lecture 4 robust design

8/14/2019 Lecture 4 Robust Design

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page 1

Introduction to Robust Design andTaguchi Method for Quality Engineering


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Product Cost and Quality

The inherent cost to make a product is afunction of its design

Minimizing the product's cost to the lowestpossible level within the limits set by itsdesign is largely a matter of avoidingdefects, tolerance deviations, and othererrors duringproduction


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page 3

Costs of Quality Deficiencies

Scrapped parts Larger lot sizes for scrap allowances

Rework, re-inspection,

Customer complaints and returns Warranty costs

Lost sales

Lost good will in the marketplace


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page 4

The Cost of Poor Quality (COPQ) Iceberg

Engineering change orders

Traditional Quality Costs

Lost Opportunity

Hidden Factory

Lost sales

Late delivery

Long cycle times

Expediting costs

Excess inventory

Additional Costs of PoorQuality

(intangible)

(tangible)

Lost Customer

Loyalty

ScrapRework

Inspection

Warranty

Rejects


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page 5

Profit

Total Cost to

manufacture

and deliver

products

Profit

Theoretical

Costs

Cost of

Poor Quality

COPQ

Why Focus on COPQ?

Price Erosion

Theoretical

Costs

Cost of

Poor Quality

COPQ

Profit

Theoretical

Costs

COPQ

Which Feels Better??


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page 6

Specifications

Remember their origin

Specifications are not targets!!

When we make them targets:

LS US

Uniform Distribution

Zero Defects!


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Uniform Distribution

LS USUniform Distribution

Target(customer preference)

AB A BC C

Do we really want as much C grade performance asA grade performance? Customers want grade A

performance. Why do we insist on providing products

that just pass with a grade of C?


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Adjust to Target

Target and small normally distributed

variation about the target produce customersatisfaction.

Normal Distribution

Target


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page 9

Use Specifications, but.

Think small variation

make performance consistent reduce sensitivity to all forms of variation

Think target

bring average performance to customerpreference


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page 10

Traditional Quality Metric

All products within specifications equality good.

All products outside specifications equally bad.

All products equally good

unacceptable

LS US


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page 11

Continuous Improvement

Move specifications closer

Increase cost

Quality and cost trade-off!

LS US

tighter

tolerances


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page 12

Taguchi Methods

G. Taguchi has had an important influenceon the development of quality engineering,especially in the design area both productdesign and process design

Taguchis contributions include:1. The Taguchi loss function

2. Robust design

3. Off line and on line quality control


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Taguchi advocates a 3 step, off-line quality control method

for product designStep 1. System Design

concept design and synthesis

innovation and creativity

Step 2. Parameter Design

parameter sizing to ensure

robustness to variations

Step 3. Tolerance Designestablish product and process

tolerances to minimize costs

Taguchi Methods


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page 14

The Taguchi Loss Function

Taguchi defines quality as "the loss a productcosts society from the time the product isreleased for shipment"

Loss includes costs to operate, failure to

function, maintenance and repair costs,customer dissatisfaction, injuries caused bypoor design, and similar costs

Some of these losses are difficult toquantify in monetary terms, but they arenevertheless real


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page 15

Taguchi Loss Function - continued

Defective products (or their components) thatare exposed before shipment are notconsidered part of this loss

Instead, any expense to the company

resulting from scrap or rework of defectiveproduct is a manufacturing cost rather thana quality loss


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page 16

Taguchi Loss Function - continued

Loss occurs when a product's functional

characteristic differs from its nominal or targetvalue

When the dimension of a component deviates

from its nominal value, the component'sfunction is adversely affected

No matter how small the deviation, there is

some loss in function The loss increases at an accelerating rate

as the deviation grows, according toTaguchi


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page 17

Determining

Quality Loss Function

Specifications are set

Specify a target with minimal variation

Increase in variation cause loss to society


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page 18

Taguchi Loss Function

.498 .502

LowerSpec Limit

UpperSpec Limit

.500


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page 19

Traditional Approach to Quality Control

If the product dimension is within the

tolerance limits, it is acceptable

Whether the dimension is close to thenominal value or close to one of the

tolerance limits, it is acceptable The reality is that products closer to the

nominal specification are better quality

In order to improve quality, one mustattempt to reduce the loss by designing theproduct and process to be as close aspossible to the nominal value


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Loss Loss

Traditional Loss View

.498 .502

LowerSpec Limit

UpperSpec Limit

.500


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page 21



.498 .502

LowerSpec Limit

UpperSpec Limit

.500


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Problem with Fraction-defective Measure


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page 23



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Quadratic Loss Function



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(a) The quadratic quality loss function(b) Loss function implicit in traditional tolerance

specification



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The Quadratic Loss Function

A0=cost of corrective action

D0=point of intolerance

m=target valuey= measured valueL=loss ($)

