145

104,796

105,087

104,796

103,799

103,197

106,395

106,831

103,488

100,872

100,872

105,087

102,906

97,383

104,360

103,633

101,017

101,162

101,453

107,848

104,651

98,110

103,779

99,563

103,197

104,651

101,162

105,813

105,337

102,906

102,470

108,430

101,744

103,633

105,232

106,540

106,104

102,616

106,831

101,744

100,726

103,924

 

101,598

 

Source: Data from E. B. Haugen, Probabilistic Mechanical Design Wiley, New York, 1980

(c) Determine the mean, median, and mode from the ungrouped data.

(d) Determine the range and standard deviation from the ungrouped data

(e) Plot the cumulative frequency distribution on normal-probability paper, and determine the mean and standard deviation.

(f), for the data given in Table .what are the 95 percent confidence limits on the mean of the population?

 

 

 

 

 

 

PROBLEM # 3 (1.0 point) (Use EXCEL and attach all spreadsheet analysis with solution)

Three sets of identical twenty five fatigue specimens were tested at the three different level of stresses.. The number of cycles to failure. The results are expressed as log, were as follows.

TABLE 1: FATIGUE LIFE DATA

NUMBER OF CYCLES TO FAILURES

No.

S1

S2

S3

 

380 MPa

340 MPa

300 MPa

1

34200

125500

954000

2

37700

156900

959400

3

42000

173600

1194600

4

42300

176900

1240500

5

48200

179400

1250400

6

52500

188500

1285500

7

55900

195100

1410500

8

58300

208100

1495100

9

61700

211900

1518700

10

64700

224100

1544700

11

65000

226000

1551400

12

65500

253000

1585900

13

70400

255500

1639100

14

71000

259000

1683700

15

72400

274000

1926100

16

75200

292000

2011300

17

77400

300400

2171800

18

77800

302300

2391500

19

87800

308300

2569400

20

93400

406300

2674900

21

94000

420700

2921700

22

97200

428500

3046500

23

99600

664800

3105500

24

116700

776100

3523200

25

122500

793900

4311700

 

Assume that the data at each stress level (S1, S2 and S3) is lognormally distributed.

Using directly the data in table determine

· What is the mean fatigue life ( μ) and its standard deviation (σ )?

· What is the mean Ln of fatigue life ( μlnN) and its standard deviation Ln of fatigue life (σlnN)?

· What are the Parameters of Lognormal distributions at S1,S2and S3.

· Fit lognormal distribution to the data using linear regression model using Excel or Use Statgraphics to fit the lognormal models to data for each stress level and comment on how good the fit is.

 

 

PROBLEM # 4 (1.5 point)

Q4. (a) The lifetime of a mechanical switch produced by a company has been determined to have a population mean of μ = 2000 h and σ = 200 h. The temper of a phosphor bronze leaf spring in the switch is changed slightly by the supplier. To determine whether this has changed the product, a sample of 100 switches is tested to give the sample values and . Has there been a change in the product? (0.75 point)

 

Q4. (b) A vendor of steel wire advertises a mean breaking load of 10,000 lb. A sample of eight tests shows a mean breaking load of 9250 lb and a standard deviation of 110 lb. Do our tests support the vendor’s claim? (0.75 point)

 

PROBLEM # 5 Control Charts (1 point)

Problem 5-Refer your Text Book above ( See Ebook provided as text book)- -Solve with appropriate calculations, tables and charts

5.1-Problem 8.1 Parts (a) and (b) –P454

5.2 -Problem 8.28 Parts (a) and (b) –P470

 

PROBLEM # 6

Regression Analysis (MUST USE STATGRAPHICS_ ATTACH COMPLETE REPORT PLUS ONE PAGE SUMMARY OF EACH FITTED MODEL) 2 points

 

Developing Cutting Forces Empirical Models of a Counter Boring Process in Aluminum.

Counter boring is an operation to enlarge the hole made using drilling. Counter boring or finish boring is a deep hole drilling process that requires a work piece with a pre-existing bore. Counter boring is used to enlarge the drilled hole to the proper depth and machine a square shoulder on the bottom to secure maximum clamping action from the faster. The drilling used to produce a circular hole by removing solid metal. The counter bore tool has a guide, called a pilot, which keep it positioned correctly in the hole. Counter boring tools are often used on low power machines were a small diameter solid boring tool is used for the pre-bore and then a counter boring tool is used to finish the job. Counter boring is also used when there is a heat treat process required after the initial hole is drilled or if a stepped hole is required. 31 d31

Pilot of diameter d , which is the predrilled hole size in the workpiece diameter of already drilled hole..

