A Statistical Career in Engineering & IndustryTim Davis PhD, CStat, CEng, FIMechE

June 17, 2013

http://www.timdavis.co.uk/career

http://www.timdavis.co.uk/technicalfellowarticle

http://scholar.google.co.uk/citations?user=54ao7XkAAAAJ&hl=en

http://www.timdavis.co.uk/lectures%26conferencepresentations

http://www.linkedin.com/in/tdavis5

Some (maybe) useful links:-

There are three main areas of human endeavour through which, by interfering with the natural order of things, we attempt to make life better for mankind – these are

• Agriculture– Experiments take a long time due to the motion of the planet around the sun– Number of treatments and sample sizes usually not a problem

• Medicine– Ethical considerations constrain experiments, and replication can be slow– Regulatory authorities like certain numbers on p-values

• Engineering– Experiments are sequential, and usually quick– Emphasis is on selection rather than estimation

Each field is contextually different. Statistical careers are probably better known in Agriculture and Medicine than Engineering

Preamble

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Engineering and the iterative learning process

“Engineering is the profession in which a knowledge of the mathematical and natural sciences, gained by study, experience, and practice, is applied with judgment to develop ways to utilize, economically, the materials and forces of nature for the benefit of mankind.”

Deduction

Induction

Box, GEP. "Science and statistics". JASA, Vol. 71, No 356, 1976, pages 791-799.

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The contribution of statistical science to engineering is toa) encourage creativity and b) to ensure convergence.

“Engineering is the profession in which a knowledge of the mathematical and natural sciences, gained by study, experience, and practice, is applied with judgment to develop ways to utilize, economically, the materials and forces of nature for the benefit of mankind.”

Deduction

Davis, TP (2006). “Science, engineering, and statistics”. Applied Stochastic Models in Business and Industry, 22, Issue 5-6, 401-430.

Engineering and the iterative learning process

Induction

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An engineer must be able to…• Recognise need• Define problems• Conceive alternatives• Predict consequences• Design experiments and draw inferences• Test and evaluate• Delineate solutions• Understand production and distribution• Be intellectually honest

This list is from a classic engineering text by E Mischke (Mathematical model building – an introduction to engineering). These criteria also describe the attributes of an engineering statistician!

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Tim Davis - Career• 1981 – BSc Statistics, Aberystwyth• 1981 – Dunlop Ltd.• 1982 – Fellow, Royal Statistical Society (RSS)• 1983 – Started PhD at University of Birmingham• 1985 – Sumitomo Rubber Industries, Japan

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Hazard functions of tire failures

[The likelihood function for the case of tied lifetimes with different failure types needed straightening out, so I wrote my PhD thesis on this.]

Estimate by 4

}Estimate by

Called competing risks

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Tim Davis - Career• 1986 – Ford Motor Company• 1988 – Captain’s Player Ford Warley CC• 1989 – Best Fielder Ford Warley CC• 1991 – PhD (Competing Risks Survival Analysis)• 1991 – Council member RSS (4 year term; VP ‘93-’95)• 1992 – Book (Engineering, Quality & Experimental Design) with Dan Grove• 1995 – Quality Manager, Ford Werke AG, Köln

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Tim Davis - Career• 1992 – Greenfield Industrial Medal, RSS• 1993 – Lecturer at UCL on Statistics MSc course• 1994 – Chartered Statistician (C.Stat.)• 1995 – Quality Manager, Ford Werke AG, Köln, Germany

https://lectopia.ncl.ac.uk/lectopia/lectopia.lasso?ut=10855&id=3841

(1) (2)

𝐷

𝐿

𝐵

𝐺=𝜋 /4 (𝐷2−𝐵2)𝐿

𝜎 𝑦❑2 =∑ ( 𝑑𝑓𝑑𝑥𝑖 )

2

. σ 𝑖2

Length,

Dia

met

er,

Amount of glass,

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

1.0

1.3

1.6

1.9

2.2

2.5

2.8

0

2

4

6

8

10

12

14

16

18

20

Transmitted variationJim Morrison’s Glass Bead example

Morrison, SJ (1957). “The study of variability in engineering design”. Applied Statistics, Vol 6, No. 2, 133-138.

