In the ‘old’ days, when a circuit seemed to have a problem, one could look at each circuit to see if they could detect a bad circuit. Today, finding a bad chip is hard to due. Seeing a chip’s circuit may not be possible, how then can one determine a bad chip? For example, in the 1970s, Memorex Corp. was designing their first “Thin Film Head” (TFH) and using micro chip components. It was soon realized that something was wrong with a small percent of its disc drives being made with these chips. But, how to detect or find the bad drives was not known. Destructive testing seemed like the only choice. Years went bye. No solution!

2. Manufacturing Tools ClassManufacturing Tools Class
Duplication ProblemsDuplication Problems
Pass/Fail Testing via Curve fittingPass/Fail Testing via Curve fitting
Total Derivative vs. Monte Carlo AnalysisTotal Derivative vs. Monte Carlo Analysis
Optimal Designs EnterpriseOptimal Designs Enterprise
goal-driven.netgoal-driven.net

3. 200 Thin-Film-Heads (TFHs) for200 Thin-Film-Heads (TFHs) for
ComparisonComparison
200 samples tested in batch mode200 samples tested in batch mode
- After testing -- After testing -
199 Responded in a 'typical' way199 Responded in a 'typical' way
1 Responded in a 'abnormal' way1 Responded in a 'abnormal' way
The Technician said he would haveThe Technician said he would have
changed the oscillascope settings ifchanged the oscillascope settings if
he saw such a response. Thus,he saw such a response. Thus,
continue hiding problem!continue hiding problem!

4. 1980s Disc Drive Development1980s Disc Drive Development
withwith
Mfg. Duplication ProblemsMfg. Duplication Problems
Thin-Film-Head (TFH) contains two parallelThin-Film-Head (TFH) contains two parallel
magnetic 'logs' as illustrated below ...magnetic 'logs' as illustrated below ...

5. Readback Isolated PulseReadback Isolated Pulse
forfor
TypicalTypical 1980s TFH1980s TFH
TT

6. Math ModelMath Model
forfor
Readback Isolated PulseReadback Isolated Pulse
1 Lorentz function 3 Lorentz functions1 Lorentz function 3 Lorentz functions

7. Math ModelMath Model
forfor
Readback Isolated PulseReadback Isolated Pulse
3 Lorentz functions summed3 Lorentz functions summed
T1 T2 T3T1 T2 T3
Time AxisTime Axis

8. TypicalTypical Readback Isolated PulseReadback Isolated Pulse
versusversus
Lorentz Math ModelLorentz Math Model
TT

9. TypicalTypical Readback Isolated PulseReadback Isolated Pulse
Curve Fit ErrorCurve Fit Error
TT
.001 to -.001 Amplitude Range.001 to -.001 Amplitude Range

10. TypicalTypical Readback Isolated PulseReadback Isolated Pulse
Key ParameterKey Parameter
for Pass/Fail Decisionfor Pass/Fail Decision
(T3 - T2)(T3 - T2)
Key Ratio = ---------------Key Ratio = ---------------
(T2 - T1)(T2 - T1)
( 38.3 - 6.12)( 38.3 - 6.12)
= ------------------= ------------------
(6.12 + 54.8)(6.12 + 54.8)
= 32.2 / 60.9 == 32.2 / 60.9 = .53 Passes !.53 Passes !
T1 T2 T3T1 T2 T3
Time AxisTime Axis

11. How to find 'bad' logs?How to find 'bad' logs?
Destructive TestingDestructive Testing
versusversus
Curve fitting dataCurve fitting data

12. Readback Isolated PulseReadback Isolated Pulse
forfor
AbnormalAbnormal 1980s TFH1980s TFH
TT

13. AbnormalAbnormal Readback Isolated PulseReadback Isolated Pulse
versusversus
Lorentz Math ModelLorentz Math Model
TT

14. AbnormalAbnormal Readback Isolated PulseReadback Isolated Pulse
Curve Fit ErrorCurve Fit Error
TT
.001 to -.001 Amplitude Range.001 to -.001 Amplitude Range

15. AbnormalAbnormal Readback Isolated PulseReadback Isolated Pulse
Key ParameterKey Parameter
for Pass/Fail Decisionfor Pass/Fail Decision
(T3 - T2)(T3 - T2)
Key Ratio = ---------------Key Ratio = ---------------
(T2 - T1)(T2 - T1)
( 111 - 0.65)( 111 - 0.65)
= ------------------= ------------------
(-0.65 + 32.7)(-0.65 + 32.7)
= 111.7 / 32.7 == 111.7 / 32.7 = 3.4 Fails !!!3.4 Fails !!! > x.x> x.x
T1 T2 T3T1 T2 T3
Time AxisTime Axis

16. Destructive TestingDestructive Testing

17. Readback Isolated PulseReadback Isolated Pulse
ImprovedImproved Math ModelMath Model
TT 1 + x
2
1 x
y


Modified LorentzianModified Lorentzian
A side note:

18. Math ModelMath Model
forfor
Sine-wave TrainSine-wave Train
'n' Sine functions each with 3 parameters'n' Sine functions each with 3 parameters
A side note:

19. Some ParametersSome Parameters
areare NOTNOT
Independent!Independent!
ffii andand thetathetaii are dependent parametersare dependent parameters
They depend uponThey depend upon aaii
So start search with 'large'So start search with 'large' aaii valuesvalues
to insure partial(to insure partial(ffii, t) & partial(, t) & partial(thetathetaii, t) will, t) will
care some weight.care some weight.

