Experimental Design and Hypothesis Testing, Summaries of Experimental Design

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Seminar

Experimental Design and

Hypothesis Testing

September 4, 2019 Ali Ashasi-Sorkhabi, PhD, EITBryan Tolson, PhD, PEng.Liping Fu, PhD, PEng.Giovanni Cascante PhD, PEng.

Experimental design

o^

What is an experiment? o^

Strategy of experimentation o^

Design guidelines

Simple comparative experiments

o^

Hypothesis testing o^

Confidence intervals o^

Choice of sample size

Error analysis methods

o^

Time independent data o^

Time dependant data

Agenda

Process/system

o

involves one or a combination of

operations

,^ machines

methods

,^ people

or other resources

o

transforms some

input, X,

(often a material) into an

output, Y,

that has one or more observable response

variables.

o

includes

variables/factors

and

material properties

that

can be

controlled

whereas other ones

cannot.

What is an experiment?

Typical

objectives

of an experiment are to determine:

-^

which variables are most influential on the response Y

-^

the optimal values of V’s so that the desired output, Y isobtained

-^

the values of V’s so that variability in Y is small

-^

the values of the influential V’s to minimize the effects ofexternal factors, W’s, are minimized.

-^

to develop a reliable model for the system/process

What is an experiment?

Remarks

-^

Experiments involve several factors (controlled & not)

-^

Main goal is to determine the influence of these factors onthe system response

-^

A successful experiment should result in a reliable modelfor the system

What is an experiment?

-^

The approach for planning and doing the experiment is calledthe

strategy of experimentation.

-^

Questions about how to vary the factors affecting thesystem/process

-^

There are different strategies for experimentation:^ o

Best‐guess approach

o

One‐factor‐at‐a‐time (OFAT)

o

Factorial experiment

Strategy of experimentation

-^

Best‐guess approach: o

Frequently used in practice by engineers

o

Consider an arbitrary combination of factors and see whathappens next:^ 

Round 1: oversized driver‐balata ball‐golf card‐water  Round 2: regular‐sized driver‐balata ball‐golf card‐water  …. This approach could be continued almost indefinitely!

o

Pros:

Could work reasonably well!

o

Cons:

if the 1

st^

guess is not good, 2

nd

one needed,

long time!

Also, If the 1

st^

guess gives acceptable results, experimenter

may stop, but no guarantee that best solution was found

Strategy of experimentation

-^

One‐factor‐at‐a‐time (OFAT): o

Select a baseline of levels for each factor, then vary each one overits range with other factors held constant at baseline o

Pros

: interpretation of OFAT graphs is straightforward.

o

Cons

: it fails to consider the

interactions

between factors that are

very common and if they occur, the OFAT produces

poor results

Strategy of experimentation

-^

factorial design

-^

Factorial experiment: o

If there are k factors, each at 2 levels, 2

k^ tests would be needed.

o

If the number of factors of interest increases (e.g. k=10), thenumber of runs increases very fast (1024 runs). It becomes^ impractical

from

time

and

resources

points of view

Strategy of experimentation

-^

Fractional factorial experiment:^4

factorial design (one‐half fraction) Strategy of experimentation

Remarks: 1. Use your non‐statistical knowledge of the problem2. Keep the design and analysis as simple as possible3. Recognize practical and statistical significances4. Experiments are usually iterative Initial experiment < %25 of resources of testing (runs, time, money)

•^

Experiments to

compare two conditions

•^

Example:

formulation of a Portland cement mortar

o

Objective:

compare the results obtained from method 1 and 2

o

2 different formulations ~

2 levels of the factor formulation

o

Findings:

Large reduction in the cure time 

Bond strength:

Simple comparative experiments

visual average comparison

-^

Review of basic statistical concepts o^

Probability distributions

: the probability structure of the random

variable o Simple comparative experiments^ Mean, expected value, variance

-^

Sampling and sampling distributions

The goal is to get conclusions about a population using a samplefrom that population^ o

Random samples:

randomly taken from the population

o Simple comparative experiments^ Sample mean and variance: Experimental Design and Hypothesis Testing