 

D Dia of the enlarged hole

 

Visit the link and download STATGRAPHICS FREE FOR 30 DAYS AND USE MULTIPLE REGRESSION MODULE (SEE EXAMPLES ON WEBSITE) TO DEVELOP FOLLOWING MODELS>

https://www.statgraphics.com/centurion-xvii

Regression Analysis https://www.statgraphics.com/regression-analysis

And Quality Control Module (PROICESS CAPABILITY BANALYSIS) from the link https://www.statgraphics.com/process-capability-analysis

Following are the results of Cutting Forces measurements experiments performed at KFUPM Workshop by Professor Anwar K Sheikh. The results are being shared for regression analysis learning objectives.

Cutting Force Fz as a Function of V,D,d and f

 

Fz

Newton

Speed , V

mm/minutes

Feed , f

Mm/revolution

d

mm

D

mm

Ln (FZ)

Ln(Speed)

Ln(feed)

Ln(D)

52

2463.007

0.03

3.5

6.5

3.951244

7.809138

-3.50656

1.252763

78

2463.007

0.05

3.5

6.5

4.356709

7.809138

-2.99573

1.252763

104

2463.007

0.08

3.5

6.5

4.644391

7.809138

-2.52573

1.252763

130

2463.007

0.12

3.5

6.5

4.867534

7.809138

-2.12026

1.252763

65

3903.426

0.03

3.5

6.5

4.174387

8.26961

-3.50656

1.252763

78

3903.426

0.05

3.5

6.5

4.356709

8.26961

-2.99573

1.252763

104

3903.426

0.08

3.5

6.5

4.644391

8.26961

-2.52573

1.252763

130

3903.426

0.12

3.5

6.5

4.867534

8.26961

-2.12026

1.252763

65

4948.004

0.03

3.5

6.5

4.174387

8.50674

-3.50656

1.252763

78

4948.004

0.05

3.5

6.5

4.356709

8.50674

-2.99573

1.252763

117

4948.004

0.08

3.5

6.5

4.762174

8.50674

-2.52573

1.252763

130

4948.004

0.12

3.5

6.5

4.867534

8.50674

-2.12026

1.252763

65

6157.516

0.03

3.5

6.5

4.174387

8.725429

-3.50656

1.252763

78

6157.516

0.05

3.5

6.5

4.356709

8.725429

-2.99573

1.252763

104

6157.516

0.08

3.5

6.5

4.644391

8.725429

-2.52573

1.252763

130

6157.516

0.12

3.5

6.5

4.867534

8.725429

-2.12026

1.252763

72

7806.851

0.03

3.5

6.5

4.276666

8.962757

-3.50656

1.252763

85

7806.851

0.05

3.5

6.5

4.442651

8.962757

-2.99573

1.252763

111

7806.851

0.08

3.5

6.5

4.70953

8.962757

-2.52573

1.252763

130

7806.851

0.12

3.5

6.5

4.867534

8.962757

-2.12026

1.252763

78

2463.007

0.03

5.5

10

4.356709

7.809138

-3.50656

1.704748

104

2463.007

0.05

5.5

10

4.644391

7.809138

-2.99573

1.704748

130

2463.007

0.08

5.5

10

4.867534

7.809138

-2.52573

1.704748

182

2463.007

0.12

5.5

10

5.204007

7.809138

-2.12026

1.704748

84

3903.426

0.03

5.5

10

4.430817

8.26961

-3.50656

1.704748

110

3903.426

0.05

5.5

10

4.70048

8.26961

-2.99573

1.704748

143

3903.426

0.08

5.5

10

4.962845

8.26961

-2.52573

1.704748

182

3903.426

0.12

5.5

10

5.204007

8.26961

-2.12026

1.704748

91

4948.004

0.03

5.5

10

4.51086

8.50674

-3.50656

1.704748

117

4948.004

0.05

5.5

10

4.762174

8.50674

-2.99573

1.704748

130

4948.004

0.08

5.5

10

4.867534

8.50674

-2.52573

1.704748

182

4948.004

0.12

5.5

10

5.204007

8.50674

-2.12026

1.704748

78

6157.516

0.03

5.5

10

4.356709

8.725429

-3.50656

1.704748

104

6157.516

0.05

5.5

10

4.644391

8.725429

-2.99573

1.704748

143

6157.516

0.08

5.5

10

4.962845

8.725429

-2.52573

1.704748

195

6157.516

0.12

5.5

10

5.273

8.725429

-2.12026

1.704748

91

