DOE Exercise 7.27.10

8/8/2019 DOE Exercise 7.27.10

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Exercise 8

A group of young engineers was task to determine the best way to process Ultrasonic sensor such that impedance will be at minimum.

Factors considered are Kunoji amt., PZT Soldering amt., Kunoji position, and PZT ZR.The PZT Zr range are

FactorsLevel

Min Max

Kunoji Amt Std Max

PZT Soldering Amt 1precut 2precut

Kunoji position near PZT near Wall

T e m p

Glue Amt Std Max

Design Matrix

Actual Y

Comb Kunoji Amt PZT Soldering Amt Kunoji position Glue Amt Impedance A

1 Std 1 precut near PZT Std

2 Std 1 precut near PZT Max

3 Std 1 precut near wall Std

4 Std 1 precut near wall Max

5 Std 2precut near PZT Std

6 Std 2precut near PZT Max

7 Std 2precut near wall Std

8 Std 2precut near wall Max

9 Max 1 precut near PZT Std

10 Max 1 precut near PZT Max

11 Max 1 precut near wall Std

12 Max 1 precut near wall Max

13 Max 2precut near PZT Std

14 Max 2precut near PZT Max

15 Max 2precut near wall Std

16 Max 2precut near wall Max

#DIV/0! ave -1 #DIV

ave +1 #DIV

effect #DIV

effect/2 #DIV

Y =

INTERACTIONS

No Interaction

1. ABA- A+

B- #DIV/0! #DIV/0!

B+ #DIV/0! #DIV/0!

2. BCC- C+

B- #DIV/0! #DIV/0!

B+ #DIV/0! #DIV/0!

3. AC Slight Interaction

C- C+

A- #DIV/0! #DIV/0!

A+ #DIV/0! #DIV/0!

217.25

217.25

A-

0

2

4

6

8

10

12

0

2

4

6

8

10

12

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Slight Interaction

-

C-

0

2

4

6

8

10

12

8/8/2019 DOE Exercise 7.27.10


Exercise 2 Factorial Experiment

A factorial design experiment was employed for PC40S-14M9 Ultrasonic Sensor

to determine the effects of Center Silicone amount and Side Silicone amount

on the finished product’s frequency and impedance.

FACTORSLEVEL

Min Max

Center Si Amount ~1mg ~3mg

Side Si Amount ~10mg ~14mg

Data : Frequency (Fr) and Impedance (Zr)

1 2 3 4

C.S S.S C.S S.S C.S S.S C.S S.S

min min min max max min max max

Sample Fr (kHz) Fr (kHz) Fr (kHz) Fr (kHz) Run Fr Zr

1 38.80 482 38.65 559 39.70 463 39.00 504 1 39.25 473

2 38.95 473 39.75 491 39.45 464 39.18 570 2 39.13 524

3 39.10 454 39.08 521 38.95 458 39.73 552 3 39.37 477

4 38.73 443 39.35 582 38.78 497 38.75 585 4 38.89 571

5 38.93 450 38.53 513 38.85 465 38.60 555 39.16 511

6 39.80 483 39.25 560 39.80 479 38.93 562

7 39.85 541 39.35 603 38.95 497 38.48 569

8 39.25 490 38.63 447 39.50 480 38.53 593

9 39.33 433 39.03 477 39.60 513 38.63 603

10 39.73 485 39.65 486 40.10 457 39.13 618

Interactions

1 FRAB

Side Si minSide Si ma

Center 39.25 39.13

Center 39.37 38.89

2 ZRSide Si minSide Si ma

Center 473 524

Center 477 571

Zr (Ω) Zr (Ω) Zr (Ω) Zr (Ω)

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Fr Zr

Center Si Side Si Center Si Side Si

A B AB A B AB

-1 -1 1 -1 -1 1

-1 1 -1 -1 1 -1

1 -1 -1 1 -1 -1

1 1 1 1 1 1

ave +1 39.13 39 39.07 ave +1 524.14 547 522

ave -1 39.19 39 39.25 ave -1 498.61 475 501

effect -0.06 -0.30 -0.18 effect 25.53 72.12 22

e/2 -0.028 -0.15 -0.09 e/2 12.77 36.059 10.85

Y= Y=

Strong Interaction Slight Interaction

39.16 - 0.028 A

- 0.149B -

0.09 AB

511 + 12.75 A +

36.06B +

10.85 AB

Side Si min Side Si max38.80

38.90

39.00

39.10

39.20

39.30

39.40

AB Interaction on Fr

Center Simin

Center Simax

Side Si min Side Si max460

480

500

520

540

560

580

AB Interactions on ZR

Center Simin

Center Simiax

8/8/2019 DOE Exercise 7.27.10


Exercise 1

The shelf life of a silicone chemicals is of interest. Ten tubes are randomly selected and tested, and t

Days: 108, 124, 124, 106, 115, 138, 163, 159, 134, 139

Assume that the alternative hypothesis is the mean shelf life is greater than 125 days. Can the null hy

8/8/2019 DOE Exercise 7.27.10


e following results are obtained.

pothesis Ho: µ = 125 be rejected?

8/8/2019 DOE Exercise 7.27.10


Exercise 2

The time to finished a batch of UT sensor is normally distributed random variable measured in minut

The processing times for such 16 batches chosen at random are as follows.

