(microsoft powerpoint - tillf\366rlitlighet variation och rdm.ppt

$: (Microsoft PowerPoint - Tillf\366rlitlighet variation och RDM.ppt$
CHALMERS

Välkomna!till workshop

Bo Bergman SKF Professor

OOOOualitySciencesOOOOualitySciences 1

till workshop

ROBUST KONSTRUKTIONSMETODIK FÖR ÖKAD TILLFÖRLITLIGHET

-Tillförlitlighet och variation

CHALMERS

Tillförlitlighet, variation

och robusthet



robusthet

Bo BergmanSKF Professor Quality SciencesDivision of Quality Sciences

Chalmers University of Technology

SE-412 96 Gothenburg, Sweden

Phone: +46 31 772 8180

E-mail: [email protected]

CHALMERS

The Kano Model

CustomerSatisfaction

Expected

Attractive



Degree offulfilment

Must – be

CHALMERS

History (industry)

AssemblyIntegrationSpecialisation

ProcessLearningVariation

OrganizationContinuous Improvement

JapanisationQuality Drivenorganisationdevelopemnt



Japanese Export

. . . . .

ManyDialects..Six SigmaLean…

Quality Drivenorganizationdevelopment

S D

PA

CHALMERS

Demings Profound Knowledge +

• Understanding Variation– Not only handling and reduction

• Psychology – Not only individual but also organisation and social



– Not only individual but also organisation and social

• Knowledge Theory– How knowledge determines what we can observe and interpret, and how new knowledge is created

• Systems Thinking– The Complexity Growth

CHALMERS

The World is full of Variation

• Big Bang (from variation, a quantum fluctuation, and in

variation)

• Physical Reality (Thermodynamics, Statistical

mechanics, Quantum Mechanics)

• Biological Reality (Evolution: Replication and

Facts about the world:



• Biological Reality (Evolution: Replication and

Increased and reduced variation)

• Humans and Human Artefacts (We find

variation everywhere!)

CHALMERS

Reliability and Safety-

must be qualityCustomer

Satisfaction

Expected

Attractive



Degree offulfilment

Must – be

CHALMERS

Why do we have failures?

Due to variation!



CHALMERS

Reliability in a World Full of Variation

Variation: For good and for bad



Without VariationNo World!Life is Variation!

Variation CreatesProblems:- Deviations- Disturbances- Noise

CHALMERS

early failure period

best period

wear-out period

z(t)

The Bathtub Curve



constant failure ratet

CHALMERS

Innervariation

early failure period

best period

wear-out period

z(t)

Manufacturingvariation

Usagevariation

Un-reliability due to Variation



variationDeteriorationconstant failure rate

t

Manufacturingvariation

variation

Production Processes

Under Statistical Control?

Usage Environment

Under Statistical Control?

Usually NOT!!!

CHALMERS

A Critique of Reliability Theory Assumptions

• Probability models under the assumption:

• Processes under statistical control?– Probably not!!!



– Probably not!!!

• Lagging indictors of reliability performance– The design is created before testing

– Usage feedback is even much later

CHALMERS

Back to Basics

Work with the failure mechanisms

and their relations to Variation!



and their relations to Variation!

CHALMERS

Six Sigma:

VariationRed c



Reduction

CHALMERS

Chance vs Assignable causes of variation

Time Time Time



a process withassignable causes

a stable process a stable morecapable process

Processes

Out of statistical In Statistical Control

Control

CHALMERS

Manufacturing controls process capabilitiesProcess

Capability

Engineering controlstolerances



defects

Lower

tolerance limitUpper

tolerance limit

Quality Deficiency CostsExpensive components

Relation to Six Sigma

CHALMERS

),...,,,( 21= nxxxfy

DFSS and Six Sigma

DfSS



...2

2

2

2

2

1

2

21+

∂

∂+

∂

∂= xxy

x

y

x

yσσσ

Six Sigma

CHALMERS

Variation/Robust Design

Quality Loss

L(y)

Quality Loss

L(y) Quality Loss

L(y) Quality Loss

L(y)

a b



TargetValue

LTL UTL

y

TargetValue

LTL UTL

y

Target Value LTL UTL

y Target Value LTL UTL

y

CHALMERS

P-diagram

Noise factors



Product

Process

SystemSignal

factorsControl

factors

Response

Ideally)(xfy = but

CHALMERS

Targeted Effects of Variation Reduction



The effects of variation focused in Design for Six Sigma programs;

based on 25 responses.

Ida G?

CHALMERS

Robust Design Methodology

Sources of Variation



ResultsPRODUCTor

PROCESS

CHALMERS

Failure Experiences and RemediesThe Growth of Reliability Engineering

• Early Problems– “Elevators” in mines; Rail Road Accidents; Fatigue Problems; Rocket Problems (fortunately); Electronics Problems (esp. in the US Navy); etc.

