ASM Metals HandBook Vol. 17 - Nondestructive Evaluation and Quality Control

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specification requirements--a costly proposition. Therefore, these two variables might be considered to be noise variables,

and perhaps the robust design/parameter design concept can be used to see how adjustments in variables 1 and 2 could be

made to reduce the transmitted variability due to variables 3 and 4.

As a result, instead of thinking in terms of a 16-run experiment design that considers four variables at two levels each, one

should think in terms of two 2

factorial experiments:

• The inner design is a 2

factorial in the two controllable variables (spring tension and method of pointer

location)

• The outer design is a 2

factorial in the two noise variables (bimetal hook twist and bimetal bracket

bend)

The outer design is conducted at each of the four unique variable settings of the inner design. A graphical representation

of this experiment design is shown in Fig. 46. The numbers in the corners of each of the four outer design squares

represent the fallback results for each of the 16 unique trails. Referring to the data in Fig. 46, and

, the mean and

standard deviation of the % deflection, are determined at each of the four test combinations of the inner design:

Test no.

1 - - 12.0

2.94

2 + - 9.0

3.37

3 - + 11.5

4.8

4 + + 9.5 2.08

Fig. 46 Inner/outer experimental design structure for the fuel-gage study data in Table 18

. Numbers at corners

of outer design squares are fallback (% deflection) values, Y.

By analyzing the above responses (average fallback and standard deviation of fallback) separately, the settings/values can

be determined for the control variables that minimize average fallback and give rise to minimum variation in fallback, that

is, the most robust process design.

Results. Figures 47 and 48 illustrate the results of the analyses. The interpretation of the results is as follows:

• In terms of average response, % deflection is reduced by increasing spring tension (Fig. 47

). This

reduction is about the same for both methods of pointer location. On the average, the pointer location

method has little effect on % deflection

• In terms of stan

dard deviation, it is best to use the other (standard) method of pointer location along

with tighter spring tension (Fig. 48)

It appears that the nominal response can be controlled by the manipulation of spring tension, while the variation in

response is controlled by manipulation of the method of pointer location.

Fig. 47

Effect of control factors on average performance. Numbers at corners of square are the means of the %

deflection, .

Fig. 48 Effect of control factors on variation in performance. Numbers

at corners of square are the standard

deviations of the % deflection,

Reference cited in this section

30.

H.L. Oh, Variation Tolerant Design, in ASME Proceedings on Quality, Design, Planning, and Control,

American Society of Mechanical Engineers, 1987, p 137-145

Statistical Quality Design and Control

Richard E. DeVor, University of Illinois, Urbana-Champaign; Tsong-how Chang, University of Wisconsin, Milwaukee

References

1. W.W. Scherkenbach, The Deming Route to Quality and Productivity: Road Maps and Roadblocks,

Mercury Press/Fairchild Publications, 1987

2. J.M. Juran, Juran on Planning for Quality, The Macmillan Free Press, 1986

3. A.V. Feigenbaum, Total Quality Control, McGraw-Hill, 1983

4. G. Taguchi and Y. Wu, Introduction to Off-Line Quality Control,

Central Japan Quality Control

Association, 1979

5. G. Taguchi, On-Line Quality Control During Production, Japanese Standards Association, 1981

6. R.A. Fisher, Design of Experiments, 8th ed., Hafner Publishing, 1966

7. G.E.P. Box and J.S. Hunter, The 2k-p Fractional Factorial Designs, Part I and Part II, Technometrics,

Vol

3, 1961

8. G.E.P. Box, W.G. Hunter, and J.S. Hunter, Statistics for Experimenters, John Wiley & Sons, 1978

9. L.P. Sullivan, Reducing Variability: A New Approach to Quality, Qual. Prog., Vol 17 (No. 7), 1985, p 15-

10. W.A. Shewhart, The Economic Control of Quality of Manufactured Product, Van Nos

trand, 1931 (ASQC,

1980)

11. W.E. Deming, Quality, Productivity, and Competitive Position,

MIT Center for Advanced Engineering,

1982

12. J.M. Juran, Quality Problems, Remedies, and Nostrums, Ind. Qual. Con., Vol 22, 1966, p 647-653

13. S.W. Roberts, Control Charts Based on Geometric Moving Averages, Technometrics, Vol 1, 1959, p 234-

250

14. A.L. Sweet, Control Charts Using Coupled Exponentially Weighted Moving Averages, Trans. IIE,

Vol 18

(No. 1), 1986, p 26-33

15. A.W. Wortham and G.F. Heinrich, Control Charts Using Exponential Smoothing Techniques,

Trans.

