statistical engineering - imperial college

7/30/2019 Statistical Engineering - Imperial College

1/31

StatisticalEngineering

Imperial

College,

February

17,

2010

1


2/31

ThebriefSomequestionstoconsider.Inyourprofessionalexperience

Whicharethefrequentlyusedstatisticalmethods?

' ,

WhatisthestatusoftheBayes/frequentist debate?

How

do

you

balance

mathematical

details

with

practical

concerns?

Howdoyoubalancestateoftheartmethodswithmoretriedandtestedmethods?

Whatarethecommonsoftwaretools?

howimportantarecomputingskills?

how

important

is

it

to

continue

to

develop

new

computing

skills?

Whatissuesarisecommunicatingsophisticatedstatisticalideas;

tostatisticall weakcollea uesandcustomers?

toseniormanagement?

Whenactingasaconsultant,

whatcommonproblemsandmisunderstandingsoccur?

Howdoyougivetheclientbadnews(eg.Theexperimentdoesnotgiveasignificant

resu

How

do

you

get

in

to

the

game?

Howdoyougetahead?2


3/31

Someoftheto icswewilldiscuss

,

importantfor

statistical

applications,

particu ar yinin ustry

Anal tical&Enumerativestudies

StatisticalProcessControl

Reliability&FailureModeAvoidance

Mistakeavoidance

Robustnessimprovement

xper men s3


4/31

InductionandDeductionH=hypothesis

;D=data

.

frequency

interpretation

aleatory.

Induction:Pr(H|D).Thisprobabilityhasa

egreeo

e ie

interpretation

epistemic

uncertainty.

e.g.H=thecoinisfair;D=45headsin100tosses

probabilitytheory hypothesistesting

statisticalscience

hypothesis

generation 4


5/31

Anengineeringexample

Anestablishedvehicledesignproducedinanewmanufacturingfacilitysufferedanunusual,high

severitystructural

welding

failure

2/3

of

the

way

Subsequentlabtestresults(data=T)fromsamples

manufacturingfacilities

showed

potentially

inferior

resultsfor arts roducedinthenewfacilit .

Thehypothesisisthatthereliabilityinthefieldof

theproduct

from

the

new

facility

will

be

the

same

asthatfromtheoriginalfacility(hyp=R).

Inordertoauthorizeproduction,doweneedto

5evaluate

Pr(T|R)

or

Pr(R|T)?


6/31

Anengineeringexample cont

99

9590

Hypothesis Hypothesis807060504030n

t New

TestingPr(T|R)

pval=0.15

GenerationPr(R|T)

Investigatethe

20

10Perc

New

facility ono re ec

nullhypothesis

erences

betweenthe2

32

1

facilityafter

counter

measures

Original

facility

Deploycounter

measures

1000100Cycles to Failure

Tryforanorderof

magnitude

Wecou say:

Statisticsisthescienceofmakinginferencesthrough6

in uctive ogican reasoningint e aceouncertainty.


7/31

Consequencesofconfusion

Mostproblemsinindustryneedinductivelogic

,improvement,suchasSixSigma&theDMAIC

inductionanddeduction.

Conse uentl man ractitionersusemethodsbetter

aimedat

deductive

inference

(e.g.

significance

tests)

whentryingtosolveinductiveproblems.

Theprobabilityyouhavemeaslesgiventhatyouhave

spots

is

not

the

same

as

the

probability

that

you

have

spotsg vent atyou avemeas es.

i.e.Pr(D|H) Pr(H|D)

7


8/31

Commonmistakesinsolving

problem

engineering

equivalent

of

a

complicatedtheoriesfitthefacts.

atat rown

nto

n ta

grope

aroun

ntheoutputforsignificantpvalues

Lackofprogressinsolvingtheproblem too

muchdata

collection/anal sis

devoted

to

eliminatingrootcausesthat,throughdeduction canbeshownnottobetrue.

8


9/31

TheiterativelearningprocessAfter

George

Box

r e a v yw

convergence solution

Time

Itist ejo o t estatistica investigator co a oratorto

ensure

convergence Spee o t isprocess eterminesw atsorto statisticaapproachisrequired(industryusuallyquick)

De uctionisana ysis,in uctionisscience,synt esisothetwothingsisengineering(Mischke) 9


10/31

Atooltoaidconvergence The

IS

/IS

NOT

Matrix

whatisthedefect?

whendid

we

first

observe

the

defect?

wheredidwefirstobservethedefect?whatisthepatternortrendinthedata?

etc... AskwhattheproblemISrelativetothesecriteria enas w att epro em og ca ycou e, ut

NOT

se eanswers o eseques ons o er epossiblerootcausetheories

eliminatedin

this

way 10


11/31

IS/ISNOTexamplePROBLEM

Vehiclessuffer

What theproblem

Whattheproblemcould THEORY1Thereisa THEORY 2Thereisa

rollover IS

ISNOT

thevehicle

thetire

Whatis

the

Tread

Separation Blow

out + +

Whatobjecthas

thedefect?

