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Microchip Mfg. problem

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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!

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Microchip Mfg. problem

  1. 1. 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
  2. 2. 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!
  3. 3. 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 ...
  4. 4. Readback Isolated PulseReadback Isolated Pulse forfor TypicalTypical 1980s TFH1980s TFH TT
  5. 5. Math ModelMath Model forfor Readback Isolated PulseReadback Isolated Pulse 1 Lorentz function 3 Lorentz functions1 Lorentz function 3 Lorentz functions
  6. 6. Math ModelMath Model forfor Readback Isolated PulseReadback Isolated Pulse 3 Lorentz functions summed3 Lorentz functions summed T1 T2 T3T1 T2 T3 Time AxisTime Axis
  7. 7. TypicalTypical Readback Isolated PulseReadback Isolated Pulse versusversus Lorentz Math ModelLorentz Math Model TT
  8. 8. TypicalTypical Readback Isolated PulseReadback Isolated Pulse Curve Fit ErrorCurve Fit Error TT .001 to -.001 Amplitude Range.001 to -.001 Amplitude Range
  9. 9. 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
  10. 10. How to find 'bad' logs?How to find 'bad' logs? Destructive TestingDestructive Testing versusversus Curve fitting dataCurve fitting data
  11. 11. Readback Isolated PulseReadback Isolated Pulse forfor AbnormalAbnormal 1980s TFH1980s TFH TT
  12. 12. AbnormalAbnormal Readback Isolated PulseReadback Isolated Pulse versusversus Lorentz Math ModelLorentz Math Model TT
  13. 13. AbnormalAbnormal Readback Isolated PulseReadback Isolated Pulse Curve Fit ErrorCurve Fit Error TT .001 to -.001 Amplitude Range.001 to -.001 Amplitude Range
  14. 14. 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
  15. 15. Destructive TestingDestructive Testing
  16. 16. Readback Isolated PulseReadback Isolated Pulse ImprovedImproved Math ModelMath Model TT 1 + x 2 1 x y   Modified LorentzianModified Lorentzian A side note:
  17. 17. 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:
  18. 18. 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.
  19. 19. 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
  20. 20. Monte Carlo MethodMonte Carlo Method forfor MultivariablesMultivariables What is its purpose?What is its purpose?
  21. 21. 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
  22. 22. Monte Carlo MethodMonte Carlo Method forfor MultivariablesMultivariables How much time is required?How much time is required? Tons!Tons!
  23. 23. Total Derivative DefinitionTotal Derivative Definition
  24. 24. 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
  25. 25. 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
  26. 26. 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
  27. 27. Curve Fit: what models to use?Curve Fit: what models to use? 1. 2. 3. 4.
  28. 28. 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
  29. 29. 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?
  30. 30. Quiz Plots ... what models to use?Quiz Plots ... what models to use?
  31. 31. Quiz Plots ... what models to use?Quiz Plots ... what models to use? 2.1 2.2 2.3 2.4
  32. 32. Quiz Plots ... what models to use?Quiz Plots ... what models to use? 3.1 3.2 3.3 3.4
  33. 33. Goal: Equal Ripple 'Goal: Equal Ripple 'ErrorError' Plot!' Plot! Example 'Error' Plots: what do they 'say'?Example 'Error' Plots: what do they 'say'?
  34. 34. 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.
  35. 35. 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.

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