ASQC, Vol 26, 1972, p 451-458

16. A.W. Wortham, The Use of Exponentially Smoothed Data in Continuous Process Control,

Int. J. Prod.

Res., Vol 10 (No. 4), 1972, p 393-400

17. A.F. Bissell, An Introduction to CuSum Charts, The Institute of Statisticians, 1984

18.

"Guide To Data Analysis and Quality Control Using CuSum Techniques," BS5703 (4 parts), British

Standards Institution, 1980-1982

19. J.M. Lucas, The Design and Use of V-Mask Control Scheme, J. Qual. Technol., Vol 8 (No. 1), 1976, p 1-

20. J. Murdoch, Control Charts, Macmillan, 1979

21. J.S. Oakland, Statistical Process Control, William Heinemann, 1986

22. I. Burr, Statistical Quality Control Methods, Marcel Dekker, 1976

23. S.M. Wu, Analysis of Rail Steel Bar Welds By Two-Level Factorial Design,

Weld. J. Research

Supplement, April 1964

24. R.E. DeVor and T.H. Chang, Quality and Productivity Design and Improvement: Module 2, in

Statistical

Process Control, Ford Motor Company, Plastic Products Division, 1988

25.

R.E. DeVor and T.H. Chang, Statistical Methods for Quality and Productivity Design and Improvement, in

The Tool and Manufacturing Engineer's Handbook, Vol 4, Society of Manufacturing Engineers, 1987

26. D.J. Finney, The Fractional Replication of Factorial Arrangements, Ann. Eugen., Vol 12, 1945, p 291-301

27. C.R. Rao, Factorial Experiments Derivable From Combinatorial Arrangements of Arrays,

J. Royal Stat.

Soc., Vol B9, 1947, p 128-140

28. L.H.C. Tippett, Applications of Statistical Methods to the Control of Quality in Industrial Production,

Manchester Statistical Society, 1934

29. R.L. Plackett and J.P. Burman, Design of Optimal Multifactorial Experiments, Biometrika,

Vol 23, 1946, p

305-325

30. H.L. Oh, Variation Tolerant Design, in ASME Proceedings on Quality, Design, Planning, and Control,

American Society of Mechanical Engineers, 1987, p 137-145

Abbreviations and Symbols

o Abbreviations and Symbols

• a

• crack length; flaw size; depth; level of significance

• A

• ampere

• A

• amplitude; area

•

• angstrom

• ac

• alternating current

• A/D

• analog-to-digital converter

• AE

• acoustic emission

• AFS

• American Foundrymen's Society

• AGC

• automatic gain control

• AIA

• Aerospace Industries Association of America

• AIPD

• acoustic impedance polarity detector

• AISI

• American Iron and Steel Institute

• AMS

• Aerospace Material Specifications

• API

• American Petroleum Institute

• ASIP

• Aircraft Structural Integrity Program

• ASTM

• American Society for Testing and Materials

• atm

• standard atmosphere

• B

• bar size; magnetic flux density

• B

• magnetic flux vector

• bcc

• body-centered cubic

• bcd

• binary coded decimal

• BIE

• boundary integral equation

• Bq

• becquerel

• BWO

• backward wave oscillator

• c

• speed of light; specific heat

• C

• coulomb

• CAD/CAM

• computer-aided design/computer-aided manufacturing

• CARP

• Committee for Acoustic Emission in Reinforced Plastics

• CCD

• charge-coupled device

• cd

• candela

• CFA

• crossed-field amplifier

• CFRP

• carbon fiber-reinforced plastic

• Ci

• curie

• CID

• charge-injected device

• CIE

• Commission Internationale de l'Eclairage (International Commission on Illumination)

