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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.
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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:
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 Factors Material Supplier Press Tonnage 3 levels of each factor SupplierPress Tonnage A 20 B 25 C 30
Example Treatments – 3 x 3 SupplierPress 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: • Main effects of factors • Effects of factor interactions
Variability 3 Sources of variability contributing to the variability in the numbers • Var. due to conditions of interest (we expect a change from manipulating some factor) • Var. due to measurement process (UNWANTED – errors in measuring equipment or technique) • Var. in experimental material (UNWANTED – trying to make material, or subjects, as similar as possible – block into groups)
Variability 3 types of variability • PLANNED, SYSTEMATIC – due to conditions of interest • CHANCE-LIKE VARIATION – background noise, an unplanned component from the measurement process • UNPLANNED, SYSTEMATIC – Biased, one of the main causes of wrong conclusions and ruined studies • Blocking: turns possible bias into planned, systematic variation • Randomization: turns bias into planned, chance like variation
Variability 3 Basic Principles • Random Assignment • Blocking • Factorial Crossing 1 and 2 are How we collect data 3 is how we construct treatments