Presentation on theme: "Introduction to Design of Experiments by Dr Brad Morantz"— Presentation transcript:
1 Introduction to Design of Experiments by Dr Brad Morantz
2 Example We have a simulation of a radar system We want to test it How do we test it in every point in variable spaceThere could be a combination of variables where the system goes postal (unstable) or does not perform correctlyAnd how do we test it in a reasonable amount of timeOften an impossibilityThere are many situations where the system is so complex that to test it at every possible combination of variables would require several years on a very fast computer. Maybe even longer than that.
3 Introduction & Overview Structured method for performing (repeated) tests or analyses on a given systemNeed (n + 1) tests to estimate n parametersNeeded to estimate interaction parametersNeed to test in the corners of the envelopeDOE changes the factors independently of each otherAllows discovery of interaction effects
4 TermsFactor – An Independent variable that can only take on a finite number of values (levels)Covariate – An independent variable that can take on a continuous range of valuesParameter – A quantity that describes a statistical population (mean or variance)Level – a setting for a factor, represented at a -1 or +1 in the design/test matrixRun – one trial at specific factor settingsRepetition – Identical runs (combinations) done at the same timeReplicate – Identical runs (combinations) at different timesResponse – the output or dependent variableFull Factorial Design – examines all possible combinations of factors and levelsFractional Factorial Design – Examines a fractional portion of the possible combinations of factors and levels
5 ValiditiesExternal validity– the results generalize to the external world, that hold across different settings, procedures, & participantsInternal validity - validity of causal inferencesConstruct validity– does the scale measure the unobservable construct that it is intendedStatistical conclusion validity - refers to the degree to which one’s analysis allows one to make the correct decision regarding the truth or approximate truth of the null hypothesis.These are classic and mandatory for any true experiment. These must be considered when designing an experimentFor further information look up Cook and Campbell, also Detmar Straub.
6 2k Screening Full factorial 2 level design has 2k experiments Tests at all possible pointsMay take too much timeIf function is not monotonic (Continues in same direction)Could miss activity in systemShould use at least a 3 level design
7 CCD Central Composite Design Also called a “Box Wilson Central Composite designContains imbedded [or fractional] factorial designAugmented with group of star pointsAllow estimation of curvatureTwice as many star points as there are factorsThree types:CircumscribedInscribedFace CenteredSee NIST web site for details and how to make and use.Each one of the three types has its application
8 D-Optimal Produced by computer algorithm Usually not orthogonal Effect estimates usually correlatedStraight optimizationsBased on the model and optimality criterionBased on optimizing |X’X|Optimality is model dependentA set of treatment combinations created by using stepping and exchanging process
9 Response Surface Designs Latin Hypercube (volume filling)Supported in GenSimTaguchiSmaller number of runs than full factorialMany othersSequential bifurcationFolded designsCombined designsMany moreEach has its strengths & weaknessesDOEPro has Taguschi
10 JMP Statistical Package Generates test matrix Easy to use Works in Linux, Mac, Or PCGenerates test matrixEasy to useProduces coded valuesFull or fractional factorialTaguchi
11 Recommended TextModeling & Simulation by Averil Law