INT 506/706: Total Quality Management

Introduction to Design of Experiments

Outline

• DOE – What is it?• Trial and error experiments• Definitions• Steps in designed experiments• Experimental designs

DOE

A method of experimenting with the complex interactions among parameters in a

process or product with the objective of optimizing the

process or product

Trial and error experiments

Involves making an educated guess about what should be

done to effect change in process or system

Trial and error experiments

Example:

Factor Level

Speed 55, 65

Tire 28 psi, 35 psi

Oil 30 weight, 40 weight

Gas Regular (R), Premium (P)

Trial and error experiments

Definitions

Factor

The variable the experimenter will vary in order to determine

its effect on a response variable

Definitions

Level

The value chosen for the experiment and assigned to

change the factor

Gas example

Tire Pressure – Level 1: 28 psi; Level 2: 35 psi

Definitions

Controllable Factor

Ability to establish and maintain level throughout experiment

Definitions

Effect

Result or outcome of the experiment

Definitions

Response Variable

The quality characteristic under study, the variable we want to

have an effect on

Definitions

Degrees of Freedom

The number of independent data points in the samples determines the available

degrees of freedom

Definitions

Degrees of Freedom• We earn a degree of freedom for every data point we collect• We spend a degree of freedom for each parameter we estimate

Definitions

Degrees of Freedom

dfTotal = N – 1 = # of observations – 1

dfFactor = L – 1 = # of levels – 1

dfInteraction = dfFactorA * dfFactorB

dfError = dfTotal – dfEverythingElse

Definitions

Interaction

Two or more factors that together produce a result

different than what the result of their separate effects would be

Definitions

Noise Factor

An uncontrollable, but measurable, source of variation in the functional characteristics

of a product or process

Definitions

Treatment

The specific combination of levels for each factor used for a

particular run

Definitions

Run

An experimental trial, the application of one treatment

Definitions

Replicate

A repeat of a treatment condition

Definitions

Repetition

Multiple runs of a particular treatment combination/setup

Definitions

Significance

Used to indicate whether a factor or factor combination

caused a significant change in the response variable

Example

FactorsMaterial SupplierPress Tonnage

3 levels of each factorSupplier Press Tonnage A 20 B 25 C 30

Example

Treatments – 3 x 3Supplier Press Tonnage A 20 A 25 A 30 B 20 B 25 B 30 C 20 C 25 C 30

Steps in planned experiments

• What are you investigating• What is the objective• What are you hoping to learn• What are the critical factors• Which factors can be controlled• What resources will be used

Step 1

Establish the purpose by defining

the problem

Step 2

Identify the components of the

experiment

Step 3

Design the experiment

Step 4

Perform the experiment

Step 5

Analyze the data

Step 6

Act on the results

Experimental Designs

OFAT or Single Factor Experiments

Allows for manipulation of only one factor during an experiment

Experimental Designs

Full Factorial Designs

Consists of all possible combinations of all selected levels of the factors to be investigated

To determine # of combinations or runs:

LevelsFactors

Experimental Designs

Determine # of combinations:

6 Factors at 2 levels = 26 or 64 combinations

4 factors, 2 with 2 levels and 2 with 3 levels =

22 x 32 = 36 treatment combinations

Experimental Designs

Full Factorials allows the most complete analysis because it can determine:

1) Main effects of factors

2) Effects of factor interactions

Variability

3 Sources of variability contributing to the variability in the numbers

1. Var. due to conditions of interest (we expect a change from manipulating some factor)

2. Var. due to measurement process (UNWANTED – errors in measuring equipment or technique)

3. Var. in experimental material (UNWANTED – trying to make material, or subjects, as similar as possible – block into groups)

Variability

3 types of variability

1. PLANNED, SYSTEMATIC – due to conditions of interest

2. CHANCE-LIKE VARIATION – background noise, an unplanned component from the measurement process

3. UNPLANNED, SYSTEMATIC – Biased, one of the main causes of wrong conclusions and ruined studies

1. Blocking: turns possible bias into planned, systematic variation

2. Randomization: turns bias into planned, chance like variation

Variability

3 Basic Principles1. Random Assignment

2. Blocking

3. Factorial Crossing

1 and 2 are How we collect data

3 is how we construct treatments