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.
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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 low-cost 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)
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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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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 product or process is said to be robust when it
  is 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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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

• Minimize the effect of noise on the performance
  of the design
• Eliminate the actual source of the noise
• 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 is to develop a
  product that functions as intended under a wide
  range of conditions for the duration of its
  design life
• Robust Design is a process to obtain product
  performance that is minimally affected by noise

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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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Transmission of Variation

• Reducing variation
• identify key input variables affecting output
• establish controls on these inputs
• establish targets (nominals)
• establish tolerances (windows)

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Robust Design Methods

• Reducing variation by the careful selection of
  targets for inputs (without necessarily
  tightening tolerances!)
• (Collectively) the different methods of selecting
  optimal targets for inputs
• Taguchi Methods
• Response Surface Approach
• Robust Tolerance Analysis

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Robust Design Methods

• Robust Tolerance Analysis
• Run a designed experiment to model the outputs
  average, then use the statistical approach to
  tolerance analysis to predict the outputs
  variation
• Requires estimates of the amounts that the inputs
  will vary during long-term manufacturing

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Robust Design Methods

• Response Surface Approach
• Run response surface studies to model the average
  and variation of the outputs separately
• Use results to select targets for the inputs that
  minimize the variation while centering the
  average on the target
• Requires that the variation during the study be
  representative of long-term manufacturing

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Robust Design Methods

• Taguchi Methods
• Run a designed experiment to get a rough
  understanding of the effects of the input targets
  on the average and variation
• Use results to select targets for the inputs that
  minimize the variation while centering the
  average on the target
• Similar to dual response approach, expect during
  study, inputs adjusted by small amounts to mimic
  long-term manufacturing variation

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Two-Step Optimization
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Approaches of 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
• 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-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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Designed Experiments

• 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 - 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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Summary

• How inputs behave and how inputs effect output is
  key to reducing variation.
• 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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END

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Reducing Variation During Design (an example)

• Design problem
• Customer need pump with flow rate between 9 and
  11 ml/min
• Specification pump with nominal flow rate of 10
  ml/min 1 ml/min
• Pump concept
• piston with two valves to control direction of
  flow

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Pump Design Parameters

• Flow rate through pump, F
• Piston travel (stroke), L
• Motor speed, S
• Piston radius, R
• Amount of backflow through valve, B

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Pump System Diagram
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Control Variation by Design

• Reduce variation in output (flow rate F) by
  establishing requirements for inputs (R, L, B, S)
• Requires knowing how inputs behave and how the
  inputs effect the output

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Variation Transmission Analysis
Pump flow rate
(Eq. 1)
(Knowledge of functional relationship replaces
the screening experiment often required to
determine key input variables)
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Analysis
Average flow rate, ?F
(Eq. 2)
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Analysis
?F, standard deviation of the flow rate, F
(Eq. 3)
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Table 1 Data from Manufacturing and Suppliers
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Table 2 Process Tolerancesfor Inputs
Max. Std. Dev. from Table 1 Tolerances 1.5 Std
Dev Mean targets for R, L from experience S
calculated (Eq. 1)
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Determining Flow Rate Variation

• Use process tolerances (Table 2) to determine
  process tolerance for flow rate F
• calculate using Eqs. 2 and 3
• Use six-sigma product tolerance
• Use worst-case Cp and Cpk
• Want six-sigma product tolerance to fit between
  specification limits (equivalent to Cpk exceeding
  1.5)

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lt 1.5
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Reduce Flow Rate Variation Through Robustness

• Many different combinations of input targets
  result in a 10 ml/min flow rate
• Robust pump design can be obtained by determining
  targets of inputs maximizing the minimum Cpk
• Optimal set of targets for inputs are
• R 0.1735, L 0.4125, S 16.96 rpm
• (results on next slide)

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lt 1.5
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Tightening Tolerances

• Which tolerances to tighten?
• By how much?
• Start by investigating effects of tightening
  different tolerances

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Table 3 Flow Rate Processes After Tightening
Tolerances
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Tightening Tolerances

• (refer to Table 3)
• Largest effects achieved by tightening tolerances
  on the motor (S)and the valve (B)
• Cost to achieve tighter tolerances
• Motor current 5 motor ? 20 motor
• Valve current 1 valve ? 2 valve

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Tightening Tolerances

• Targets reoptimized after change in tolerances
• New set of targets
• R 0.1520
• L 0.4236
• S 22.04 rpm
• Resulting flow rate variation on next slide

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gt 1.5