20. CurvFit (tm) ProgramCurvFit (tm) Program
-Freeware--Freeware-
Requires Windows OSRequires Windows OS
Download from goal-driven/apps/curvfit.htmlDownload from goal-driven/apps/curvfit.html
CurvFit has Lorentz, Modified Lorentz,CurvFit has Lorentz, Modified Lorentz,
Sine, Damped Sine,Sine, Damped Sine, et al.et al. demosdemos

21. Monte Carlo MethodMonte Carlo Method
forfor
MultivariablesMultivariables
What is its purpose?What is its purpose?

22. What is its purpose?What is its purpose?
Find Total Variance of a ProcessFind Total Variance of a Process
Monte Carlo MethodMonte Carlo Method
forfor
MultivariablesMultivariables

23. Monte Carlo MethodMonte Carlo Method
forfor
MultivariablesMultivariables
How much time is required?How much time is required?
Tons!Tons!

24. Total Derivative DefinitionTotal Derivative Definition

25. Total DerivativeTotal Derivative
Will the Total Derivative replace the need forWill the Total Derivative replace the need for
Monte CarloMonte Carlo Analysis?Analysis?
Not sure ... need moreNot sure ... need more
industry experience to answer this questionindustry experience to answer this question

26. FortranCalculusFortranCalculus
Code 4 Total VarianceCode 4 Total Variance
x = 123: y = 3.21: z = .0123: etc.x = 123: y = 3.21: z = .0123: etc.
varX = .456: varY = .654: varZ = .000911: etc.varX = .456: varY = .654: varZ = .000911: etc.
Invoke Gradient onInvoke Gradient on x, y, z, etc.x, y, z, etc.
InIn ABCABC
oooooo
Model ABCModel ABC
F = f( x, y, z, etc.)F = f( x, y, z, etc.)
dx =dx = #Partial#Partial( F, x): dy =( F, x): dy = #Partial#Partial( F, y)( F, y)
dz =dz = #Partial#Partial( F, z)( F, z)
varF = varX*dx + varY*dy + varZ*dz + ...varF = varX*dx + varY*dy + varZ*dz + ...
EndEnd

27. Code 4 Finding Unknown Var.sCode 4 Finding Unknown Var.s
x = 123: y = 3.21: z = .0123: etc.x = 123: y = 3.21: z = .0123: etc.
varX = 1: varY = .654: varZ = 1:varX = 1: varY = .654: varZ = 1: varF =varF = 4.56: etc.4.56: etc.
Invoke Gradient on x, y, z, etc.Invoke Gradient on x, y, z, etc.
In ABCIn ABC
FindFind varX, varYvarX, varY inin ABCABC to matchto match gg
oooooo
Model ABCModel ABC
F = f( x, y, z, etc.)F = f( x, y, z, etc.)
dx = #Partial( F, x): dy = #Partial( F, y)dx = #Partial( F, x): dy = #Partial( F, y)
dz = #Partial( F, z)dz = #Partial( F, z)
gg == varFvarF - (varX*dx + varY*dy + varZ*dz)- (varX*dx + varY*dy + varZ*dz)
EndEnd

28. Curve Fit: what models to use?Curve Fit: what models to use?
1. 2.
3. 4.

29. 1.1. Lorentzian:Lorentzian: y=1/(1+x*x)y=1/(1+x*x)
2 . Mod. Lorentzian:2 . Mod. Lorentzian: y=(1+x)/(1+x*x)y=(1+x)/(1+x*x)
3. Sinusoidal:3. Sinusoidal: yyii= a Sin( 2 pi freq= a Sin( 2 pi freqii + phi+ phiii))
4. Damped Sin.: y4. Damped Sin.: yii= a= aii Exp( bExp( bii x) Sin( 2 pi freqx) Sin( 2 pi freqii + phi+ phiii))
5. Exponental: y5. Exponental: yii= a= aii Exp( bExp( bii x)x)
6. Polynomial:6. Polynomial: yyii= a= aii xxii
Model Choices to choose fromModel Choices to choose from

30. Quiz TimeQuiz Time
What would be a good model to useWhat would be a good model to use
for following data plots?for following data plots?

31. Quiz Plots ... what models to use?Quiz Plots ... what models to use?

32. Quiz Plots ... what models to use?Quiz Plots ... what models to use?
2.1 2.2
2.3 2.4

33. Quiz Plots ... what models to use?Quiz Plots ... what models to use?
3.1 3.2
3.3 3.4

34. Goal: Equal Ripple 'Goal: Equal Ripple 'ErrorError' Plot!' Plot!
Example 'Error' Plots: what do they 'say'?Example 'Error' Plots: what do they 'say'?

35. Helpful SuggestionsHelpful Suggestions
Normalize your data ... between -1 & 1 or 0 & 1Normalize your data ... between -1 & 1 or 0 & 1
To start ... use '1' amplitude valuesTo start ... use '1' amplitude values
Once model is looking good, round last results to 2Once model is looking good, round last results to 2
or 3 digits and try again.or 3 digits and try again.

36. Comments & FeedbackComments & Feedback
Have a new Curve Fit Model?Have a new Curve Fit Model?
Have data set for Human Heart Beat, 1-cycle?Have data set for Human Heart Beat, 1-cycle?
If so, please contact us atIf so, please contact us at optim.designs@gmail.comoptim.designs@gmail.com
Once model is looking good, round last results to 2Once model is looking good, round last results to 2
or 3 digits and try again.or 3 digits and try again.