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

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: FactorRange of Variation X1Catalyst Concentration, %1.00 to 1.80 X2Reactor Temperature, oC130 to 190 X2Amount of Additive, kg1.0 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 RandomBias Cause:UnknownIdentifiable Nature:RandomPatterned Management:Replication Randomization & 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. Screening Designs Full Factorial Designs Response Surface Designs Many Independent Variables Fewer independent variables (<5) “Crude” Information Quality Linear Prediction Quality non-linear Prediction

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 (2 k )  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, HI LO, 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 TrialX1X2X3 X1* X2 X1* X3 X2* X3 X1* X2* X

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(Si 2 )/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. 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 (Si 2 ) of each run Calculate the average variance for the high level and low level interaction (Si 2 (+)avg, Si 2 (-)avg) Calculate the F statistic  Fcalc = Si 2 avg larger / Si 2 avg smaller

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