• CL

• control limit; confidence level

• CMM

• coordinate measuring machine

• CMS

• coordinate measuring system

• COD

• crack opening displacement

• CRT

• cathode ray tube

• C-SAM

• C-mode scanning acoustic microscopy

• cSt

• centiStokes

• CT

• computed tomography

• CuSum

• cumulative sum

• CW

• continuous wave

• d

• deuteron

• d

• used in mathematical expressions involving a derivative (denotes rate of change); depth; diameter

• D

• diameter; duration; dislocation density

• da/dN

• fatigue crack growth rate

• DAC

• digital-to-analog converter

• dB

• decibel

• dBae

• decibel of acoustic emission amplitudes

• dc

• direct current

• DCC

• direct computer control

• diam

• diameter

• DIN

• Deutsche Industrie-Normen (German Industrial Standards)

• DIP

• dual-in-line package

• DLM

• digital light meter

• dpi

• dots per inch

• DR

• digital radiography; digital radiograph

• e

• natural logarithm base, 2.71828; random error

• E

• modulus of elasticity; electric field strength; emissive power; electromotive force; energy counts

(acoustic emission); applied voltage

• EC

• eddy current

• ECP

• electric current perturbation

• EDM

• electrical discharge machining

• EMA

• electromagnetic acoustic (transducer)

• ENSIP

• Engine Structural Integrity Program

• EPA

• Environmental Protection Agency

• Eq

• equation

• et al.

• and others

• ET

• eddy current testing

• eV

• electron volt

• EWMA

• exponentially weighted moving average

• f

• frequency; transfer function

• F

• eddy current inspection test frequency

• FERPIC

• ferroelectric photoconductor image camera

• FET

• field-effect transistor

• FFT

• fast Fourier transform

• FID

• flame ionization detector

• Fig.

• figure

• fm

• femtometer

• FM

• frequency modulation

• FMR

• ferromagnetic resonance

• FR

• felicity ratio

• FRP

• fiber-reinforced plastic

• ft

• foot

• ftc

• footcandle

• ft-L

• footlambert

• g

• gram

• G

• gauss

• G

• film gradient

• GBq

• gigabecquerel

• GPa

• gigapascal

• GTO

• gate turnoff

• Gy

• gray (unit of absorbed radiation)

• h

• convection heat transfer coefficient

• h

• hour

• H

• magnetic field strength

• H

• magnetic field vector

• HAZ

• heat-affected zone

• HB

• Brinell hardness

• HIP

• hot isostatic pressing

• HNDT

• holographic nondestructive test

• HR

• Rockwell hardness (requires scale designation, such as HRC for Rockwell C hardness)

• HSL

• hue, saturation, luminance

• i

• for a complex variable; a summation index

• i

• unit vector along the x-axis

• I

• intensity; electrical current

• <I>

• average intensity

• IACS

• International Annealed Copper Standard

• IBIS

• integrated blade inspection system

• IC

• integrated circuit

• ID

• inside diameter

• IF

• intermediate frequency

• IGA

• intergranular attack

• IMPATT

• impact avalanche transit time

• in.

• inch

• IQI

• image quality indicator

• IR

• infrared

• j

• for a complex variable; a summation index

• j

• unit vector along the y-axis

• J

• joule

• k

• thermal conductivity; wave number

• k

• unit vector along the z-axis

• K

• stress intensity factor; kernel

• K

• plane-stress fracture toughness

• K

• plane-strain fracture toughness

• K

Iscc

• threshold stress intensity for stress-corrosion cracking

• kg

• kilogram

• km

• kilometer

• kPa

• kilopascal

• ksi

• 1000 lb (1 kip) per square inch

• kV

• kilovolt

• kVp

• kilovolt peak

• l

• average rate of occurrence of defects per sample; length

• L

• length; likelihood (function)

• lb

• pound

• LCC

• life cycle cost

• LCF