7806.851

0.03

5.5

10

4.51086

8.962757

-3.50656

1.704748

117

7806.851

0.05

5.5

10

4.762174

8.962757

-2.99573

1.704748

143

7806.851

0.08

5.5

10

4.962845

8.962757

-2.52573

1.704748

195

7806.851

0.12

5.5

10

5.273

8.962757

-2.12026

1.704748

117

2463.007

0.03

7.5

15

4.762174

7.809138

-3.50656

2.014903

143

2463.007

0.05

7.5

15

4.962845

7.809138

-2.99573

2.014903

195

2463.007

0.08

7.5

15

5.273

7.809138

-2.52573

2.014903

234

2463.007

0.12

7.5

15

5.455321

7.809138

-2.12026

2.014903

123

3903.426

0.03

7.5

15

4.812184

8.26961

-3.50656

2.014903

156

3903.426

0.05

7.5

15

5.049856

8.26961

-2.99573

2.014903

208

3903.426

0.08

7.5

15

5.337538

8.26961

-2.52573

2.014903

234

3903.426

0.12

7.5

15

5.455321

8.26961

-2.12026

2.014903

123

4948.004

0.03

7.5

15

4.812184

8.50674

-3.50656

2.014903

169

4948.004

0.05

7.5

15

5.129899

8.50674

-2.99573

2.014903

208

4948.004

0.08

7.5

15

5.337538

8.50674

-2.52573

2.014903

247

4948.004

0.12

7.5

15

5.509388

8.50674

-2.12026

2.014903

130

6157.516

0.03

7.5

15

4.867534

8.725429

-3.50656

2.014903

169

6157.516

0.05

7.5

15

5.129899

8.725429

-2.99573

2.014903

208

6157.516

0.08

7.5

15

5.337538

8.725429

-2.52573

2.014903

247

6157.516

0.12

7.5

15

5.509388

8.725429

-2.12026

2.014903

143

7806.851

0.03

7.5

15

4.962845

8.962757

-3.50656

2.014903

182

7806.851

0.05

7.5

15

5.204007

8.962757

-2.99573

2.014903

208

7806.851

0.08

7.5

15

5.337538

8.962757

-2.52573

2.014903

247

7806.851

0.12

7.5

15

5.509388

8.962757

-2.12026

2.014903

156

2463.007

0.03

9.5

18

5.049856

7.809138

-3.50656

2.251292

208

2463.007

0.05

9.5

18

5.337538

7.809138

-2.99573

2.251292

260

2463.007

0.08

9.5

18

5.560682

7.809138

-2.52573

2.251292

338

2463.007

0.12

9.5

18

5.823046

7.809138

-2.12026

2.251292

208

3903.426

0.03

9.5

18

5.337538

8.26961

-3.50656

2.251292

234

3903.426

0.05

9.5

18

5.455321

8.26961

-2.99573

2.251292

260

3903.426

0.08

9.5

18

5.560682

8.26961

-2.52573

2.251292

364

3903.426

0.12

9.5

18

5.897154

8.26961

-2.12026

2.251292

208

4948.004

0.03

9.5

18

5.337538

8.50674

-3.50656

2.251292

234

4948.004

0.05

9.5

18

5.455321

8.50674

-2.99573

2.251292

260

4948.004

0.08

9.5

18

5.560682

8.50674

-2.52573

2.251292

364

4948.004

0.12

9.5

18

5.897154

8.50674

-2.12026

2.251292

208

6157.516

0.03

9.5

18

5.337538

8.725429

-3.50656

2.251292

260

6157.516

0.05

9.5

18

5.560682

8.725429

-2.99573

2.251292

286

6157.516

0.08

9.5

18

5.655992

8.725429

-2.52573

2.251292

338

6157.516

0.12

9.5

18

5.823046

8.725429

-2.12026

2.251292

234

7806.851

0.03

9.5

18

5.455321

8.962757

-3.50656

2.251292

286

7806.851

0.05

9.5

18

5.655992

8.962757

-2.99573

2.251292

312

7806.851

0.08

9.5

18

5.743003

8.962757

-2.52573

2.251292

 

 

 

 

Moment Mz as a Function of V,D,d and f

Mz Newton-meter

Speed , V

mm/minutes

Feed , f

Mm/ revolution

d

mm

D

mm

Ln (Mz)

Ln(Speed)

Ln(feed)

Ln(D)

 

39

2463.007

0.03

3.5

6.5

3.663562

7.809138

-3.50656

1.252763

 

59

2463.007

0.05

3.5

6.5

4.077537

7.809138

-2.99573

1.252763

 