TireBrandA TireBrandB +

enwas e

defectfirst

observed?

years a er

vehicleon

sale

date

mme a e y e

vehicleswent

on

sale /+ +

defectfirst

observed?

StatesoftheUS

states +

inthedefects

Xhaveahigher

failureratethan

fromFactoryY

factoryhavethe

samefailurerate

+

Whatisthe

natureof

the

failurerate?

IFRwithtime CFRorDFRwith

time

/+ + 11


12/31

Analyticvs.Enumerativestudies

Greatemphasis

placed

on

this

by

WE

Deming

e.g.Howmanydefectivepartsarethereinthisparticular

batchof

incoming

material?

Requiresustoconstructacarefullyselectedrandomsubsamplethatdescribestheentity.Actionistakenontheentit .

Analyticalstudy

predicts

the

state

of

future

entitiese.g.Howmanydefectivepartsaretherelikelytobein

futurebatchesofincomingmaterialnotyetproduced?

yetexist.Actionistakenontheprocessthatproducestheentities

These

two

types

of

study

present

different

methodologicalchallenges 12


13/31

AwordonStatisticalProcessControl

Maintoo t eContro C art, ueto

Shewhart. Helpswithanalyticalstudies(changethe

futuretomakeitmore redictable .

How?Provides

an

operational

definition

of

orcommon cause.

auss an s r u on e c no mpor anforControlChartstowork.

13


14/31

Reliability Probabilisticdefinitions

e a y s epro a y a aun w

perform

its

intended

function

until

a

given

point

in

meun erspec e usagecon ons

Pr[T>t|Ns]

Reliabilityis

the

probability that

aunit

will

performitsintendedfunctionuntilagivenpointin

timeunderencounteredusageconditions

Pr T>t N Pr NTheseprobabilitiescanonlybeestimatedfrom

,

theyare

analytical

(predictive). 14


15/31

Reliability Informationbaseddefinition

informationisacountermeasureforanidentified

modes,engineerandevaluatecountermeasures

a ainstaran eofconditions

Thisis

recognised

as

an

analytical

problem.

Key

tool

is

theFMEA barel referencedinreliabilit textbooks

We

have

to

choose

between

an

enumerative

studyorananalyticalstudy wecantdoboth!

SeeFe nmansinflameda endix hisre ort

intothe

1986

Challenger

disaster. 15


16/31

Reliability

Twocausesoffailuremodes

Mistakes

Preventionofmistakesisprimarilyamatterof

vigilance

approach.

FailureModeAvoidanceprovidesatreatmentforbothsituations

16


17/31

Mistakeavoidanceexample

Guide armConcept BConcept A

CDchanger

in

acar

Eject

F

CD

Loading roller

F

R

Eject

R = retention force F = ejection force

InconceptA,theadditionofapaperlabelontheCDallows

R>F.

CD

sticks InconceptB,evenwith apaperlabel,R


18/31

Robustness

Robustness=product&processperformance.

Disturbancesarecallednoisefactorse.g.

. .

ii. Variationinproductcharacteristicsduetousage.

iii. Customerusageprofile(drivesfast,drivesslow,etc)

iv. Environment

(hot,

cold,

etc)v. Systeminterfaces(vibration,heattransferetc)

Two

uestionsemer e

1. Howshouldwemeasurerobustness?

2. How should we search the desi n s ace for

robustsolutions? 18


19/31

Measuringrobustness To

answer

Q1,

Taguchi

used

asignal

to

noise

ratio:

=average

product

performance; =variationinperformanceinducedbynoises.

Much controvers ensued in the statistical

literature,in

conferences,

and

11conversations

....

19


20/31

Engineeringsolution(withexample)

t(y)

ratio Failure Engineeringfunctionisabout

Noise(N)

e. .airtem .

+15oC

Outpu

ltoAir

(mixturetoo

rich)

Energy

Materials

15oC

(conserved)e.g.

Fu

Information

Sincetheseareconserved

Mode

(mixturetoolean)

quan es, e as c rans er

functionbetweeninput&output

Input(x)e.g.Fuel

Ideal

Function:

Noise

Disturbed

Function:y=0x.

Robustnessismeasuredby1,aparameterinthetransferfunction.

y=0(1+1N)x.

: = 0 01 = 1 .

1 measuresthedistancefromthefailuremode(s) 20


21/31

Runningengineeringexperiments

WithregardstoQ2;somecontroversyintroduced

treatmentofinteractionsinexperiments.

muchemphasisonfullfactorials,ANOVA,andau eca abilit attheex enseoffractional

factorials,graphical

methods

and

hidden

replication.

Ifwegetbacktofundamentals,wecanperhaps,starttoovercomesomeofthispoorteaching.

Deficienciesintheskillsrequiredtorunwellplannedexperimentsisaseriousimpedimentto

.

21


22/31

DimensionalAnalysis Buckinghams

Pi

theorem:

A

functional

unitscanberewrittenintermsofN>nm

Thisisanextremelyusefultheoremtodrastically.

Requiressome

basic

knowledge

of

the

physics

of

.