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𝑇 ∝𝐷2 𝑙𝐴 𝑙𝑀 𝜃𝜌𝑀𝑙𝐷𝑅𝑤 ( 𝑓 𝐷−𝑝𝐷)

= motor torque= wire diameter= wire length= wire conductivity= armature length= magnet length

= magnet thickness= internal diameter of

motor housing= rotor core diameter= magnet angle= magnet density

Electric motor in a window winder

Variability in Torque causes variability in window closing times

R Parry-Jones (with TP Davis, G Green) - 1999. Engineering for corporate success in the new millennium. Royal Academy of Engineering. ISBN 1 871634 83 0.

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Engine modeling involves predicting how an engine performs (in terms of torque, yT, or emissions, yE) as a result of changing load (xL), RPM (xR), spark advance (xS) air & fuel mixture (xA), amount of exhaust gas recycled (xE), etc. It is an important activity in Engine Mapping.

There are two possible ways to view the (empirical) model:

Either as a “one shot” response function, written asyT = f(xL, xR, xS, xA, xE) {# of parameters = # of coefficients}

Or as a “two-stage” response function, written as

1st stage: yT = fs(xS; b1, b2, b3,…); fs(.) are know as “spark sweeps”2nd stage: {# of parameters < # of coefficients}

Hence, the 2-stage approach reduces model complexity (design parsimony) – hence less prediction error.

Engine ModelingT Holliday, AJ Lawrance, & TP Davis. "Engine mapping experiments: a two-stage regression approach". Technometrics, Vol. 40 #2, pages 120-126.

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-3

-2

-1

0

1

2

3

0 10 20 30 40 50

Spark advance (deg BTDC)

Res

idua

l

Engine mapping with Spark Sweeps

-3

-2

-1

0

1

2

3

0 10 20 30 40 50

Spark advance (deg BTDC)R

esid

ual

𝑦 𝑇= 𝑓 (𝑥 𝐿 , 𝑥𝑅 , 𝑥𝑆 , 𝑥 𝐴 ,𝑥𝐸)

𝑥𝑠

𝑦𝑇

# of parameters = # of coefficients

𝑦 𝑇= 𝑓 𝑠(𝑥 𝑆 ;𝜷)1st stage:2nd stage: )

# of parameters < # of coefficients

𝑥𝑠

𝑦𝑇

Residual Plot

Residual Plot

𝑅2≈0.98

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Tim Davis - Career• 1995 – Member, American Society of Quality (now a Senior member)• 1999 – Quality Director, Ford Motor Company, Detroit, USA• 2000 – Firestone Tire crisis• 2001 – 10th Henry Ford Technical Fellow (for Quality Engineering)• 2002 – Created the Office of the Technical Fellow to support the CTO

“Established in 1994, the Henry Ford Technical Fellow distinction is the most prestigious technical expert position in the Ford Motor Company. It is intended to recognize exceptional engineers or scientists in research, product development, and manufacturing. The position was created for top technical experts with an international reputation in their particular field of automotive expertise. Fellows provide technical expertise and leadership in the application of relevant engineering and scientific principles to manufacturing and product development teams. They also play a major consultative role in the development of corporate technical strategy.”

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The 2000/01 Firestone tire crisis• In 2000, it was reported in the US media that people

had been killed (~300 in total) in roll-over accidents involving tread separations .

• All the accidents involved certain Firestone tires• Most of the accidents involved Ford Explorers• In September 2000, Firestone recalled some (~5m)

of the suspect tires• In May 2001, Ford recalled another ~20m tires that,

it was determined (based on my work), might also fail.• Several trips to Washington DC during the crisis, and legal

depositions & taking the witness stand for 1½ days in the high profile court case followed.