0m

A0

L

y

L=k(y-m)2

k=

A0

0

2


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page 27

Robust Design

A basic purpose of quality control is tominimize variations

Taguchi calls these noise factors

Sources of variation that are impossible ordifficult to control and that affect thefunctional characteristics of the product


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Robust Design - continued

A robust design is:

A design in which the product's function andperformance are relatively insensitive tovariations in design and manufacturing

parameters Involves the design of both the product and

process so that the manufactured product willbe relatively unaffected by all noise factors


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page 29

Robust Design Concept

Traditional approach:

Minimize noise & variation by better control ofdesign parameters of product/process

Often expensive and may or may not work

Robust design approach:Identify design parameters and noise factorsDetermine an optimal set of parameters which

makes product/process insensitive to variation ofparameters and noise factors via design ofexperiments

Determine the optimal trade-off among

parameters


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page 30

Three Types of Noise Factors in Robust Design

1. Unit to unit - random variations in the

process

2. Internal - variations internal to the product orprocess, such as wear or improper settings

on the production machine3. External - variations external to the product

or process, such as outside temperature,humidity, raw material supply


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page 31

Off Line and On Line Quality Control

Off line quality control - concerned withdesign issues, bothproduct design andprocess design

It precedes on line control

On line quality control - concerned with

production operations and customerrelations after shipment

Objective is to manufacture productswithin the specifications defined inproduct design, using methods andprocedures developed in process design


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Two Stages in Off Line Quality Control

1. Product design stage - involves development of

a new product or a new model of an existingproduct

Goals: to properly identify customer needsand to design a product that meets those

needs but can also be made consistently andeconomically

2. Process design stage - the manufacturingengineering function

Concerned with specifying the processesand equipment, setting work standards,documenting procedures, and developingclear and workable specifications for

manufacturing


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page 33

Three Step Approach in Product Design andProcess Design

System design - application of engineeringknowledge and analysis to develop a prototypedesign that will meet customer needs

Parameter design - determining optimalparameter settings for the product and process

This stage is where a robust design isachieved

Tolerance design - attempts to achieve abalance between setting wide tolerances tofacilitate manufacture and minimizingtolerances to optimize product performance


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page 34

The Quadratic Loss Function

A0=cost of corrective action

D0=point of intolerance

m=target valuey=measured valueL=loss ($) 0m

A0

L

y

L=k(y-m)2

k=

A0

0

2

L F ti


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page 35

Loss Function

The steeper the slope, the more important the

loss function

Assuming that the functional tolerance range is

m-, m+ and we know the consumer loss as

A($) we calculate:A = k2 or k = A/2

So

L(y) = (A/2)(y-m)2


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Expected Loss

Expected loss is the mean loss over over n products

The expectation is taken with respect to thedistribution of the quality characteristic y

E[L(y)] = E[k(y - m)2]

= k(variance of y + squared bias of y)= k[Var(y) + ( m)2]

= k (MSD)

Where Mean Square Deviation - MSD is givenby

nmyMSDn

i

i/)(

1

2

=

=


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Example

The customer tolerance for the height of a steering

mechanism are 1.50.02mm. For a product that

just exceeds these limits, the cost to the consumer

for getting it fixed is $50.

Ten products are randomly selected and yield the

following heights

1.53 1.49 1.5 1.49 1.521.54 1.53 1.51 1.52 1.48

Find the average loss per unit of the product


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Example

Loss given by

L(y) = k(y - m)2

Given information and nominal, m = 1.5m yields

K = A/2

= 50/(0.02)2

= 125000Giving

L(y) = 125000(y 1.5)2

And expected loss is

E[L(y)] = 125000 E(y 1.5)2


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page 39

Example

E(y 1.5)2 is estimated as

00049.0

10/0049.0

/)5.1(10

1

2

==

=

=

nyi

i

Hence, expected loss per unit is

E[L(y)] = 125000 (0.00049)

= $61.25

E ercise


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40

Exercise A medical company produces a part that has a hole

measuring 0.5" + 0.050". The tooling used to make the

hole is worn and needs replacing, but management doesn'tfeel it necessary since it still makes "good parts". All

parts pass QC, but several parts have been rejected byassembly. Failure costs per part is $0.45. Using the lossfunction, explain why it may be to the benefit of the

company and customer to replace or sharpen the toolmore frequently. Use the data below

Measured Value0.459 | 0.478 | 0.495 | 0.501 | 0.511 | 0.527

0.462 | 0.483 | 0.495 | 0.501 | 0.516 | 0.5320.467 | 0.489 | 0.495 | 0.502 | 0.521 | 0.5320.474 | 0.491 | 0.498 | 0.505 | 0.524 | 0.5330.476 | 0.492 | 0.500 | 0.509 | 0.527 | 0.536

lecture 4 robust design

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