Exemplifiestheiterativenatureofthedeductive/n u c ve

earn ng

process

scusse

ear er

22


23/31

Example paperhelicopterMaximize

the

flight

time,

T,

of

the

helicopter

usedinaresponsesurface

Rotorradius(xR)Body

a eng xL

Tailwidth(xW)Tail

T=f(xR, xL, xW)aper

Clip

nd

surfacewhichwouldneed~15runstoestimate.

2

RWRLWLRRWL xxxxxxxxxx.- ....... =

23(onthe

face

of

it)

Dimensionally

Inconsistent


24/31

Paperhelicopterphysics Thehelicopterveryquicklycomestoasteadystatevelocity(Vss)

Timeoffli ht T isdeterminedb V andthelaunchhei ht h

Vss determinedbythebalancebetweentheforceofgravityFg

anddrag

Fd

Fg isdeterminedbythemassofthehelicopter(M)andg

Fd isdeterminedbytheareasweptoutbytherotorradius(RR)

air .

WithoutknowingtheFd formoftherelationship

wecan

write

down

the

Fgimportantvariables.

T=F (M,g, ,R ,h)

24


25/31

Paperhelicopterphysics T=F1(M,g,air,AR,h) FromthephysicswealreadyknowexactlyhowT dependsonh

T=h/Vss

So

we

are

looking

for

an

expression

of

the

form

=

ss = 2 ,g,air, R

ss

M kg

g m s

airkg/m3

RR m

= =

wecan

express

this

in

terms

of

53=2

non

dimensional

parameters.25


26/31

DimensionalAnalysisforthehelicopter

cbaRVDefine2corevariables

R

fed

M

gMRR air

Analyzethedimensionsofthecorevariables

[ ] ( )cb

a

Vmkgmm23 [ ] ( )

fe

d

Mmkgmkg23

cbcba

skgm

2131 ++

=

fefed

skgm

213 ++

=Enforcenondimensionallity 0;1;3;

2

1;0;

2

1====== fedcba

3,Rair

MRR

ss

V RgRTgR === 26


27/31

Paperhelicopterexperiment

Wenowneedtofita(dimensionless)equationof V 3 M

3experimental

runs

is

the

minimum

that

is

neededtomeasureanycurvaturebetween Vand

M.

ChangexR,

xL,

xW, measure

T,

calculate

Vand M.

Length

Width

Radius M V

5 3.2 12 1.975 1.069

5 3.438 8.744 3.410 1.405

7 5.1 7.62 4.845 1.675

MV ..

27(Dimensionless)


28/31

Paperhelicoptertransferfunction The

non

dimensional

form

is

converted

back

.

MV += 211.0664.0(Dimensionless)

=T

3

..rair

rR

g

28

(Dimensionallyconsistent)


29/31

PaperHelicopterValidationPerform

some

validation

experiments

13experiments

6fitted

arameters

.

3experiments

2fitted

arameters

Box-Behnken 13 Experiments

2.6

DA Results 3 Experiments

2.6

2.3

2.4

2.5

dicted

2.3

2.4

2.5

edicted

2

2.1

2.2Pr

2

2.1

2.2Pr

29

. . .

Actual

. . .

Actual

uc ng am s eorem sno c e nanyothe

well

know

texts

on

response

surface

design29


30/31

Concludingremarks The

application

of

statistical

thinking

and

statistical

methods

ishighlydependentonthenatureoftheproblemtobe

solved.

Anunderstanding

of

the

scientific

context

of

the

problem

is

crucialforstatisticstobeatitsmostproductive,andmost

effective(thisismuchmoreimportantthananyBayesian/

requentist argument p ease on tgetsi etrac e .

Thereisadifferencebetweenstatisticalmathematicsandstat st ca sc ence ma esureyou noww c sw c ,an know whatyouareorwanttobe.

n essyou

are

very

very goo ,

spec a ze,

on

genera ze.

Thejobofthescientististodecidenotwhichtheoryistrue,u w c eory smore e y o e rue ma esure a

youkeep

this

at

the

forefront

of

your

thinking. 30


31/31

Appendix:TimDavis Career 1981 BScStatistics,Univ.OfWales DunlopLtd. 1982 Fellow,RoyalStatisticalSociety(RSS)

,

1986 FordMotorCompany

1988 Captains

Player

Ford

Warley

CC es e er or ar ey 1991 PhD(CompetingRisksSurvivalAnalysis) 1991 Council memberRSS(4yearterm;VP9395) oo ng neer ng, ua y xper men a es gn w an rove 1992 Greenfield

Industrial

Medal,

RSS

1994 CharteredStatistician(C.Stat.) ua y anager, or er e , ln, ermany 1999 QualityDirector,Detroit,USA 2000 FirestoneTirecrisis 2001 HenryFor Tec n ca Fe ow orQua tyEng neer ng 2004 FellowI.Mech.E,andCharteredEngineer(C.Eng.) 2005 DonaldJuliusGroen Prizeinreliability,I.Mech.E. 2007 Qua ityDirectoran Boar Mem er JaguarLan Rover

2010 CouncilmemberRSS,2nd term 31

statistical engineering - imperial college

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