CHEN 4860 Unit Operations Lab

Design of Experiments (DOE)With excerpts from “Strategy of Experiments” from Experimental Strategies, Inc.

The DOE Lab

Objectives – Help students be better experimenters through the methodology of modern experimental design, and the strategy of its application

Contents – Lecture, workshop, project Questions – No question is unimportant Resources – Slides, examples, instructor Benefits – ???

DOE Lab Schedule

Wk of M T W R F

Apr. 3 DOE Lecture 1 DOE Lecture 1DOE Proposal due for M1, M2

groups

Apr. 10Review DOE

Proposals with M1, M2

DOE Lecture 2; DOE Proposal due for R1, R2

groups

Review DOE Proposals with

R1, R2

Apr. 17

Apr. 24Formal Memo due for M1, M2

Formal Memo due for R1, R2

Location & Time Txt 235 (3-5PM) AE 355 (1-2PM) Txt 235 (3-5PM)

DOE Lab Schedule Details

Lecture 1 Introduction Workshop Fundamentals of

Strategy Factorial Design Redo Workshop

DOE Proposal Students develop

own written project proposal

Must be approved by Dr. Placek

Lecture 2 Work In-Class

Example Screening Designs Response Surface

Designs Formal Memo

Experimental plan Expected results Actual results Theory on differences Plan for further

experimentation

Introduction

What is Experimentation?

Objective of Experimentation

Improve process or product performance and yields

Improve product quality and uniformity Ensure your product (end-result) meets

your customer’s needs Ensure it ALWAYS does (Six Sigma) This is an ISO 9000 & above

requirement

Five Stages of Experimentation

Design Data Collection Data Analysis Interpret Results Communicate Results

DESIGN One of the most important (and

often the most important) stages in experimentation

If you can see how the pieces should fit together, it is much easier to interpret and communicate your results.

Experimentation Design

Objectives of the experiment Diagnosis of the environment Variables to be controlled Properties to measure Size of the effects to be detected Variable settings Number of experimental runs Carrying out the experiment Data analysis

Obstacles to Experimenters

Belief that “ad hoc” methods work well

Lack of awareness of the advantages of “planning”

Hesitancy to use unfamiliar techniques

Lack of awareness of compromising conditions in the experimental situation

Workshop

A typical R&D problem

Problem Statement

Problem: R&D has developed a new resin. There is a problem. During start-up, the color of the resin, Y, has been too yellow. Retrospective data and chemistry suggest that yellowness probably is affected by three process factors, which are:

Factor Range of Variation

X1 Catalyst Concentration, % 1.00 to 1.80

X2 Reactor Temperature, oC 130 to 190

X2 Amount of Additive, kg 1.0 to 5.0

Workshop Tasks

Where do you set the levels of the 3 process variables, X1, X2, and X3?

Support your findings with a description of the effects of the 3 factors on Y1 and draw a simple line chart

Describe strategy you used in your experiment

Boss’s best guess for a place to start is: X1 = 1.25 %, X2 = 137 oC, X3 = 3.0 kg

Workshop Counter

Breakup into your M1, M2 and R1, R2 groups.

You have 15 min.

Workshop Summary

What were the optimum set points for each variable?

What were the effects of each variable on the “yellowness” of the resin?

How many experiments did it take you to determine these results?

Fundamentals of Strategy

What is experimentation strategy?

Overall Strategy of Experiments

Minimize experimental error Maximize usefulness of each

experiment Ensure objectives of experiment are

met

Minimize Experimental Error

High amounts of error in an experiment can make it extremely difficult (and time consuming) to interpret the results

In some cases, the error is so high that it is impossible to discern any influence the factors had on the response variable.

This could lead to a costly “redo” of the experiment.

Experimental Error

Random Bias

Cause: Unknown Identifiable

Nature: Random Patterned

Management: ReplicationRandomization

& Blocking

Random Error

Examples… Arrival at school when leaving home at

the same time and taking the same route

Readings from a platform chemical balance for the same sample

Continuous measurement often gives random error.

Bias Error

Examples… Step Functions – a change in a shift, a

change in raw material or batch, a change in equipment, etc.

Cycles – a rhythmic variation due to weather, time of day, etc.

Drift – a deterioration of catatlyst, bearing or tool wear, etc.

Discrete measurement will often give bias error

Managing Error

Random Error Ensure instruments are calibrated Replicate to take out the noise

Bias Error Block – estimate factor effects within

homogeneous blocks Randomize – convert bias error into

random error

Maximize Usefulness of Data

To maximize the usefulness of data, put significant effort into the planning stage of the experiment

Both minimizing error and maximizing usefulness of the data will ensure the objectives of the experiment are met

Planning the Experiment

Objectives of the experiment Diagnosis of the environment Variables to be controlled Properties to measure Size of the effects to be detected Variable settings Number of experimental runs Carrying out the experiment Data analysis

Objectives of the Experiment

Set objective It should be specific, measurable, and have

practical consequence Determine the potential variables

Independent – Factors (X’s) Process variables and/or control knobs Must be influential, controllable, and

measurable Dependent – Reponses (Y’s)

Product yield, quality, and/or stability Can be more than one

Diagnosing the Environment

Considering the objectives, level of knowledge, number of independent variables, and nature of independent variables, determine which type of experimental design to use.