72

2463.007

0.08

3.5

6.5

4.276666

7.809138

-2.52573

1.252763

 

104

2463.007

0.12

3.5

6.5

4.644391

7.809138

-2.12026

1.252763

 

39

3903.426

0.03

3.5

6.5

3.663562

8.26961

-3.50656

1.252763

 

52

3903.426

0.05

3.5

6.5

3.951244

8.26961

-2.99573

1.252763

 

78

3903.426

0.08

3.5

6.5

4.356709

8.26961

-2.52573

1.252763

 

117

3903.426

0.12

3.5

6.5

4.762174

8.26961

-2.12026

1.252763

 

39

4948.004

0.03

3.5

6.5

3.663562

8.50674

-3.50656

1.252763

 

59

4948.004

0.05

3.5

6.5

4.077537

8.50674

-2.99573

1.252763

 

78

4948.004

0.08

3.5

6.5

4.356709

8.50674

-2.52573

1.252763

 

117

4948.004

0.12

3.5

6.5

4.762174

8.50674

-2.12026

1.252763

 

39

6157.516

0.03

3.5

6.5

3.663562

8.725429

-3.50656

1.252763

 

52

6157.516

0.05

3.5

6.5

3.951244

8.725429

-2.99573

1.252763

 

78

6157.516

0.08

3.5

6.5

4.356709

8.725429

-2.52573

1.252763

 

124

6157.516

0.12

3.5

6.5

4.820282

8.725429

-2.12026

1.252763

 

39

7806.851

0.03

3.5

6.5

3.663562

8.962757

-3.50656

1.252763

 

59

7806.851

0.05

3.5

6.5

4.077537

8.962757

-2.99573

1.252763

 

72

7806.851

0.08

3.5

6.5

4.276666

8.962757

-2.52573

1.252763

 

117

7806.851

0.12

3.5

6.5

4.762174

8.962757

-2.12026

1.252763

 

52

2463.007

0.03

5.5

10

3.951244

7.809138

-3.50656

1.704748

 

72

2463.007

0.05

5.5

10

4.276666

7.809138

-2.99573

1.704748

 

98

2463.007

0.08

5.5

10

4.584967

7.809138

-2.52573

1.704748

 

163

2463.007

0.12

5.5

10

5.09375

7.809138

-2.12026

1.704748

 

65

3903.426

0.03

5.5

10

4.174387

8.26961

-3.50656

1.704748

 

84

3903.426

0.05

5.5

10

4.430817

8.26961

-2.99573

1.704748

 

110

3903.426

0.08

5.5

10

4.70048

8.26961

-2.52573

1.704748

 

169

3903.426

0.12

5.5

10

5.129899

8.26961

-2.12026

1.704748

 

65

4948.004

0.03

5.5

10

4.174387

8.50674

-3.50656

1.704748

 

98

4948.004

0.05

5.5

10

4.584967

8.50674

-2.99573

1.704748

 

110

4948.004

0.08

5.5

10

4.70048

8.50674

-2.52573

1.704748

 

169

4948.004

0.12

5.5

10

5.129899

8.50674

-2.12026

1.704748

 

65

6157.516

0.03

5.5

10

4.174387

8.725429

-3.50656

1.704748

 

98

6157.516

0.05

5.5

10

4.584967

8.725429

-2.99573

1.704748

 

117

6157.516

0.08

5.5

10

4.762174

8.725429

-2.52573

1.704748

 

169

6157.516

0.12

5.5

10

5.129899

8.725429

-2.12026

1.704748

 

65

7806.851

0.03

5.5

10

4.174387

8.962757

-3.50656

1.704748

 

98

7806.851

0.05

5.5

10

4.584967

8.962757

-2.99573

1.704748

 

130

7806.851

0.08

5.5

10

4.867534

8.962757

-2.52573

1.704748

 

163

7806.851

0.12

5.5

10

5.09375

8.962757

-2.12026

1.704748

 

81

2463.007

0.03

7.5

15

4.394449

7.809138

-3.50656

2.014903

 

130

2463.007

0.05

7.5

15

4.867534

7.809138

-2.99573

2.014903

 

195

2463.007

0.08

7.5

15

5.273

7.809138

-2.52573

2.014903

 

260

2463.007

0.12

7.5

15

5.560682

7.809138

-2.12026

2.014903

 

104

3903.426

0.03

7.5

15

4.644391

8.26961

-3.50656

2.014903

 

143

3903.426

0.05

7.5

15

4.962845

8.26961

-2.99573

2.014903

 

