Robust Design

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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.
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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

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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

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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

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System Diagram (P-Diagram)
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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

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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

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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

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Noise

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

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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

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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

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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

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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

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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

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Robust Design and Quality in the Product
Development Process
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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

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VARIATIONS
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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)
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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

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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

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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)

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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

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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

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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 µ mean of experimental
observation s2 variance of experimental
observation t target value
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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)

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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

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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!

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One-Factor-At-A-Time
Process Yield f(temperature, pressure)
Max yield 50 at 78?C, 130 psi?
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One-Factor-At-A-Time
A better view of the maximum yield!
Process Yield f(temperature, pressure)
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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

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Major Approaches to DOE

• Factorial Design
• Taguchi Method
• Response Surface Design

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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,

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DOE - Factorial Designs - 23
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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

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DOE Factorial Designs (Fractional 7 factor, 2
level 128 ? 8)
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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

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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

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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
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Step 4 Run the Experiment

• Step 4 Conduct the experiment.
• Vary the control and noise factors
• Record the performance metrics
• Compute the objective function

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Paper Airplane Experiment
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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)

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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
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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.

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Robust Design ExampleSeat Belt Experiment
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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
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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

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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
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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
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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
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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

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END