CHEN 4860 Unit Operations Lab

1
CHEN 4860 Unit Operations Lab

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

2
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 ???

3
DOE Lab Schedule
4
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

5
Introduction

• What is Experimentation?

6
Objective of Experimentation

• Improve process or product performance and yields
• Improve product quality and uniformity
• Ensure your product (end-result) meets your
  customers needs
• Ensure it ALWAYS does (Six Sigma)
• This is an ISO 9000 above requirement

7
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.

8
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

9
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

10
Workshop

• A typical RD problem

11
Problem Statement

• Problem RD 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
12
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
• Bosss best guess for a place to start is
• X1 1.25 , X2 137 oC, X3 3.0 kg

13
Workshop Counter

• Breakup into your M1, M2 and R1, R2 groups.
• You have 15 min.

14
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?

15
Fundamentals of Strategy

• What is experimentation strategy?

16
Overall Strategy of Experiments

• Minimize experimental error
• Maximize usefulness of each experiment
• Ensure objectives of experiment are met

17
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.

18
Experimental Error
Random Bias
Cause Unknown Identifiable
Nature Random Patterned
Management Replication Randomization Blocking
19
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.

20
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

21
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

22
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

23
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

24
Objectives of the Experiment

• Set objective
• It should be specific, measurable, and have
  practical consequence
• Determine the potential variables
• Independent Factors (Xs)
• Process variables and/or control knobs
• Must be influential, controllable, and measurable
• Dependent Reponses (Ys)
• Product yield, quality, and/or stability
• Can be more than one

25
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.

26
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

27
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

28
Factorial Design

• Statistics in experimental design

29
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

30
Factorial Design (2k)

• K is number of factors
• 2 is number of levels (low, high)

LO, HI, HI
HI, HI, HI
HI, LO, HI
LO, HI, LO
X3
Pts (X1, X2, X3)
LO, HI, LO
HI, HI, LO
X2
X1
LO, LO, LO
HI, LO, LO
31
Main Effects

• Factor Effect Y()avg Y(-)avg
• Hidden Replicates 4 runs at X2() and 4 runs
  at X1(-)

-
X2effect Y(X2)avg Y(X2-)avg
X2
32
Interaction Effects

• Hidden Replicates 4 runs at X1X2() and 4 runs
  at X1X2(-)

X1X2 Interaction Y(X1X2)avg Y(X1X2-)avg
-
X2
X1
33
Other Interaction Effects

• X1X2X3 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

34
One Factor at a Time (OFT)

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

X3
X2
X1
35
Factorial Design Tabular Form
Trial X1 X2 X3 X1X2 X1X3 X2X3 X1X2X3
1 - - - -
2 - - - -
3 - - - -
4 - - - -
5 - - - -
6 - - - -
7 - - - -
8
36
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 Sesqrt(4/trials)

37
Significance of Effects and Interactions

• To determine the variance of the normal curve,
  use Students 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)

38
Significance of Effects and Interactions

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

DL
DL
E(X1)
E(X2)
E(X3)
39
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

40
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

41
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

42
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

43
Workshop Redo

• Using Factorial Design

44
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

45
Workshop Redo Counter

• Breakup into your M1, M2 and R1, R2 groups.
• You have 15 min.

46
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?

47
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