• Aircraft Safety and Availability– Improvements based on a serious feedback process

• Life Cycle Cost based Acquisitions



• Life Cycle Cost based Acquisitions– Defence Industry, Process Industry

• Competitiveness– Automobile Industry– AC equipment producers (Garvin, 1988)

• Today, most industries have been forced to realise the problem

• Warranty costs – often as high as 50% of the Development costs

CHALMERS

Aim of Reliability efforts

Causes• Find• Estimate• Reduce• Eliminate



Consequences

Fault

• Reduce• Eliminate

• Find• Estimate• Reduce• Eliminate

ExperienceFeed-back

CHALMERS

Stress & StrengthDemand and Capacity

Stress Strength

Probability density


OOOOualitySciencesOOOOualitySciences 24Strength/Stress

••••• •• •

•••

••••••

••

•

•

•• •

•

• •••

•••

•

••

CHALMERS

Failure Mode Avoidance

• Lusser (in the 1950-ties)– Robert Lusser

• The V1 rocket

• Lusser´s Law



• Lusser´s Law

• Starfighter F104 (“widowmaker”)

• Missile development criteria

CHALMERS

Reliability, Stress, and Strength



Lusser, 1955

CHALMERS



• FMEA– Failure Mode and Effects analysis– Physics of Failure



– Physics of Failure

• Clausing (Xerox/MIT)– Operating Window

• Pat O´Connor• Taguchi• Davis (Ford)

CHALMERS

Failure Mode Avoidancein Robust Design Methodology

Ideal Function

Response



Signal

CHALMERS


Ideal Function

Response



Signal

S/N ratio

An Engineering

Measure of Reliability?

CHALMERS



• FMEA– Failure Mode and Effects analysis– Physics of Failure



– Physics of Failure

• Clausing (Xerox/MIT)– Operating Window

• Pat O´Connor• Taguchi• Davis (Ford)• Frame: DfSS e.g Park, Creveling et al. ….

CHALMERS

P-diagram

Noise factors



Product

Process

SystemSignal

factorsControl

factors

Response

Ideally but

CHALMERS

Product representation as a System of P-Diagrams



CHALMERS

Robust Design

• System design

– Decide on the products characteristics so that the requirements are fulfilled and it can be produced easily. Creative Robustness should be looked for!



easily. Creative Robustness should be looked for!• Parameter Design

– Find a set-up of the construction parameters that make the product independent of disturbances.

• Tolerance Design

– Decide on tolerances, but strive for the target value

CHALMERS

Creative solutions: some illustrations

The self aligning bearing

A Creative

Reliability

Improvement



Improvement

1907

1995

Sven Wingquist

CHALMERS

Inspiration

• Creative yesterday – commonplace today

Replacing the chain with a wire



DFA - solutions

CHALMERS

Poka-Yoke Principles

1. Make it easier for the person to do the right thing than the wrong thing

2. Make mistakes obvious to the person immediately so that some



2. Make mistakes obvious to the person immediately so that some correction can be made on the spot

3. Allow the person to take corrective action or stop before any irreversible step occurs

CHALMERS

How to create a robust design?

y

y



xx0

y0

x1

X1 results in less variation in y

CHALMERS

Transfer function

1. Is the transfer function known to the experimenter?

? ? ?)*,,( NCNCfy =



1. Is the transfer function known to the experimenter?

2. Is it possible to use Design of Experiments to estimate

the transfer function ?

3. Is the transfer function possible to estimate by use

of simulation?

CHALMERS

Pump design – transfer function known

Tubing

Flow rate (F) (l/min)

Transfer function:

F = (3.141 x R2 x L - B) N

One wayvalve



Piston

F = (3.141 x R2 x L - B) N

R = Piston radius (dm)

L = Stroke length (dm)

B = Back flow (l)

N = Motor speed (rpm)

Customer requirement: F=10±0.75l/min

CHALMERS

Pump design

Factors Nominal value Standard Deviation

Radius 0.2-0.8 dm 0.001

Stroke length 0.2-0.8 dm 0.002MA

KE



Stroke length 0.2-0.8 dm 0.002

Back flow 0.001-0.004 l 0.00005 0.00002

N (rpm) 50-100rpm 2 1

Low cost High cost

(Inlet Valve)

BU

Y

(Electrical motor)

CHALMERS

The tolerance design approach

First Design

• Piston Radius R =0.4 dm

• Stroke length L=0.4 dm

• Back flow B=0,002 l (low cost)

• Motor speed N=50rpm (low cost)

The target is 10 l/min, but

• 3 sigma process



• Motor speed N=50rpm (low cost)

Tightening the specifications of the motor (the high cost type)

gives better performance

• 5 sigma process

CHALMERS

A robust design approachThe effect of the factors on

the mean and the variance of the flow

Variance

(flo

w)



Variance

Mean

(flo

w)

R B NL0.2

0.8

0.0

01

500.2

0.8

0.0

04

100

R B NL0.2

0.8

0.0

01

500.2

0.8

0.0

04

100

CHALMERS

A robust design approach

• Set R and L as low as possible, i.e. R=L=0,2dm

• Use low cost back flow (B)

• Bring the flow rate to target (F=10 l/min) by adjusting N



• The resulting performance is:

– Almost a 5 sigma process!

