lecture 4 robust design
TRANSCRIPT
-
8/14/2019 Lecture 4 Robust Design
1/40
page 1
Introduction to Robust Design andTaguchi Method for Quality Engineering
-
8/14/2019 Lecture 4 Robust Design
2/40
page 2
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
-
8/14/2019 Lecture 4 Robust Design
3/40
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
-
8/14/2019 Lecture 4 Robust Design
4/40
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
-
8/14/2019 Lecture 4 Robust Design
5/40
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??
-
8/14/2019 Lecture 4 Robust Design
6/40
page 6
Specifications
Remember their origin
Specifications are not targets!!
When we make them targets:
LS US
Uniform Distribution
Zero Defects!
-
8/14/2019 Lecture 4 Robust Design
7/40
page 7
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?
-
8/14/2019 Lecture 4 Robust Design
8/40
page 8
Adjust to Target
Target and small normally distributed
variation about the target produce customersatisfaction.
Normal Distribution
Target
-
8/14/2019 Lecture 4 Robust Design
9/40
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
-
8/14/2019 Lecture 4 Robust Design
10/40
page 10
Traditional Quality Metric
All products within specifications equality good.
All products outside specifications equally bad.
All products equally good
unacceptable
LS US
-
8/14/2019 Lecture 4 Robust Design
11/40
page 11
Continuous Improvement
Move specifications closer
Increase cost
Quality and cost trade-off!
LS US
tighter
tolerances
-
8/14/2019 Lecture 4 Robust Design
12/40
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
-
8/14/2019 Lecture 4 Robust Design
13/40
page 13
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
-
8/14/2019 Lecture 4 Robust Design
14/40
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
-
8/14/2019 Lecture 4 Robust Design
15/40
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
-
8/14/2019 Lecture 4 Robust Design
16/40
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
-
8/14/2019 Lecture 4 Robust Design
17/40
page 17
Determining
Quality Loss Function
Specifications are set
Specify a target with minimal variation
Increase in variation cause loss to society
-
8/14/2019 Lecture 4 Robust Design
18/40
page 18
Taguchi Loss Function
.498 .502
LowerSpec Limit
UpperSpec Limit
.500
-
8/14/2019 Lecture 4 Robust Design
19/40
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
-
8/14/2019 Lecture 4 Robust Design
20/40
page 20
Taguchi Loss Function
Loss Loss
Traditional Loss View
.498 .502
LowerSpec Limit
UpperSpec Limit
.500
-
8/14/2019 Lecture 4 Robust Design
21/40
page 21
Taguchi Loss Function
Taguchi Loss Function
.498 .502
LowerSpec Limit
UpperSpec Limit
.500
-
8/14/2019 Lecture 4 Robust Design
22/40
page 22
Problem with Fraction-defective Measure
-
8/14/2019 Lecture 4 Robust Design
23/40
page 23
Specify a target with minimal variation
-
8/14/2019 Lecture 4 Robust Design
24/40
page 24
Quadratic Loss Function
Specify a target with minimal variation
-
8/14/2019 Lecture 4 Robust Design
25/40
page 25
(a) The quadratic quality loss function(b) Loss function implicit in traditional tolerance
specification
Taguchi Loss Function
-
8/14/2019 Lecture 4 Robust Design
26/40
page 26
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
-
8/14/2019 Lecture 4 Robust Design
27/40
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
-
8/14/2019 Lecture 4 Robust Design
28/40
page 28
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
-
8/14/2019 Lecture 4 Robust Design
29/40
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
-
8/14/2019 Lecture 4 Robust Design
30/40
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
-
8/14/2019 Lecture 4 Robust Design
31/40
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
-
8/14/2019 Lecture 4 Robust Design
32/40
page 32
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
-
8/14/2019 Lecture 4 Robust Design
33/40
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
-
8/14/2019 Lecture 4 Robust Design
34/40
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
-
8/14/2019 Lecture 4 Robust Design
35/40
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
-
8/14/2019 Lecture 4 Robust Design
36/40
page 36
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
=
=
-
8/14/2019 Lecture 4 Robust Design
37/40
page 37
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
-
8/14/2019 Lecture 4 Robust Design
38/40
page 38
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
-
8/14/2019 Lecture 4 Robust Design
39/40
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
-
8/14/2019 Lecture 4 Robust Design
40/40
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