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Robust Design

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Title: Robust Design


1
Robust Design

References Engineering Methods for Robust
Product Design, W. Y. Fowlkes and C. M.
Creveling, Addison Wesley, 1995 Reducing
Variation During Design, Wayne A. Taylor, Taylor
Enterprises, Inc.
2
Robust Dictionary Definition
  • 1 a having or exhibiting strength or vigorous
    health b having or showing vigor, strength, or
    firmness lta robust debategt lta robust faithgt c
    strongly formed or constructed STURDY lta robust
    plasticgt
  • Source Merriam-Webster On-Line, 1999

3
Robust Design
  • A disciplined engineering process that seeks to
    find the best expression of a product design
  • Best means the design is the most economical
    solution to the product design specifications
  • Costs manufacturing cost, life-cycle, losses to
    society
  • High-quality products minimize costs by
    performing consistently

4
System Diagram (P-Diagram)
  • Input Signal
  • energy, material, or information to the system
    that causes a response in the product or process
  • Output Response/Quality Characteristic
  • Output of the system some attribute that is
    measurable and comparable to design specs

5
System Diagram (P-Diagram)
6
System Diagram (P-Diagram)
  • Control Parameter
  • Design factors specified by the design engineers
  • Noise
  • Uncontrollable factors that cause variation in
    the performance of the product or process

7
Robust Design
  • A robust product or process
  • insensitive to the effects of sources of
    variability, even though the sources themselves
    have not been eliminated.
  • Noise is the cause of the variability

8
Robust Designs
  • A robust product or process performs correctly,
    even in the presence of noise factors.
  • Noise factors may include
  • parameter variations
  • environmental changes
  • operating conditions
  • manufacturing variations

9
Noise
  • Three types of noise factors
  • External noise factors
  • Unit-to-unit noise factors
  • Deterioration noise factors

10
Noise
  • External Noise Factors variability that comes
    from outside the product
  • Temperature/humidity in which product is used
  • Any unintended input of energy (heat, vibration,
    radiation)
  • Dust in the environment
  • Human error, including misuse

11
Noise
  • Unit-to-Unit Noise result of never being able
    to make any two items exactly the same
  • Manufacturing process variations
  • Process nonuniformity
  • Process drift
  • Material property variations

12
Noise
  • Deterioration Noise internal noise factor
  • Aging during use or storage
  • Compression set or creep of a washer
  • Loss of plasticizer in an auto dashboard
  • Weathering of paint on a house

13
Robust Design
  • To minimize the effect of noise on the
    performance of the design
  • Eliminate the actual source of the noise
  • OR
  • Eliminate the products sensitivity to the source
    of the noise
  • Eliminating the source is costly, time-consuming

14
Robust Design
  • The objective of the design team
  • develop a product that functions as intended
    under a wide range of conditions for the duration
    of its design life
  • Robust Design
  • a process to obtain product performance that is
    minimally affected by noise

15
Robust Design and Quality in the Product
Development Process
16
Robust Design Processes
  • Concept Design
  • Define a system that functions under an initial
    set of nominal conditions
  • Parameter Design
  • Optimize the concept design identify control
    factor set points that make the system least
    sensitive to noise
  • Tolerance Design
  • Specify allowable deviations in parameter values
    loosen tolerances where possible and tighten
    where necessary

17
(No Transcript)
18
VARIATIONS
19
Exploiting Non-Linearity to Achieve Robust
Performance
Response to Factor B
fA
fB
B1
B2
Response fA(A) fB(B) What level of factor B
gives the robust response?
(B1 minimizes the variation)
20
Summary
  • Keys to reducing variation
  • How inputs behave
  • How inputs effect output
  • Robust design considers variation reduction while
    setting targets - NOT by arbitrarily reducing
    tolerances
  • Start with low-cost tolerances - then selectively
    tighten to meet specifications