Minutes : 159, 280, 101, 212, 224, 379, 179, 264, 222, 362, 168, 250, 149, 260, 485, 170

Does it seem reasonable that the true mean processing time is greater than 225 hours?

8/8/2019 DOE Exercise 7.27.10


s.

8/8/2019 DOE Exercise 7.27.10


Exercise 3

Two machines are used for filling plastic bottles with a net volume of 16.0 ounces.

The filling process can be assumed to be normal, with standard deviations of s1 = 0.015 and s2 = 0.0

The quality engineering department suspects that both machines fill to the same net volume, whether

A random sample is taken from the output of each machine.

Machine 1:16.03 16.04 16.05 16.05 16.02 16.01 15.66 15.98 16.02 15.99Machine 2: 16.02 15.97 15.96 16.01 15.99 16.03 16.04 16.02 16.01 16.00

Do you think the quality engineering is correct?

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18.

or not this volume is 16.0 ounces.

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Exercise 4

An Engineer want to compare two types of structural steel if the strengths (in 1000 lbs/sq. in.) are the

Steel 1 Steel 2

25 13

29 2521 16

20 23

22 21

20 27

24 16

24 22

23 15

22 27

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samame or different:

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Exercise 5

•An article in Solid State Technology, “Orthogonal Design for Process OptiApplication to Plasma Etching” by GZ Yin and DW Jillie (May 1987) descridetermine the effect of the C2F6 floe rate on the uniformity of etch on a

integrated circuit manufacturing. Data for two flow rates are as follows:C2F6 Uniformity Observation125 2.7 4.6 2.6 3.0 3.2 3.8

200 4.6 3.4 2.9 3.5 4.1 5.1Does the C2F6 flow rate affect the wafer-to-wafer variability and avera

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mization and Itses an experiment toilicone wafer used in

ge etch uniformity?

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Exercise 6

•An article in the Journal of Strain Analysis (vol. 18, no 2, 1983) comparesfor predicting the shear strength for steep plate girders. Data for nine girratio of predicted to observed load for two of these procedures, the Karlsr

methods are as follows:Girder 1 2 3 4 5 6 7 8 9KM 1.186 1.151 1.322 1.339 1.200 1.402 1.365 1.537 1.559LM 1.061 0.992 1.063 1.062 1.065 1.178 1.037 1.086 1.052

Is there any difference between the two methods?

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several proceduresers in the form of theuhe and Lehigh

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Exercise 7

•The diameter of ball bearing was measured by 12 inspectors, each usingof calipers. The result wereInsp 1 2 3 4 5 6 7 8 9 10 11 12

Caliper 1 0.265 0.265 0.266 0.267 0.267 0.265 0.267 0.267 0.265Caliper 2 0.264 0.265 0.264 0.266 0.267 0.268 0.264 0.265 0.265Is there a significant difference between the means of the population of represented by the two samples? Use = 0.05

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two different kinds

.268 0.268 0.265

.267 0.268 0.269easurements

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Exercise 8

A group of young engineers was task to determine the best way to process Ultrasonic sensor such that impedance will be at minimum.

Factors considered are aging temperature, the length of aging and the amount of glue being applied.The aging process specification is 85ºC to 95ºC from 3hrs to 4hours. Allowable amount of silicone to be applied is 2mg ~ 6mg.

FactorsLevel

Min Max

Aging Temperature 85ºC 95ºC

Aging Time 3hrs 4hrs

Glue Amount 2mg 6mg

T e m p

T i m e

G l u e A m o u n t

Design Matrix

Actual Y

Comb Temp Time Si Amt Impedance A B C AB BC AC ABC

1 85 3 2 185 -1 -1 -1 1 1 1 -1

2 85 3 6 227 -1 -1 1 1 -1 -1 1

3 85 4 2 210 -1 1 -1 -1 -1 1 1

4 85 4 6 226 -1 1 1 -1 1 -1 -1

5 95 3 2 200 1 -1 -1 -1 1 -1 1

6 95 3 6 230 1 -1 1 -1 -1 1 -1

7 95 4 2 225 1 1 -1 1 -1 -1 -1

8 95 4 6 235 1 1 1 1 1 1 1

217.25 ave -1 212 210.5 205 216.5 223 219.5 216.5

ave +1 222.5 224 229.5 218 211.5 215 218

effect 10.5 13.5 24.5 1.5 -11.5 -4.5 1.5

effect/2 5.25 6.75 12.25 0.75 -5.75 -2.25 0.75

Y =

INTERACTIONS

No Interaction

1. ABA- A+

B- 206 215

B+ 218 230

2. BCC- C+

B- 192.5 228.5

B+ 217.5 230.5

3. AC Slight InteractionC- C+

A- 197.5 226.5

A+ 212.5 232.5

Slight Interaction

217.25 + 5.25 A + 6.75B + 12.25C + 0.75 AB - 5.75BC - 2.25 AC + 0.75 ABC

217.25 + 5.25 A + 6.75B + 12.25C + 0.75 AB + 0.75 ABC - 5.75BC - 2.25AC

A- A+

190

195

200

205

210

215

220

225

230

235

B-

B+

C- C+

170

180

190

200

210

220

230

240

B-

B+

190

200

210

220

230

240

A-

A+

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C- C+

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DOE Exercise 7.27.10