Taguchi1 Design of Experiments and Taguchi Experimental Design
Professor Joe Greene CSU, Chico
Slide 2
Taguchi2 Design of Experiments Need for Experiments Factorial
Experiments Two-Factor Factorial Experiments Statistical Analysis
for Two-Factor Experiments Other Factorial Experiments General
Factorial Experiments Randomized Complete Block Design 2k Factorial
Design Taguchi Designs
Slide 3
Taguchi3 Need for Need for Experiments Need to establish cause
and effect relationships Home Car repair- Trouble-shooting
starting, noise, and braking problems Home repair- Electrical and
mechanical problems, cooking, etc. Gardening and lawn maintenance-
watering and pesticide use School Studying versus grades
performance Attendance versus grade performance Industry
Maintenance and trouble-shooting of equipment Effects of moisture,
line rate, operators on productivity and quality Trouble shooting
production problems for incoming Materials Trouble shooting
production problems on Target values for performance or
appearance
Slide 4
Taguchi4 Experimental Goals Statistical Accuracy Proper
selection of the responses to be measured Determination the number
of factors that affect a response The interactions between the
factors The number of repetitions per run The form of analysis to
be completed Cost Minimize the cost Reduce the number of
experiments to the minimum Study the main factors Thoroughly
understand the process under study Choose the minimum number of
experiments
Slide 5
Taguchi5 Factorial Experiments Study the effects of 2 or more
factors with factorial experiments Each factor and each combination
of factors are studied Example Factor A has 2 levels (high, low)
Factor B has 2 levels (on, off) Then the total number of
experiments is 2x2=4, or high-on, high-off, low-on, low-off
Experiments measure the difference of the response from one level
of the factor (high for A) and another level (low for A).
Slide 6
Taguchi6 Factorial Experiments- Design Example Factor A- 2
levels- A1, A2 Factor B- 2 levels- B1, B2 Measured values are 10,
20 30, 40 The effect Factor A has on the experiment is the average
difference between the levels A= 30+40 - 10+20 = 20 2 2 B= 20+40 -
30+10 = 10 2 2 Conclusion Changes in Factor A causes more of an
effect than B. Factor A is more significant than Factor B
Slide 7
Taguchi7 Factorial Experiments- Interaction Example- No
Interactions Interactions
Slide 8
Taguchi8 Two-Factor Factorial Experiments Problem- Molding
problems on Injection Molder has caused defects to sky rocket. The
problems started when the PP resin was switched to a different
supplier. Additionally, a new operator was added Experiment design
to determine the cause of the defect Factor A- 2 levels: Resin 1=
PP_old and Resin 2 PP_new Factor B- 2 levels- Operator 1= Tom and
Operator 2= Bob Experiment run to see what is the cause- Operator
or Resin
Taguchi10 Significance of Difference Level Averages Sum
Differences from Table Graph Results Analysis of Variance
Statistical Measurement Method Measures the total variability in
the data measured by the Sum of Squares Separate out the the
differences caused by the individual factors Calculates the
differences caused by the error Uses the F statistic to calculate
the significance
Slide 11
Taguchi11 ANOVA Example Analysis of Variance Note: F Statistic
determines significance. If F is greater than a specified value
than the factor is significant.
Slide 12
Taguchi12 ANOVA Example Calculation Analysis of Variance SS T =
Sum (results) 2 - y.. 2 N = (10) 2 + (20) 2 + (30) 2 ++(70) 2 -
(1280) 2 8 SS Resin = Sum (Resin y.) 2 - y.. 2 n N SS Operator =
Sum (Operator y.) 2 - y.. 2 n N SS Error = SS T - SS Resin - SS
Operator
Slide 13
Taguchi13 Other Factorial Experiments General Factorial
Experiments Involves experiments with more than 2 factors Requires
many experiments to run Randomized Complete Block Design Special
design of experiment that blocks out certain extraneous effects
Used to investigate the effects of one ore more factors when entire
experiment cannot be run under homogeneous conditions 2 k Factorial
Design Special design for 2 levels and k factors
Slide 14
Taguchi14 Taguchi Experimental Design History of Dr. Genichi
Taguchi After WWII, the Japanese initiated a major effort to
participate in the world market. The first products were
inexpensive, but of poor quality. The Japanese government set up
government agencies modeled after US companies (Bell Labs). One
such company, Electrical Communication Laboratories of Japan (ECL),
hired Dr. Taguchi to reduce the cost of experimentation. Dr.
Taguchi developed a series of experiments that resembled partial
factorial designs and featured orthogonal (balanced) arrays. The
experimental method is called The Taguchi Approach
Slide 15
Taguchi15 Comparison: Taguchi vs. Conventional Experimental
Design Traditional experimental designs were introduced by R.A.
