18 A Systematic Problem Solving Flowchart Using Taguchi Methods Define the scope of the problemState the objective of the experimentBrainstorm and Select numbers and levels for controllable and noise factorsStage 1Build an orthogonal design ( Inner and outer Array);L12(211), L18(2 x 37) and L36(23 x 313) are recommendedDetermine the replications for each run.Stage 2
19 A systematic Problem Solving Flowchart for Taguchi Methods Stage 3Run the experiment and collect the dataConduct graphical analysis using the S/N RatioDetermine the key factors and select an “optimal condition“ or the “experimental champion” based on the best y (mean) or largest S/NStage 4Develop the Prediction equation for S/N ratioConduct confirmatory runs and compare the actual results versus the predicted oneUse Taguchi’s Loss Function for tolerance design and assess the performance of “optimal condition”.
27 Common Orthogonal Arrays Number of FactorsNumber of LevelsL4(23)32L8(27)7L12(211)11L16(215)15L32(231)31L9(34)4L18(21, 37)1 and 72 and 3L27(313)13L16(45)5L32(21,49)1 and 92 and 4L36(23,313)3 and 13L64(421)21The L12 and L18 orthogonal arrays are special designs in which interactions are generally spread across all columns. They should not be used for experiments which include the study of interactions
28 Common Orthogonal Arrays 直交表列數最大因子個數在這些水準的行數最大值2345L4-L887L99L121211L161615L’16L18181L25256L272713L323231L’3210L363623L’36L5050L545426L646463L’6421L818140*2-水準表：L4、L8、L12、L16、L32、L643-水準表：L9、L’27、L812、3-水準表：L18、L36、L’36、L54
29 Taguchi Designs (1) Linear Graph of Table a b -ab A 1 C 4 7 B 2 No.1234123a b abNo.12345678A1C47B2a b -ab c -ac -bc abc
32 L12(211)The L12(211) is a specially designed array, in that interactions are distributed more or less uniformly to columns. Note that there is no linear graph for this array. It should not be used to analyze interactions. The advantage of this design is its capability to investigate 11 main effects, making it a highly recommended array.
35 L18(2137)Note: Like the L12(211), this is a specially designed array. An interaction is built in between the firs two columns. This interaction information can be obtained without sacrificing any other column. Interactions between tree-level columns are distributed more less uniformly to all the other three-level columns, which permits investigation of main effects. Thus, it is a highly recommended array for experiments.
40 Taguchi’s Quadratic Loss Function yi is the quality characteristic of interest for product iT is the quality characteristic targetk is a constant that converts deviation to a monetary valuewhere
41 Average Loss for n Products It may be shown that:
42 correct rank (intuitive ranking) S/N 比responses: the small is betterRundataMeanVariancecorrect rank (intuitive ranking)S/N Ratio154-13.0123786.5-14.680.4-9.342.5-10.332.40.8-7.92
43 Signal to Noise (Variable Data) A logarithmic transformation of experimental data which considers both the mean and variability in an effort to reduce lossSmaller is BetterNominal is BetterLarger is Better
44 Signal to Noise (Attribute Data) 不良率 (P) Ω轉換(Omega transformation)缺點數先將缺點數作分類，然後計算累積個數之比率值最後再透過不良率轉換公式計算S/N比
52 An Example of Using Orthogonal Arrays Because several different types of assemblies are run through a wave soldering process, two different types of assemblies were used. The objective is to find the optimal setting for the wave soldering process that is suitable for both types of assemblies.In addition to product noise, both the conveyor speed and solder pot temperature are moved around the initial setting given by the controllable array. This is because it is difficult to set the conveyor speed with any degree of accuracy and it is also difficult to maintain solder pot temperature.So the project team chose to include these variables in the noise array variables to determine how much noise affects the process.
53 An Example of Using Orthogonal Arrays A Wave Soldering Experimental DesignControllableFactors(1) Solder Pot Temperatures (S)(2) Conveyor Speed (C)(3) Flux Density (F)(4) Preheat Temperature (P)(5) Wave HeightNoise(1) Product Noise(2) Conveyor Speed Tolerance(3) Solder Pot ToleranceLevelsLowHigh480°F510°F7.2 ft/m10 ft/m0.9°1.0°150°F200°F0.5”0.6”Assembly #1Assembly #2-0.2 ft/m0.2 ft/m-5°F
54 An Example of Using Orthogonal Arrays Eight runs will be used to test effects of the five controllable factors in Taguchi L8 design (see Table 1). Notice that for each factor, there are four runs with the factor set at the high setting. This balancing is a property of the orthogonal design.Table 2 lists the array of noise factors to be run at each of the eight setting of the controllable. This is a Taguchi L8 design. The combination of the inner and outer arrays results in each run of the controllables being repeated over the 4 combinations of the noise factors.
56 Outer ArrayAt each combination of the inner array, an outer array of noise factors is run.Table 2Run1234ParametersAssm#1Assm#2Product Noise-0.2+0.2Conveyor Tolerance-5+5Solder Tolerance
57 An Example of Using Orthogonal Arrays Combined Inner and Outer Arrays ResultsRunControllable FactorsMeanS/NSolderConveyorFluxPreheatWave151010.01.01500.5194197193275215-46.7520.92000.6136132135-42.6137.2185261264244-47.814471251274285-39.515480295216204293352-48.156234159231157195-45.977328236247322305-49.768186187105104145-43.59
58 An Example of Using Orthogonal Arrays AnalysisNote: These are the optimum level settings for each factor based on S/N. Factors without an asterisk *are not significant and their levels can be based on other considerations.ParameterLevelMeanS/NSolder Pot Temperature480510225170-46.87-44.17*Conveyor Speed7.21.0195200-45.17-45.87Flux Density0.9140255-42.91*-48.11Preheat Temperature150194-46.03-45.01Wave Height0.50.6174220-44.50-46.54Interaction-45.68-45.36
79 Advantages of Taguchi Methods Loss functionSimplicity in selecting a design matrixParameter design strategy for making products robust to noiseDesigns quality into the products as opposed to inspecting it outThousands of success stories have been compiled through the American Supplier Institute
80 Disadvantages of Taguchi Methods Simplicity in selecting a design matrixPoor modelingUsing only signal to noise ratios, S/Ns, S/NN, and S/NL to identify dispersionNeed for replication to identify dispersion effectsDe-emphasis of modeling interactionsSome analysis techniques are unnecessarily complexNot providing guidance to experimenters on how to recover from unsuccessful experiments