Bias error. The total error - the difference between the exact and computed response - is composed of a random and a bias component. The bias component is a systematic deviation between the chosen model (approximation type) and the exact response of the structure (FEA analysis is usually considered to be the exact response). Also known as the modeling error. (See also random error).

Center Point. Point at the center value of all factor ranges.

Design of Experiments. See experimental design.

Design matrix. A matrix description of an experiment that is useful for constructing and analyzing experiments.

Design parameter. See design variable.

Design space. A region in the -dimensional space of the design variables ( through ) to which the design is limited. The design space is specified by upper and lower bounds on the design variables. Response variables can also be used to bound the design space.

Design variable. An independent design parameter which is allowed to vary in order to change the design. Symbolized by or (vector containing several design variables).

DOE. Design of Experiments. See experimental design.

D-optimal. The state of an experimental design in which the determinant of the moment matrix of the least squares formulation is maximized.

Effect. How changing the settings of a factor/design variable changes the response. The effect of a single factor is also called a main effect.

Experimental Design. The selection of designs to enable the construction of a design response surface. Sometimes referred to as the Point Selection Scheme.

Factors. Process inputs an investigator manipulates to cause a change in the output. Some factors cannot be controlled by the experimenter but may affect the responses. If their effect is significant, these uncontrolled factors should be measured and used in the data analysis.

Interaction. Occurs when the effect of one factor on a response depends on the level of another factor(s).

Iteration. A cycle involving an experimental design, function evaluations of the designs, approximation and optimization of the approximate problem.

Latin Hypercube Sampling. The use of a constrained random experimental design as a point selection scheme for response approximation.

Least Squares Approximation. The determination of the coefficients in a mathematical expression so that it approximates certain experimental results by the minimization of the sum of the squares of the approximation errors. Used to determine response surfaces as well as calibrating analysis models.

Model. Mathematical relationship which relates changes in a given response to changes in one or more factors.

Noise. See random error.

Point selection scheme. Same as experimental design.

Process. A series of analysis stages (or steps) designed to produce a result. Multistage process. Example: metal forming analysis which consists of several stages, e.g. gravity loading, stamping, springback, trimming, etc.

Random error. The total error - the difference between the exact and computed response - is composed of a random and a bias component. The random component is, as the name implies, a random deviation from the nominal value of the exact response, often assumed to be normally distributed around the nominal value. (See also bias error).

Response. A numerical indicator of the performance of the design.

Saturated design. An experimental design in which the number of points equals the number of unknown coefficients of the approximation. For a saturated design no test can be made for the lack of fit.

Sampling. In general, Sampling is synonymous with Point Selection or Experimental Design.

Scale factor. A factor which is specified as a divisor of a response in order to normalize the response.

Stochastic. Involving or containing random variables. Involving probability or chance.