Fisher in 1920s in England Limitations of traditional design
Limited variety of layouts and difficult data analysis Limited
number of variables with many required repetitions Passive approach
to interactions. Difficulty in resolving them F statistic only
recognized as fully significant. Partial effects are not calculated
Taguchi has Multiple layouts and designs and efficient data
analysis Minimum number of experiments Active approach to
interactions and calculates partial contribution
Slide 16
Taguchi16 Features of Taguchi Orthogonal Arrays Efficient data
collection Separated effects from one another Balanced, separable,
or not mixed Minimum number of experiments Experimental Designs Two
Level- L 8, L 16, L 32 have 8 experiments, 16 experiments, and 32
experiments, respectively Three Level- L 9, L 27 have 9 experiments
and 27 experiments. Data Analysis- Software available Level
Averages ANOVA
Slide 17
Taguchi17 Examples Taguchi Design of Experiment for
thermoplastic composites Objectives What is the best combination of
Twintex composites and GMT? What are the optimum process
conditions? Paper for SAE
Slide 18
Taguchi18 DOE Study Evaluate Effectiveness of Prepreg
Technology to Selectively Increase Stiffness & Impact
Performance Find Optimum Combination of the 2 Materials 4 Variables
were Compared vs Static Load : Prepreg Type BMC Glass % Weight
Fraction of Prepreg Tonnage of Press Improving Performance of BMC
Bumper Beams
Slide 19
Taguchi19 DOE Study 3-Point Loading Test (ASTM D790), with
FMVSS 581 Pendulum Impactor head Typical mid-sized Vehicle Bumper
was Used Test loaded Beam at Centerline @ 51 mm/min Load/Deflection
Response Measured & Recorded Tests Measurable was Beams Static
Load, Recorded at 25 mm of Deflection Specific Load = Static
Load/Beam Weight Improving Performance of BMC Bumper Beams
Slide 20
Taguchi20 Static Test Setup with a Pendulum Face Moving at a
Constant Speed into a Rigidly Mounted Beam
Slide 21
Taguchi21 TP-BMC Glass Weight Percentage: 20%, 30%, and
40%..Weight percentage of prepreg: 25%, 50%, and 75%..Press Tonnage
(metric): 450 t, 675 t, and 900 t..Prepreg type: satin weave
(1:1),: twill weave (4:1), and unidirectional (uni); DOE Study
Slide 22
Taguchi22 DOE Study
Slide 23
Taguchi23 Select Material Properties of Test Products
Slide 24
Taguchi24 DOE Study Materials Processed on conventional BMC and
GMT Equipment BMC logs were extruded. Prepreg Plates Cut to Shape
and heated in GMT oven Projected Area of Part was 370 x 1520 mm,
with Nominal Thickness of 8 mm GMT & Prepreg added in
Combinations of Fractions of Prepreg to Total Beam Weight 3 Beams
in each Combination Molded for Experiment Improving Performance of
BMC Bumper Beams
Slide 25
Taguchi25 Process Conditions for Experiments
Slide 26
Taguchi26 DOE Study Pre-preg Materials Placed & Indexed in
Oven to exit at the Same Time as BMC log Material Temperature
210-240C @ Oven Exit Prepreg Heated at same Rate due to Similar
Thermal Properties & Thickness Materials Placed in Tool
(Transfer Time 20-30 sec) and then compression molded Improving
Performance of GMT Bumper Beams
Slide 27
Taguchi27 Experimental Layout for the Taguchi L-9 Note:
Equivalent Full Factorial Design would require 81 experiments :
Number of Experiments = (levels) Factors = 3 4 = 81
experiments
Slide 28
Taguchi28 DOE Study 27 Beams, 3 each of 9 Variants, plus 15
BMC- Only Control Beams were BMC 20%, BMC 30%, and BMC 40%,
Experiment was not Randomized to Minimize Duration Taguchi Study
Permits Interpolation of Results to Other Variants not Physically
Manufactured or Tested Improving Performance of BMC Bumper
Beams
Slide 29
Taguchi29 Static Load for BMC and Prepreg Experiment
Number
Slide 30
Taguchi30 Mass of Beams for GMT/Prepreg 123456789 GMT GMT+
C-GMT30+C-GMT40+ Experiment Number
Slide 31
Taguchi31 Mean Static Load vs. Beam Mass for BMC/Prepreg Static
Load versus Beam Mass for GMT/Prepreg Experiment
Slide 32
Taguchi32 Mean Specific Static Load for BMC/Prepreg GMT GMT+
C-GMT30+C-GMT40+ Experiment Number
Slide 33
Taguchi33 Level Averages for GMT/Prepreg
Slide 34
Taguchi34 Analysis of Variance(ANOVA) Results Significance Of
Each Variable 14985 19.68 2844618.96 GMT Type 2 82651 41325 54.28
8112854.08 9531 12.52 17539 11.69 Lay-Up 2 4622 2311 3.04 3100 2.07
e1 0 0 e2 18 13704 761 1979513.20 Total 26 150007 5770100
Slide 35
Taguchi35 Optimum Levels of Each Variable as Determined from
Level Averages Graph
Slide 36
Taguchi36 Confirmation Run Confirmation Run used same Process
Settings Used the GMT product with 30% Chopped Fiber & Each of
the Prepreg Materials 5 Beams with Each Prepreg Material were made,
plus 5 Control Beams Test Results confirmed C-GMT 30+ Product was
Improved by Adding Prepreg Material Improving Performance of GMT
Bumper Beams
Slide 37
Taguchi37 Comingled thermoplastic prepregs improve the
stiffness properties of TP-BMC composites by 15% to 20%. The static
load of composite bumper beams increases with up to a maximum of
22% to 25% glass (by volume). Comingled thermoplastic prepregs
improve the static bumper performance of TP-BMC composites to a
level superior to published results for standard GMT materials. The
significant material and processing parameters in this experiment
are TP-BMC glass weight percentage, weight percentage prepreg,
press tonnage, and prepreg type. The optimum levels for maximum
dimensionless static load are: TP-BMC glass weight percentage = 30%
Weight percentage prepreg = 75% Press tonnage (metric) = 900 t
Prepreg type = Satin Conclusions