21
Robust Design Process
  • Identify control factors, noise factors, and
    performance metrics
  • Formulate an objective function
  • Develop the experimental plan
  • Run the experiment
  • Conduct the analysis
  • Select and confirm factor setpoints
  • Reflect and repeat

22
Step 1 Parameter Diagram
  • Step 1 Select appropriate controls, response,
    and noise factors to explore experimentally.
  • Control factors (input parameters)
  • Noise factors (uncontrollable)
  • Performance metrics (response)

23
Example Brownie Mix
  • Control Factors
  • Recipe Ingredients (quantity of eggs, flour,
    chocolate)
  • Recipe Directions (mixing, baking, cooling)
  • Equipment (bowls, pans, oven)
  • Noise Factors
  • Quality of Ingredients (size of eggs, type of
    oil)
  • Following Directions (stirring time, measuring)
  • Equipment Variations (pan shape, oven temp)
  • Performance Metrics
  • Taste Testing by Customers
  • Sweetness, Moisture, Density

24
Step 2 Objective Function
  • Step 2 Define an objective function (of the
    response) to optimize.
  • maximize desired performance
  • minimize variations
  • target value
  • signal-to-noise ratio

25
Types of Objective Functions
Smaller-the-Better e.g. variance h 1/s2
Larger-the-Better e.g. performance h m2
Nominal-the-Best e.g. target h 1/(mt)2
Signal-to-Noise e.g. trade-off h 10logm2/s2
? objective function ยต mean of experimental
observation s2 variance of experimental
observation t target value
26
Step 3 Plan the Experiment
  • Step 3 Plan experimental runs to elicit desired
    effects.
  • Approaches to experimentation
  • Build-test-fix
  • One-factor-at-a-time (the classical approach)
  • Designed experiments (DOE)

27
Approaches to Experimentation Build-Test-Fix
  • Build-test-fix
  • the tinkerers approach
  • pound it to fit, paint it to match
  • impossible to know if true optimum achieved
  • you quit when it works!
  • consistently slow
  • requires intuition, luck, rework
  • reoptimization and continual fire-fighting

28
Approaches to Experimentation One-Factor-at-a-Tim
e
  • One-factor-at-a-time
  • procedure (2 level example)
  • run all factors at one condition
  • repeat, changing condition of one factor
  • continuing to hold that factor at that condition,
    rerun with another factor at its second condition
  • repeat until all factors at their optimum
    conditions
  • slow, expensive many tests
  • can miss interactions!

29
One-Factor-At-A-Time
Process Yield f(temperature, pressure)
Max yield 50 at 78?C, 130 psi?
30
One-Factor-At-A-Time
A better view of the maximum yield!
Process Yield f(temperature, pressure)
31
Approaches to Experimentation DOE
  • Design of Experiments (DOE)
  • A statistics-based approach to designed
    experiments
  • A methodology to achieve a predictive knowledge
    of a complex, multi-variable process with the
    fewest trials possible
  • An optimization of the experimental process itself

32
Major Approaches to DOE
  • Factorial Design
  • Taguchi Method
  • Response Surface Design

33
DOE - Factorial Designs
  • Full factorial
  • simplest design to create, but extremely
    inefficient
  • each factor tested at each condition of the
    factor
  • number of tests, N N yx
  • where y number of conditions, x number of
    factors
  • example 8 factors, 2 conditions each,
  • N 28 256 tests
  • results analyzed with ANOVA
  • cost resources, time, materials,

34
DOE - Factorial Designs - 23
35
DOE - Factorial Designs
  • Fractional factorial
  • less than full
  • condition combinations are chosen to provide
    sufficient information to determine the factor
    effect
  • more efficient, but risk missing interactions

36
DOE Factorial Designs (Fractional 7 factor, 2
level 128 ? 8)
37
DOE - Taguchi Method
  • Taguchi designs created before desktop computers
    were common
  • pre-created, cataloged designs intended to
    quickly find a set of conditions that meet the
    criteria of success
  • previous slide an example of an L8 template
  • Designs cannot support response surface models
    and are limited to only predicting at the points
    where data was taken

38
DOE - Response Surface RSM
  • Goal develop a model that describes a continuous
    curve, or surface, that connects the measured
    data taken at strategically important places in
    the experimental window

39
DOE - Response Surface RSM
  • RSM uses a least-squares curve-fit (regression
    analysis) to
  • calculate a system model (what is the process?)
  • test its validity (does it fit?)
  • analyze the model (how does it behave?)

