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CHAPTER 1:STATISTICS IN ENGINEERING

Wandaliz Torres-García, Ph. D.

Image Source: pinterest.com

Reference: Most slides adapted from Montgomery et al. (2011)

ININ 5559ENGINEERING STATISTICS

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1-1 THE ENGINEERING METHOD ANDSTATISTICAL THINKING

Engineers solve problems of interest to society by theefficient application of scientific principles

The engineering or scientific method is the approach toformulating and solving these problems.

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1-1 THE ENGINEERING METHOD ANDSTATISTICAL THINKING

The Field of Probability• Used to quantify likelihood or chance• Used to represent risk or uncertainty in engineering

applications• Can be interpreted as our degree of belief orrelative frequency

The Field of Statistics• Deals with the collection, presentation, analysis, anduse of data to make decisions and solve problems .

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Reference: Most slides adapted from Montgomery et al. (2011)

1-1 THE ENGINEERING METHOD ANDSTATISTICAL THINKING

• Statistics is the science of data.•Statistical techniques are useful fordescribing and understanding variability.

• By variability, we mean successiveobservations of a system or phenomenondo not produce exactly the same result.

• Statistics gives us a framework fordescribing this variability and for learningabout potential sources of variability .

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1-1 THE ENGINEERING METHOD ANDSTATISTICAL THINKING

Engineering ExampleSuppose that an engineer is developing a rubber compound foruse in O-rings. The O-rings are to be employed as seals in plasmaetching tools used in the semiconductor industry, so their resistanceto acids and other corrosive substances is an importantcharacteristic. The engineer uses the standard rubber compound toproduce

eight O-rings in a development laboratory and measuresthe tensile strength of each specimen after immersion in a nitricacid solution at 30°C for 25 minutes [refer to the American Society for Testing and Materials (ASTM)] .

The tensile strengths (in psi) of the eight O-rings are 1030, 1035,1020, 1049, 1028, 1026, 1019, and 1010.

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1-1 THE ENGINEERING METHOD ANDSTATISTICAL THINKING

Engineering Example• The dot diagram is a very useful plot for displaying asmall body of data - say up to about 20 observations.• This plot allows us to see easily two features of the

data; the location , and the scatter or variability .• Good tool to observe outliers and clusters .

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1-1 THE ENGINEERING METHOD ANDSTATISTICAL THINKING

Engineering Example• The dot diagram is also very useful for comparingsets of data.

• What are obvious questions to ask?

Added Teflon

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1-1 THE ENGINEERING METHOD ANDSTATISTICAL THINKING

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1-2 COLLECTING ENGINEERING DATA

Three basic methods for collecting data:A retrospective study using historical data, all or a sample, todetermine relationships among factors and response(s).

An observational study observes the process of populationduring a period of routine operation.

A designed experiment is used to make changes tocontrollable variables, factors, to observe the responseoutput. In contrast with the other two studies the combinationsof factors are performed in a randomized manner with

replicates. This permits to establish cause-and-effectrelationships.

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1-2 COLLECTING ENGINEERING DATA

Example: Acetonebutyl alcohol destillation column

Response random variable: Acetonebutyl concentration (g/L)Controllable factors: Condenser Temp, Reboil Temp., Reflux Rate(all at two levels, low (-) & high(+)).

23 factorial design with 2 replicates

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1-2 COLLECTING ENGINEERING DATA

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1-2 COLLECTING ENGINEERING DATA

1-2.4 Random Samples

Example: Measuring mathematical skills at University of Puerto Rico

How to sample from the population to infer statistical knowledge?

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1-3 MECHANISTIC AND EMPIRICAL MODELS

A mechanistic model is built from our underlyingknowledge of the basic physical mechanism thatrelates several variables.

Example: Ohm’s Law

Current = voltage/resistance

I = E/R

I = E/R +

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1-3 MECHANISTIC AND EMPIRICAL MODELS

An empirical model is built from our engineering andscientific knowledge of the phenomenon, but is notdirectly developed from our theoretical or first-principles understanding of the underlying mechanism.

Sometimes models are not well understood and highlycomplex.

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1-3 MECHANISTIC AND EMPIRICAL MODELS

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1-3 MECHANISTIC AND EMPIRICAL MODELS

PullStrength(y)

WireLength(x1)

DieHeight(x2)

9.95 2 50

24.45 8 110

31.75 11 120

35 10 550

25.02 8 295

16.86 4 200

14.38 2 375

9.6 2 52

24.35 9 100

27.5 8 300

17.08 4 412

37 11 400

41.95 12 500

11.66 2 360

21.65 4 205

17.89 4 400

69 20 600

10.3 1 585

34.93 10 540

46.59 15 250

44.88 15 290

54.12 16 510

56.63 17 590

22.13 6 100

21.15 5 400

Example: Observational Study: Semiconductor Wire bond data

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1-3 MECHANISTIC AND EMPIRICAL MODELS

In general, this type of empirical model is called aregression model .

The estimated regression line is given by

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1-4 OBSERVING PROCESSES OVER TIME

Whenever data are collected over time it is important to plotthe data over time. Phenomena that might affect the systemor process often become more visible in a time-oriented plotand the concept of stability can be better judged.

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1-4 OBSERVING PROCESSES OVER TIME

Experiment 1 Experiment 2

Drop marbles one after theother but never moving thefunnel.

Drop first marble and thenadjust funnel before droppingnext marble.

Higher variance on Experiment 2 (over control or tampering)

Adjustments can help to reduce non-random shifts.

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1-4 OBSERVING PROCESSES OVER TIME

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1-4 OBSERVING PROCESSES OVER TIME

When to applyadjustments?How much adjustment?

Understanding Variation.

Control Charts are veryuseful to study variation oftime series data.