int 506/706: total quality management introduction to design of experiments
Post on 28-Dec-2015
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• 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:
Factor Level
Speed 55, 65
Tire 28 psi, 35 psi
Oil 30 weight, 40 weight
Gas Regular (R), Premium (P)
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
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
Significance
Used to indicate whether a factor or factor combination
caused a significant change in the response variable
Example
FactorsMaterial SupplierPress Tonnage
3 levels of each factorSupplier Press Tonnage A 20 B 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
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:
1) Main effects of factors
2) Effects of factor interactions
Variability
3 Sources of variability contributing to the variability in the numbers
1. Var. due to conditions of interest (we expect a change from manipulating some factor)
2. Var. due to measurement process (UNWANTED – errors in measuring equipment or technique)
3. Var. in experimental material (UNWANTED – trying to make material, or subjects, as similar as possible – block into groups)
Variability
3 types of variability
1. PLANNED, SYSTEMATIC – due to conditions of interest
2. CHANCE-LIKE VARIATION – background noise, an unplanned component from the measurement process
3. UNPLANNED, SYSTEMATIC – Biased, one of the main causes of wrong conclusions and ruined studies
1. Blocking: turns possible bias into planned, systematic variation
2. Randomization: turns bias into planned, chance like variation
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