Bond f(temperature, pressure, duration) Y a0
a1T a2P a3D a11T2 a22P2 a33D2
a12TP a13TD a23PD
40
Step 4 Run the Experiment
  • Step 4 Conduct the experiment.
  • Vary the control and noise factors
  • Record the performance metrics
  • Compute the objective function

41
Paper Airplane Experiment
42
Step 5 Conduct Analysis
  • Step 5 Perform analysis of means.
  • Compute the mean value of the objective function
    for each factor setting.
  • Identify which control factors reduce the effects
    of noise and which ones can be used to scale the
    response. (2-Step Optimization)

43
Analysis of Means (ANOM)
  • Plot the average effect of each factor level.

Choose the best levels of these factors
m
Scaling factor?
Prediction of response Eh(Ai, Bj, Ck, Dl) m
ai bj ck dl
44
Step 6 Select Setpoints
  • Step 6 Select control factor setpoints.
  • Choose settings to maximize or minimize objective
    function.
  • Consider variations carefully. (Use ANOM on
    variance to understand variation explicitly.)
  • Advanced use
  • Conduct confirming experiments.
  • Set scaling factors to tune response.
  • Iterate to find optimal point.
  • Use higher fractions to find interaction effects.
  • Test additional control and noise factors.

45
Robust Design ExampleSeat Belt Experiment
46
Parameter Diagram
Passenger Restraint Process
Control Factors
Performance Metrics
Back angle Slip of buttocks Hip rotation Forward
knee motion
Belt webbing stiffness Belt webbing friction Lap
belt force limiter Upper anchorage
stiffness Buckle cable stiffness Front seatback
bolster Tongue friction Attachment geometry
Noise Factors
Shape of rear seat Type of seat fabric Severity
of collision Wear of components Positioning of
passenger Positioning of belts on body Size of
passenger Type of clothing fabric Web
manufacturing variations Latch manufacturing
variations
47
Seat Belt Experiment Factors
  • Belt webbing stiffness
  • Belt webbing friction
  • Lab belt force limiter
  • Upper anchorage stiffness
  • Buckle cable stiffness
  • Front seatback bolster
  • Tongue friction
  • Objective Functions
  • Minimize
  • Avg back angle at peak
  • Range of back angle at peak

48
DOE Plan and Data
Data from seat belt experiment Back angle
(radians)
Avg (N- N)/2 Range (N-) (N) Effect
of Factor A at Level 1 on Avg A1
(0.31590.42960.36550.2804)/4 0.3478 Effect
of Factor A at Level 1 on Range A1
(0.04880.06240.00550.0314)/4 0.0370
49
Factor Effects Charts
Set Points to minimize average A1 B2 C2 E1 F1 G1
Set Points to minimize range A2 B2 C2 D1 E1 F2 G1
Selected Set Points A1 B2 C2 D1 E1 F1 G1
50
Confounding Interactions
  • Generally the main effects dominate the response.
    BUT sometimes interactions are important. This
    is generally the case when the confirming trial
    fails.
  • To explore interactions, use a fractional
    factorial experiment design.

S/N
A1
A2
A3
B1
B2
B3
51
Key Concepts of Robust Design
  • Variation causes quality loss
  • Two-step optimization
  • Matrix experiments (orthogonal arrays)
  • Inducing noise (outer array or repetition)
  • Data analysis and prediction
  • Interactions and confirmation

52
END
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