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Plackett–Burman designs are experimental designs presented in 1946 by Robin L. Plackett and J. P. Burman while working in the British Ministry of Supply.(Their goal was to find experimental designs for investigating the dependence of some measured quantity on a number of independent variables (factors), each taking L levels, in such a way as to minimize the variance of the estimates of these dependencies using a limited number of experiments.
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Plackett–Burman designs are experimental designs presented in 1946 by Robin L. Plackett and J. P. Burman while working in the British Ministry of Supply.(Their goal was to find experimental designs for investigating the dependence of some measured quantity on a number of independent variables (factors), each taking L levels, in such a way as to minimize the variance of the estimates of these dependencies using a limited number of experiments.
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Interactions between the factors were considered negligible. The solution to this problem is to find an experimental design where each combination of levels for any pair of factors appears the same number of times, throughout all the experimental runs (refer to table).
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A complete factorial design would satisfy this criterion, but the idea was to find smaller designs.
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These designs are unique in that the number of trial conditions (rows) expands by multiples of four (e.g. 4, 8, 12, etc.).
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The max number of columns allowed before a design increases the number of rows is always one less than the next higher multiple of four.
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A complete factorial design would satisfy this criterion, but the idea was to find smaller designs.
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These designs are unique in that the number of trial conditions (rows) expands by multiples of four (e.g. 4, 8, 12, etc.).
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The max number of columns allowed before a design increases the number of rows is always one less than the next higher multiple of four.
Special property of this grid is that points are not placed on the boundaries of the hypercube, but at centroids of the subcells constituted by individual samples.
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This design offers optimal results for the covering radius regarding distances based on the max-norm.
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Special property of this grid is that points are not placed on the boundaries of the hypercube, but at centroids of the subcells constituted by individual samples.
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This design offers optimal results for the covering radius regarding distances based on the max-norm.
In statistics, Box–Behnken designs are experimental designs for response surface methodology, devised by George E. P. Box and Donald Behnken in 1960, to achieve the following goals:
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* Each factor, or independent variable, is placed at one of three equally spaced values, usually coded as −1, 0, +1. (At least three levels are needed for the following goal.)
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* The design should be sufficient to fit a quadratic model, that is, one containing squared terms, products of two factors, linear terms and an intercept.
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* The ratio of the number of experimental points to the number of coefficients in the quadratic model should be reasonable (in fact, their designs kept it in the range of 1.5 to 2.6).*estimation variance should more or less depend only on the distance from the centre (this is achieved exactly for the designs with 4 and 7 factors), and should not vary too much inside the smallest (hyper)cube containing the experimental points.
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In statistics, Box–Behnken designs are experimental designs for response surface methodology, devised by George E. P. Box and Donald Behnken in 1960, to achieve the following goals:
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* Each factor, or independent variable, is placed at one of three equally spaced values, usually coded as −1, 0, +1. (At least three levels are needed for the following goal.)
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* The design should be sufficient to fit a quadratic model, that is, one containing squared terms, products of two factors, linear terms and an intercept.
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* The ratio of the number of experimental points to the number of coefficients in the quadratic model should be reasonable (in fact, their designs kept it in the range of 1.5 to 2.6).*estimation variance should more or less depend only on the distance from the centre (this is achieved exactly for the designs with 4 and 7 factors), and should not vary too much inside the smallest (hyper)cube containing the experimental points.
In statistics, a central composite design is an experimental design, useful in response surface methodology, for building a second order (quadratic) model for the response variable without needing to use a complete three-level factorial experiment.
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The design consists of three distinct sets of experimental runs:
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* A factorial (perhaps fractional) design in the factors studied, each having two levels;
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* A set of center points, experimental runs whose values of each factor are the medians of the values used in the factorial portion. This point is often replicated in order to improve the precision of the experiment;
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* A set of axial points, experimental runs identical to the centre points except for one factor, which will take on values both below and above the median of the two factorial levels, and typically both outside their range. All factors are varied in this way.
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In statistics, a central composite design is an experimental design, useful in response surface methodology, for building a second order (quadratic) model for the response variable without needing to use a complete three-level factorial experiment.
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The design consists of three distinct sets of experimental runs:
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* A factorial (perhaps fractional) design in the factors studied, each having two levels;
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* A set of center points, experimental runs whose values of each factor are the medians of the values used in the factorial portion. This point is often replicated in order to improve the precision of the experiment;
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* A set of axial points, experimental runs identical to the centre points except for one factor, which will take on values both below and above the median of the two factorial levels, and typically both outside their range. All factors are varied in this way.
Latin hypercube sampling (LHS) is a form of stratified sampling that can be applied to multiple variables. The method commonly used to reduce the number or runs necessary for a Monte Carlo simulation to achieve a reasonably accurate random distribution. LHS can be incorporated into an existing Monte Carlo model fairly easily, and work with variables following any analytical probability distribution.
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Latin hypercube sampling (LHS) is a form of stratified sampling that can be applied to multiple variables. The method commonly used to reduce the number or runs necessary for a Monte Carlo simulation to achieve a reasonably accurate random distribution. LHS can be incorporated into an existing Monte Carlo model fairly easily, and work with variables following any analytical probability distribution.
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