195

3903.426

0.08

7.5

15

5.273

8.26961

-2.52573

2.014903

 

260

3903.426

0.12

7.5

15

5.560682

8.26961

-2.12026

2.014903

 

117

4948.004

0.03

7.5

15

4.762174

8.50674

-3.50656

2.014903

 

156

4948.004

0.05

7.5

15

5.049856

8.50674

-2.99573

2.014903

 

221

4948.004

0.08

7.5

15

5.398163

8.50674

-2.52573

2.014903

 

260

4948.004

0.12

7.5

15

5.560682

8.50674

-2.12026

2.014903

 

130

6157.516

0.03

7.5

15

4.867534

8.725429

-3.50656

2.014903

 

156

6157.516

0.05

7.5

15

5.049856

8.725429

-2.99573

2.014903

 

195

6157.516

0.08

7.5

15

5.273

8.725429

-2.52573

2.014903

 

286

6157.516

0.12

7.5

15

5.655992

8.725429

-2.12026

2.014903

 

130

7806.851

0.03

7.5

15

4.867534

8.962757

-3.50656

2.014903

 

169

7806.851

0.05

7.5

15

5.129899

8.962757

-2.99573

2.014903

 

221

7806.851

0.08

7.5

15

5.398163

8.962757

-2.52573

2.014903

 

299

7806.851

0.12

7.5

15

5.700444

8.962757

-2.12026

2.014903

 

221

2463.007

0.03

9.5

18

5.398163

7.809138

-3.50656

2.251292

 

260

2463.007

0.05

9.5

18

5.560682

7.809138

-2.99573

2.251292

 

357

2463.007

0.08

9.5

18

5.877736

7.809138

-2.52573

2.251292

 

487

2463.007

0.12

9.5

18

6.188264

7.809138

-2.12026

2.251292

 

227

3903.426

0.03

9.5

18

5.42495

8.26961

-3.50656

2.251292

 

325

3903.426

0.05

9.5

18

5.783825

8.26961

-2.99573

2.251292

 

357

3903.426

0.08

9.5

18

5.877736

8.26961

-2.52573

2.251292

 

487

3903.426

0.12

9.5

18

6.188264

8.26961

-2.12026

2.251292

 

195

4948.004

0.03

9.5

18

5.273

8.50674

-3.50656

2.251292

 

292

4948.004

0.05

9.5

18

5.676754

8.50674

-2.99573

2.251292

 

357

4948.004

0.08

9.5

18

5.877736

8.50674

-2.52573

2.251292

 

520

4948.004

0.12

9.5

18

6.253829

8.50674

-2.12026

2.251292

 

292

6157.516

0.03

9.5

18

5.676754

8.725429

-3.50656

2.251292

 

445

6157.516

0.05

9.5

18

6.098074

8.725429

-2.99573

2.251292

 

650

6157.516

0.08

9.5

18

6.476972

8.725429

-2.52573

2.251292

 

747

6157.516

0.12

9.5

18

6.616065

8.725429

-2.12026

2.251292

 

357

7806.851

0.03

9.5

18

5.877736

8.962757

-3.50656

2.251292

 

487

7806.851

0.05

9.5

18

6.188264

8.962757

-2.99573

2.251292

 

650

7806.851

0.08

9.5

18

6.476972

8.962757

-2.52573

2.251292

 

 

Using STATGRAPHICS -MULTIPLE LINEAR REGRESSION MODULE develop the empirical model for cutting force Fz and Torque (Moment) Mz can be writing as following

Proposed Model 1 Force (Model 1 F)
Proposed Model 1 Moments (Model 1 M)

 

Proposed Model 2 Force (Model 1 F) .In spread sheet create a new column of val;ues.
Proposed Model 2 Moments (Model 1 M). In spread sheet create a new column of values.

 

Find A,f ,b and c d e etc in Fz model using first data table ,and Find B,d,e,f d using second Data table for each of the odel.. Write one page summary based upon completer regression report generated by STATGRAPHICS for each fitted model .Its goodness of fit as measured by R2 values and other important coefficients tabulated and plotted in the report. (Attach PDF copy of each full report of STATGRAPHICS output and your EXCEL File used as input data.

 

c

b

a

V

D

f

A

Fz

´

´

´

=

f

e

d

V

D

f

B

Mz

´

´

´

=

c

b

a

V

d

D

f

A

Fz

´

´

´

=

)

(

2

2

)

(

2

2

d

D

f

e

d

V

d

D

f

B

Mz

´

´

´

=

)

(

2

2

)

(

2

2

d

D

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