Propagation of Error Robust Design

Robust Design,Propagation of Error and Tolerance Analysisp g y

Webinar presented by: Pat Whitcomb

Presentation is posted at www statease com/webinar html

Robust Design 1

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Robust Design,Propagation of Error and Tolerance Analysisp g y

Robust Design Concepts Robust Design Concepts Propagation of Error (POE) RSM Analysis with TA Lathe Machined Parts HDTV signal (as time allows)

1. Raymond H. Myers, Douglas C. Montgomery and Christine M. Anderson-Cook (2009), 3rd edition, Response Surface Methodology, John Wiley and Sons, Inc, Sections 2.7-2.8 and 6.6, Chapters 1, 7, 8 and 10.

2. George E.P. Box, William G. Hunter and J. Stuart Hunter (2005), Statistics for Experimenters, 2ndditi J h Wil Ch t 12edition John Wiley, Chapter 12.

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Agenda Transition

Robust Design Concepts Propagation of Error (POE) Propagation of Error (POE) RSM Analysis with TA Lathe Machined Parts Lathe Machined Parts HDTV signal (as time allows)

Robust Design 3

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Robust Design

The goal of robust design is to increase profits by consistently ti f i t dsatisfying customer needs.

This is accomplished by generating robust designs toMi i i d i k ft d i f Minimize design re-work after design freeze

Minimize surprises during design verification Accelerate scale up and commercializationcce e a e sca e up a d co e c a a o

Robust designs depends heavily on DOE to translate the Voice-of-Customers (VOCs) and product specifications into process specifications

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Robust Design

Functional Design: Strategy of ExperimentationStrategy of Experimentation

Use DOE to model response mean as a function of controllable factor levels

Phase: ScreeningKnownFactors

UnknownFactors

Screening


UnknownFactors

Screening

controllable factor levels.

Choose levels of controllable factors to achieve targeted

Phase: Characterization

Factor effectsand interactions

Curvature?no



Curvature?no

values of the responses. Phase: Optimization

Ph V ifi i

yes

ResponseSurfaceMethods

Phase: Optimization

Ph V ifi i

yes


Phase: Verification Confirm? BackupCelebrate!

no

yes


no

yes

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Robust Design

Robust Design: Strategy of ExperimentationStrategy of Experimentation

Use DOE to model response variability as a function of control and uncontrolled


UnknownFactors

Screening


UnknownFactors

Screening

control and uncontrolled factor levels.

Choose levels of control Phase: Characterization


Curvature?no



Curvature?no

factors to reduce variation caused by: Lack of control of the

Phase: Optimization

Ph V ifi i

yes


Phase: Optimization

Ph V ifi i

yes


control factors. Variation of the

uncontrolled factors


no

yes


no

yes

uncontrolled factors.

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Robust Design Concepts

Concept: Choose levels of the control1 factors in a way that d t t i ti I th d k th d treduces output variation. In other words, make the product,

process or system robust to variation in the inputs; both control and uncontrolled2 factors. Quality is then improved without

i th f i tiremoving the cause of variation.1 Control factors (x) are parameters whose nominal values can

be cost-effectively adjusted by the engineerbe cost effectively adjusted by the engineer. Example: oven temperature.

2 Uncontrolled factors (z) are parameters that are difficult, expensive, or impossible to control.Example: ambient temperature.

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Control vs Uncontrolled Factors

Determining whether a factor is an uncontrolled or a controlled one ft d d th t bj ti th f th j toften depends on the teams objective or the scope of the project.

A factor considered controlled in some cases might be considered uncontrolled in others.

For example material durometer (hardness):

is controllable to a design engineer, who gets to chose the s co o ab e o a des g e g ee , o ge s o c ose ematerial.

but may be uncontrolled to a process engineer who only th i ti ithi th h t i lsees the variation within the chosen material.

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Agenda Transition

Robust Design Concepts Propagation of Error (POE) Propagation of Error (POE) RSM Analysis with TA Lathe Machined Parts Lathe Machined Parts HDTV signal (as time allows)

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Propagation of Error (POE)Transmitted Variation

Objective: Reduce the variation transmitted to the response from variation in control factorsresponse from variation in control factors.

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Propagation of ErrorHow it works

Once a relationship has been established between a factor and a th i ti i th t t bresponse, the variation in the output can be:

1. Dependent on the level of the control factor

2. Independent of the level of the control factor

See pictures on next two pages See pictures on next two pages

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Propagation of errorDependentp

The transmitted variation is d d t th l l f

Effect of Inputdependent on the level of the control factor.

Therefore, set the level of the

on Response

Therefore, set the level of the control factor to reduce variation transmitted to the response from variationresponse from variation (lack-of-control) of the control factor.

Control Factor

A B

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Propagation of errorIndependentp

The transmitted variation is i d d t f th l lindependent of the level of the control factor.

Therefore, set the level of theTherefore, set the level of the control factor to center the process mean on target.

R

e

s

p

o

n

s

e

Effect of Inputon Response

R

Control FactorA B

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Power Circuit Design Example

Consider two control factors:1. Transistor Gain nonlinear relationship to output voltage 2. Resistance linear relationship to output voltage

The variation in gain and resistance about their nominal values isThe variation in gain and resistance about their nominal values is known. Both variances are constant over the range of nominal values being considered.

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Power Circuit Design Example(reduce variation)( )

Variation is reduced by using a nominal gain of 350.

That shifts the output off target to 125 voltsThat shifts the output off-target to 125 volts.

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Propagation of Error Robust Design

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