• As N≤100, keep R low and increase L until F=10 l/min

CHALMERS

Manufacturing process of composite material

y – bending strenght response variable

A – curing temperature

B – pressure

C – holding time

control factors

(process variables)

D – proportion of hardener

y = f (A,B,C,D,E,F,G,H)?

Composite material experiment: transfer function unknown



• Four different process conditions• Eight batches of raw material

D – proportion of hardener

E – thermo-plastic content

F – proportion of epoxy

G – material ageing

H – process type

noise factors

?

CHALMERS

Experimental designD E F G H-1 -1 -1 1 -1 2075

1 -1 -1 1 1 2117

-1 1 -1 -1 1 2221

1 1 -1 -1 -1 2227

-1 -1 1 -1 1 2201

1 -1 1 -1 -1 2179

-1 1 1 1 -1 1988

1 1 1 1 1 1858

-1 -1 -1 1 -1 1829

1 -1 -1 1 1 1978

-1 1 -1 -1 1 2111

1 1 -1 -1 -1 2205

-1 -1 1 -1 1 2127

A B C 1 -1 1 -1 -1 2106

Process variables (control factors)A Curing temperature

B Pressure

C Holding time

Incoming material (noise factors)D Proportion of hardener

E Thermo-plastic content

F Proportion of epoxyProcess

Product



A B C 1 -1 1 -1 -1 2106

-1 -1 1 -1 1 1 1 -1 1870

1 -1 -1 1 1 1 1 1 1879

-1 1 -1 -1 -1 -1 1 -1 2245

1 1 1 1 -1 -1 1 1 2242

-1 1 -1 -1 1 2245

1 1 -1 -1 -1 2258

-1 -1 1 -1 1 2206

1 -1 1 -1 -1 2207

-1 1 1 1 -1 2053

1 1 1 1 1 2188

-1 -1 -1 1 -1 2219

1 -1 -1 1 1 2145

-1 1 -1 -1 1 2174

1 1 -1 -1 -1 2265

-1 -1 1 -1 1 2241

1 -1 1 -1 -1 2187

-1 1 1 1 -1 2208

1 1 1 1 1 2181

F Proportion of epoxy

G Material aging

H Type of process

CHALMERS

-1

0

1

2

3

-1 5 0 -1 0 0 -5 0 0 5 0 1 0 0 1 5 0

Sta

ndar

d d

evia

tio

n

-1

0

1

2

3

-1 5 0 -1 0 0 -5 0 0 5 0 1 0 0 1 5 0

Sta

ndar

d d

evia

tio

n

-

1

0

1

2

3

-1 5 0 -1 0 0 -5 0 0 5 0 1 0 0 1 5 0

Sta

ndar

d d

evia

tio

nB

G

BG

Identification of location effects



-3

-2

Contrasts

Sta

ndar

d d

evia

tio

n

-3

-2

Contrasts

Sta

ndar

d d

evia

tio

n

-

3

-

2

Contrasts

Sta

ndar

d d

evia

tio

n

G

• Location effects B, G and BG was determined to be active based

on engineering knowledge and the normal plots

Process factors Factors and interactionsassociated with incoming material

Interactions between ”process factors”and ”incoming material factors”

CHALMERS

Model

( )

ˆ( , ) 2132 72 65 46

2132 72 46 65

y B G B G BG

B B G

= + − + =

+ + −



( )2132 72 46 65B B G+ + −

B ≈ 1.4

CHALMERS

Conclusions

• The storage time of the incoming material (G) is causing variation in the bending strength of the composite



bending strength of the composite material.

• If the pressure (B) is set at high level the bending strength is made insensitive to the storage time.

CHALMERS

Robust Testing

TheDesign

Variation of

Noise factors

N1 N2 …. Nn



DesignNoise factors

Evaluate the Design

CHALMERS

Design reviews

good design Robust



good designgood discussion good dissection

RobustDRBFM*

Design Review

*Design Review Based on Failure Mode

(microsoft powerpoint - tillf\366rlitlighet variation och rdm.ppt

Documents