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Software that is used for designing factorial experiments plays an important role in scientific experiments and represents a route to the implementation of design of experiments procedures that derive from statistical and combinatorial theory. In principle, easy-to-use design of experiments (DOE) software should be available to all experimenters to foster use of DOE.
Factorial experimental design software drastically simplifies previously laborious hand calculations needed before the use of computers.
During World War II, a more sophisticated form of DOE, called factorial design, became a big weapon for speeding up industrial development for the Allied forces. These designs can be quite compact, involving as few as two levels of each factor and only a fraction of all the combinations, and yet they are quite powerful for screening purposes. After the war, a statistician at Imperial Chemical, George Box, described how to generate response surfaces for process optimization. [1] From this point forward, DOE took hold in the chemical process industry, where factors such as time, temperature, pressure, concentration, flow rate and agitation are easily manipulated.
DOE results, when discovered accurately with DOE software, strengthen the capability to discern truths about sample populations being tested: see Sampling (statistics). Statisticians [2] [3] describe stronger multifactorial DOE methods as being more “robust”: see Experimental design.
As DOE software advancements gave rise to solving complex factorial statistical equations, statisticians began in earnest to design experiments with more than one factor (multifactor) being tested at a time. Simply stated, computerized multifactor DOE began supplanting one-factor-at-a-time experiments. Computer software designed specifically for designed experiments became available from various leading software companies in the 1980s and included packages such as JMP, Minitab, Cornerstone and Design–Expert.
Notable benefits when using DOE software include avoiding laborious hand calculations when:
Today, factorial DOE software is a notable tool that engineers, scientists, geneticists, biologists, and virtually all other experimenters and creators, ranging from agriculturists to zoologists, rely upon. DOE software is most applicable to controlled, multifactor experiments in which the experimenter is interested in the effect of some process or intervention on objects such as crops, jet engines, demographics, marketing techniques, materials, adhesives, and so on. Design of experiments software is therefore a valuable tool with broad applications for all natural, engineering, and social sciences.
Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means. In other words, the ANOVA is used to test the difference between two or more means.
The design of experiments is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in which natural conditions that influence the variation are selected for observation.
Engineering statistics combines engineering and statistics using scientific methods for analyzing data. Engineering statistics involves data concerning manufacturing processes such as: component dimensions, tolerances, type of material, and fabrication process control. There are many methods used in engineering analysis and they are often displayed as histograms to give a visual of the data as opposed to being just numerical. Examples of methods are:
Taguchi methods are statistical methods, sometimes called robust design methods, developed by Genichi Taguchi to improve the quality of manufactured goods, and more recently also applied to engineering, biotechnology, marketing and advertising. Professional statisticians have welcomed the goals and improvements brought about by Taguchi methods, particularly by Taguchi's development of designs for studying variation, but have criticized the inefficiency of some of Taguchi's proposals.
Design for Six Sigma (DFSS) is an Engineering design process, business process management method related to traditional Six Sigma. It is used in many industries, like finance, marketing, basic engineering, process industries, waste management, and electronics. It is based on the use of statistical tools like linear regression and enables empirical research similar to that performed in other fields, such as social science. While the tools and order used in Six Sigma require a process to be in place and functioning, DFSS has the objective of determining the needs of customers and the business, and driving those needs into the product solution so created. It is used for product or process design in contrast with process improvement. Measurement is the most important part of most Six Sigma or DFSS tools, but whereas in Six Sigma measurements are made from an existing process, DFSS focuses on gaining a deep insight into customer needs and using these to inform every design decision and trade-off.
In the design of experiments, optimal designs are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statistics has been credited to Danish statistician Kirstine Smith.
In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors. A full factorial design may also be called a fully crossed design. Such an experiment allows the investigator to study the effect of each factor on the response variable, as well as the effects of interactions between factors on the response variable.
Data farming is the process of using designed computational experiments to “grow” data, which can then be analyzed using statistical and visualization techniques to obtain insight into complex systems. These methods can be applied to any computational model.
In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. The method was introduced by George E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an optimal response. Box and Wilson suggest using a second-degree polynomial model to do this. They acknowledge that this model is only an approximation, but they use it because such a model is easy to estimate and apply, even when little is known about the process.
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.
In statistics, fractional factorial designs are experimental designs consisting of a carefully chosen subset (fraction) of the experimental runs of a full factorial design. The subset is chosen so as to exploit the sparsity-of-effects principle to expose information about the most important features of the problem studied, while using a fraction of the effort of a full factorial design in terms of experimental runs and resources. In other words, it makes use of the fact that many experiments in full factorial design are often redundant, giving little or no new information about the system.
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:
A glossary of terms used in experimental research.
Stat-Ease, Inc. is a privately held company producing statistical software in Minneapolis, Minnesota founded by Pat Whitcomb in 1982. The company currently has 14 employees. The company provides software packages for engineers and scientists using design of experiments methods (DOE) for optimizing development of products and processes. It also provides DOE training and consulting services.
Red Cedar Technology is a software development and engineering services company. Red Cedar Technology was founded by Michigan State University professors Ron Averill and Erik Goodman in 1999. The headquarters is located in East Lansing, Michigan, near MSU's campus. Red Cedar Technology develops and distributes the HEEDS Professional suite of design optimization software. HEEDS is based on spin-out technology from Michigan State University. On June 30, 2013 Red Cedar Technology was acquired by CD-adapco. CD-adapco was acquired in 2016 by Siemens Digital Industries Software.
Optimus is a Process Integration and Design Optimization (PIDO) platform developed by Noesis Solutions. Noesis Solutions takes part in key research projects, such as PHAROS and MATRIX.
A robust parameter design, introduced by Genichi Taguchi, is an experimental design used to exploit the interaction between control and uncontrollable noise variables by robustification—finding the settings of the control factors that minimize response variation from uncontrollable factors. Control variables are variables of which the experimenter has full control. Noise variables lie on the other side of the spectrum. While these variables may be easily controlled in an experimental setting, outside of the experimental world they are very hard, if not impossible, to control. Robust parameter designs use a naming convention similar to that of FFDs. A 2(m1+m2)-(p1-p2) is a 2-level design where m1 is the number of control factors, m2 is the number of noise factors, p1 is the level of fractionation for control factors, and p2 is the level of fractionation for noise factors.
Design–Expert is a statistical software package from Stat-Ease Inc. that is specifically dedicated to performing design of experiments (DOE). Design–Expert offers comparative tests, screening, characterization, optimization, robust parameter design, mixture designs and combined designs. Design–Expert provides test matrices for screening up to 50 factors. Statistical significance of these factors is established with analysis of variance (ANOVA). Graphical tools help identify the impact of each factor on the desired outcomes and reveal abnormalities in the data.
Design Space Exploration (DSE) refers to systematic analysis and pruning of unwanted design points based on parameters of interest. While the term DSE can apply to any kind of system, we refer to electronic and embedded system design in this article.
pSeven is a DSE software platform developed by DATADVANCE, extending design, simulation and analysis capabilities and assisting in faster design decisions. It provides integration with third party CAD and CAE software tools, multi-objective and robust optimization algorithms, data analysis, and uncertainty quantification tools.