TAGUCHI METHOD for STATIC PROBLEMS

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1 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP 8Feb-1Mar 01 Module 5 TAGUCHI METHOD for STATIC PROBLEMS 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 1 TAGUCHI'S CONCEPT of QUALITY-LOSS FUNCTION Products meetig tolerace also iflict a quality loss Best quality whe performace is o target 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio Static S/N Ratio - 1

2 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP 8Feb-1Mar Quality Loss Fuctios (a) Quality Loss - Step Fuctio L ( y ) Quality Loss Quality 0.0 m- m m+ (b) Quality Loss - Quadratic Fuctio 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 3 TAGUCHI'S QUADRATIC LOSS FUNCTION Step Fuctio Quality Loss L ( y ) = 0 for y - m o = o otherwise Quadratic Loss Fuctio Quality Loss L ( y ) = k ( y - m ) where k is called the quality coefficiet 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 4 Static S/N Ratio -

3 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP 8Feb-1Mar 01 INTERPRETATION of ENGINEERING TOLERANCES Step Quality Loss Fuctio misrepresets quality from customer's poit of view Quadratic Loss Fuctio defied by Taguchi L( y ) = k ( y - m ) 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 5 AVERAGE QUALITY LOSS Quadratic quality loss fuctio measures quality loss of a sigle uit with quality characteristic, say, ' y 1 ' The Quality Loss, L ( y 1 ) = k ( y 1 m ) For ' ' uits with y 1, y, y 3,.., y the quality loss for each uit is L( Y 1) = k ( Y - m ) 1 L( Y ) = k ( Y - m )... L( Y ) = k ( Y - m ) 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 6 Static S/N Ratio - 3

4 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP 8Feb-1Mar 01 AVERAGE QUALITY LOSS The sum of all quality losses is L( Y ) + L( Y ) L ( Y ) 1 Average quality loss is [ ] 1 = k (Y m ) (Y m ) Q av k = _ [(Y 1 m ) (Y m ) ] Fially Q av = k [ ( m ) + ]. 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 7 MEASURE OF QUALITY TOTAL LOSS TO SOCIETY DUE TO FUNCTIONAL VARIATIONS HARMFUL SIDE EFFECTS 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 8 Static S/N Ratio - 4

5 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP 8Feb-1Mar 01 TAGUCHI'S QUADRATIC LOSS FUNCTION REFRIGERATOR EXAMPLE Assume k = 1, target value m = -10 C Q = [ ( m - µ ) + σ ) ] Case 1 : mea µ = C, variace =.1 Quality Loss = 0.35 ( C ) Case : mea µ = - 11 C, variace =. Quality Loss = 1. ( C ) 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 9 INTERPRETATION OF AVERAGE QUALITY LOSS Q = k [ ( m - µ ) + σ ) ] Taguchi's quality loss fuctio is a cost fuctio, with MONEY elemet cotaied i ' k ' ' k ' occurs as multiplicatio factor or 'magificatio factor ' of the statistical term [ ( m - µ ) + σ ) ] Thus reducig [ ( m - µ ) + σ ) ] will reduce quality loss 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 10 Static S/N Ratio - 5

6 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP 8Feb-1Mar 01 INTERPRETATION OF AVERAGE QUALITY LOSS ' k ' ca be expressed as a product k1.k.k3...k k1 > Purchasig efficiecy k > Servicig efficiecy k3 > Admiistratio efficiecy k4 > Marketig & Sales efficiecy. k > Orgaisatioal efficiecy Miimisig ' k ' leads to about 7% to 10% reductio i quality loss Reducig [ ( m - µ ) + σ ) ] leads to more tha 70% reductio i quality loss Reducig [ ( m - µ ) + σ ) ] also reduces ' k ' due to syergistic effects For Robust Desig applicatio we assume k = 1 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 11 REDUCING AVERAGE QUALITY LOSS (a) by brigig mea o target Q = k [ ( m - µ ) + σ ) ] Two terms are ( m - µ ) ad σ ( m - µ ) : Brig mea o target to reduce this term Covetioal desig cocetrates o o brigig mea o target 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 1 Static S/N Ratio - 6

7 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP 8Feb-1Mar 01 REDUCING AVERAGE QUALITY LOSS (b) by reducig variace σ : Variace must be reduced. Covetioal desig reduces variace by screeig or by tolerace desig Robust desig cocetrates o reducig variace ' σ ' without addig to the cost Fially, the mea 'µ' is put o target 'm' 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 13 ROBUST DESIGN METHODOLOGY - STEP OPTIMIZATION STEP 1 : REDUCE VARIATION IRRESPECTIVE OF TARGET VALUE STEP : ADJUST PERFORMANCE ON TARGET LEAVING VARIATION UNDISTURBED FREQUENCY OR PERFORMANCE STEP STEP 1 START m µ PARAMETER SETTINGS 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 14 Static S/N Ratio - 7

8 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP 8Feb-1Mar 01 Beefits of variace reductio No. of Uits Guard Bad Guard Bad After Robust Desig Before Robust Desig Freezer Temperature ( C ) 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 15 EXPLOITING NONLINEARITY Y = f ( X, Z ) If where X = ( x, x,..., x ) oise factors 1 Z = ( z, z,..., z ) cotrol factors 1 m 1 are radom deviatios i the oise factors ( X ), the each oe of these causes deviatios i ' y If y is the sum of all the deviatios due to chage i the oise factors, the f... f y = x X + 1 x X x f X. 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 16 Static S/N Ratio - 8

9 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP 8Feb-1Mar 01 EXPLOITING NONLINEARITY f X X fx 1 1 fx y = X x f fx X 1 1 fx X y = x X Terms are called SENSITIVITY COEFFICIENTS Robust desig reduces sesitivity coefficiets by adjustig levels of cotrol factors ( Z ) 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 17 Noliear Relatioship Exploitatio Audio amplitude y% For a particular set of levels of cotrol factors For differet set of levels of cotrol factors T1 T Ambiet Temperature ( C ) 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 18 Static S/N Ratio - 9

10 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP 8Feb-1Mar 01 EXAMPLES OF S / N RATIOS (1) Smaller - the - Better type problems = 10 Log 10 1 ( Y + Y Y ) 1 () Nomial - the - Best type problems = 10 Log 10. 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 19 CLASSIFICATION OF DESIGN PROBLEMS Classificatio is based o type of SIGNAL factor Static Problems : Dyamic Problems : (Sigal Factor is Costat) (Respose follows Sigal) Smaller - the - Better Nomial - the - Best Larger - the - Better Siged Target Fractio Defective Ordered Categorical Curve or Vector Respose Cotiuous - Cotiuous (C-C) Cotiuous - Digital (C-D) Digital - Cotiuous (D-C) Digital - Digital (D-D) 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 0 Static S/N Ratio - 10

11 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP 8Feb-1Mar 01 Thak You 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP Static SN Ratio 1 Static S/N Ratio - 11

TAGUCHI METHOD for DYNAMIC PROBLEMS

TAGUCHI METHOD for DYNAMIC PROBLEMS Dr. P. R. Apte IIT Bombay SIGNAL - TO - NOISE RATIO 8Feb-1Mar 01 P.R. Apte : 3-Day Taguchi Method Workshop at UNIMAP S/N ratio (Dynamic) - Dyn S/N Ratio - 1 NOISE X