• This crisis was my “Challenger accident”. A heady mix of science, ethics, legal wrangles, and politics. The science & ethics won.

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Cumulative hazard analysis Increasing Failure Rate. Note differences between factory of origin for the same tire type.

The hazard function (again)

0

50

100

150

200

250

300

350

400

450

500

0 1 2 3 4 5 6 7 8 9 10

Subject Tires(colour relates to factory)

Other tires(colour relates to brand)

Tire age (years)

Cum

ulati

ve h

azar

d x1

0-6

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Factorial design – to develop a lab test to replicate the failure mode, and the relative failure frequency

18psi

22psi

26psi

30psi

100oF 70oF

1300lbs

1785lbs

1500lbs

32psi

Standard

Load

Pressure

AmbientTemp.

Developing a lab test to mimic the field

= no tread separation= tread separation

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The recall decision was made to replace 20 million tires ($3Bn) before the authorities asked us to do it.

“… the set of cumulative hazard function curves for the recalled tires… demonstrate that if they are not removed from service, the focus tires from these plants – … will experience a similar increase in tread separation failures over the next few years.…”

Engineering Analysis Report and Initial Decisionregarding

EA0023: Firestone Wilderness AT Tires

U.S. Department of TransportationNational Highway Safety Administration

Safety AssuranceOffice of Defect Investigation

October 2001

NHTSA report available at www.nhtsa.gov/nhtsa/announce/press/Firestone/

The 2000/01 Firestone tire crisis

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Tim Davis - Career• 2004 – Fellow I.Mech.E, and Chartered Engineer (C.Eng.)• 2005 – IMechE Donald Julius Groen Prize in reliability, for Failure Mode

Avoidance.• 2006 – Honorary Professor, University of Warwick• 2007 – Quality Director and Board Member – Jaguar Land Rover• 2008 – Business sold to Tata Motors

Failure Mode Avoidance• Treats failure modes as due to 2 causes (due to Don

Clausing)– Lack of robustness– Mistakes

• Doesn’t need the statistical mathematics of defining reliability as a probability; instead it uses an information based approach, combined with the FMEA.

• The job of the engineer is to select the design that will fail the least, not to estimate the failure rate of the selected design

• “If a guy tells me the probability of failure is 1 in 105, I know he’s full of crap” – Richard Feynmanhttp://history.nasa.gov/rogersrep/v2appf.htm

Release Part A

Asynchronous material and information flow in product/technology development

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Release Part B

Release Part C

Release Part D

Easy to detect, hard to fix

Latit

ude

to ta

keco

unte

r-m

easu

res

time

① release drawings ② build ③ detect, fix

Release Part A

Synchronous material and information flow in product/technology development

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Release Part B

Release Part C

Release Part D

② release drawings ③ build① detect, fix

Easy to detect, hard to fixHard to detect, easy to fix

Latit

ude

to ta

keco

unte

r-m

easu

res

time

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Tim Davis - Career• 2010 – Council & Executive Committee member RSS, 2nd term• 2010 – Established timdavis consulting ltd. (www.timdavisconsulting.com)• 2012 – CTO at We Predict Ltd. (www.wepredict.co.uk)• 2012 – Elected member of International Statistical Institute• 2013 – Fellow of the American Statistical Association (ASA), and P.Stat.

My Statistical Philosophy• Statistics should be seen as a branch of science, and statisticians

should be the custodians of the scientific method (induction vs. deduction);

• Therefore, statistical science not statistical mathematics;• Focus on hypothesis generation, not just hypothesis testing;• Recognize that often, the problem is one of selection, not

estimation (the job of the engineer is to select the design that will fail the least, not predict the failure rate of the chosen design);

• Graphical methods vs. numerical/tabular methods;• Exploit observations with strange residuals;• Parsimony over complexity;• Context – timescales, loss function, sequential vs. “one-shot”.

… and finally

• More statisticians need to get into positions of senior management if we as a profession are to make an impact on business and industry.