ScreeningDesigns

Full FactorialDesigns

Response SurfaceDesigns

Many IndependentVariables

Fewer independent variables (<5)

“Crude”Information

Quality LinearPrediction

Quality non-linearPrediction

Variables to be Controlled

Determine Properties (Effects) List of independent variables you wish

to measure Controlled Variables

List of other independent variables that affect the response variable that you wish to control

Size of an Experiment

General Rules Must be large enough to detect factor

effects with necessary precision Must be small enough to conserve

resources Must be small enough to be timely

Set effect ranges accordingly Evaluate need for replication

Factorial Design

Statistics in experimental design

Factorial Design Overview

Factorial Design is one of many tools used in DOE

Pooling experimental error Determines significance of main effects Determines significance of interactions Evaluates variation contribution from

main effects

Factorial Design (2k) K is number of factors 2 is number of levels (low, high)

X1

X2

X3

LO, HI, LO

LO, LO, LO

Pts (X1, X2, X3)

HI, LO, LO

HI, HI, LO

HI, LO, HI

HI, HI, HILO, HI, HI

LO, HI, LO

+

Main Effects

Factor Effect = Y(+)avg – Y(-)avg “Hidden” Replicates: 4 runs at X2(+) and

4 runs at X1(-)

X2

-

X2effect = Y(X2+)avg – Y(X2-)avg

Interaction Effects

“Hidden” Replicates: 4 runs at X1X2(+) and 4 runs at X1X2(-)

X2

+

X1X2 Interaction = Y(X1X2+)avg – Y(X1X2-)avg

-

X1

Other Interaction Effects

X1*X2*X3 interactions work on same principle (X1X2X3(+)avg – X1X2X3(-)avg)

3 factor interactions are not common and are generally not significant

The exception to this rule is often interactions between chemical constituents

One Factor at a Time (OFT)

No hidden replication Not space-filling No way to determine interactions

X1

X2

X3

Factorial Design Tabular Form

Trial X1 X2 X3X1*X2

X1*X3

X2*X3

X1*X2*X3

1 - - - + + + -

2 + - - - - + +

3 - + - - + - +

4 + + - + - - -

5 - - + + - - +

6 + - + - + - -

7 - + + - - + -

8 + + + + + + +

Significance of Effects and Interactions

If effects or interactions are significant, then they will be outside the variance of a normal curve

To determine the variance of the experiment Calculate the Stdev of the experiment

Se = sqrt(sum(Si2)/runs) Calculate the Stdev of the effects

Seff = Se*sqrt(4/trials)

Significance of Effects and Interactions

To determine the variance of the normal curve, use Student’s t-test Estimate alpha as 0.05 for 95%

confidence. Estimate the degrees of freedom

degfree = (reps/run – 1)*(runs) Read the t statistic from table Calculate the decision limit

DL = t*(Seff)

Significance of Effects and Interactions

If Si > DL, then effect is significant If not, move on.

-1.5 -1 -0.5 0 0.5 1 1.5

DL DL

E(X1) E(X2) E(X3)

Significance of Variance

Replicate each run to learn which variables will reduce variation in the response variable Calculate the variance (Si2) of each run Calculate the average variance for the

high level and low level interaction (Si2(+)avg, Si2(-)avg)

Calculate the F statistic Fcalc = Si2avglarger / Si2avgsmaller

Significance of Variance

To determine the two-tailed F statistic Estimate alpha as 0.10 Estimate the degrees of freedom as

degfree = (reps/run – 1)*(runs) Read the F statistic from table Evaluate F vs. Fcalc

Factorial Example

Chemical Process Yield Improve process yield without knowing

reaction rates or chemical constituents Ink Transfer

Improve transfer of ink to industrial wrapping paper

Factorial Design: Summary

Use the “cube” approach Set each factor as a dimension Code: Low = “-” and High = “+” Effects are comparisons of planes Hidden replication High-order interactions

Workshop Redo

Using Factorial Design

Workshop Tasks

Where do you set the levels of the 3 process variables, X1, X2, and X3?

Support your findings with a description of the effects of the 3 factors on Y

Describe strategy you used in your experiment

Workshop Redo Counter

Breakup into your M1, M2 and R1, R2 groups.

You have 15 min.

Workshop Redo Summary

What were the optimum set points for each variable?

What were the effects of each variable on the “yellowness” of the resin?

How many experiments did it take you to determine these results?

Benefits Revisited

Maximize benefit/cost ratio of experiments

Improve productivity and yields Minimize process sensitivity to

variation (Maximize Robustness) Achieve better process design Shorten development time Improve product quality