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Response Surface Methods
In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. RSM is an empirical model which employs the use of mathematical and statistical techniques to relate input variables, otherwise known as factors, to the response. RSM became very useful because other methods available, such as the theoretical model, could be very cumbersome to use, time-consuming, inefficient, error-prone, and unreliable. 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. Statistical approaches such as RSM can be employed to maximize the production of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Response Surface Metodology
Response may refer to: *Call and response (music), musical structure *Reaction (other) *Request–response **Output (computing), Output or response, the result of telecommunications input *Response (liturgy), a line answering a versicle *Response (music) or antiphon, a response to a psalm or other part of a religious service *Response, a phase in emergency management *Response rate (survey) Proper names and titles *''Response'', a print and online magazine of Christian thought published by Seattle Pacific University *Response (album), ''Response'' (album), a studio album by Phil Wickham *Response (company), a call centre company based in Scotland *The Response (film), ''The Response'' (film) *The National War Memorial (Canada), titled ''The Response'' *The Northumberland Fusiliers Memorial in Newcastle upon Tyne, titled "The Response" See also *Action (other) *Answer (other) *Reply (other) *Response variable, or the realization thereof *Res ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimal Design
In the design of experiments, optimal experimental designs (or optimum 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 the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum variance. A non-optimal design requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design. In practical terms, optimal experiments can reduce the costs of experimentation. The optimality of a design depends on the statistical model and is assessed with respect to a statistical criterion, which is related to the variance-matrix of the estimator. Specifying an appropriate model and specifying a suitable criterion function both require understanding of statistical theory and practical knowledge with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Industrial Engineering
Industrial engineering (IE) is concerned with the design, improvement and installation of integrated systems of people, materials, information, equipment and energy. It draws upon specialized knowledge and skill in the mathematical, physical, and social sciences together with the principles and methods of engineering analysis and design, to specify, predict, and evaluate the results to be obtained from such systems. Industrial engineering is a branch of engineering that focuses on optimizing complex processes, systems, and organizations by improving efficiency, productivity, and quality. It combines principles from engineering, mathematics, and business to design, analyze, and manage systems that involve people, materials, information, equipment, and energy. Industrial engineers aim to reduce waste, streamline operations, and enhance overall performance across various industries, including manufacturing, healthcare, logistics, and service sectors. Industrial engineers are employe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. Optimization problems Opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Design Of Experiments
The design of experiments (DOE), also known as experiment design or experimental design, 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. In its simplest form, an experiment aims at predicting the outcome by introducing a change of the preconditions, which is represented by one or more independent variables, also referred to as "input variables" or "predictor variables." The change in one or more independent variables is generally hypothesized to result in a change in one or more dependent variables, also referred to as "output variables" or "response variables." The experimental design may also identify ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequential Experiments
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called the ''length'' of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an ''arbitrary'' index set. For example, (M, A, R, Y) is a sequence of letters with the letter "M" first and "Y" last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be ''finite'', as in these examples, or '' inf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephen M
Stephen or Steven is an English given name, first name. It is particularly significant to Christianity, Christians, as it belonged to Saint Stephen ( ), an early disciple and deacon who, according to the Book of Acts, was stoned to death; he is widely regarded as the first martyr (or "protomartyr") of the Christian Church. The name, in both the forms Stephen and Steven, is often shortened to Steve or Stevie (given name), Stevie. In English, the female version of the name is Stephanie. Many surnames are derived from the first name, including Template:Stephen-surname, Stephens, Stevens, Stephenson, and Stevenson, all of which mean "Stephen's (son)". In modern times the name has sometimes been given with intentionally non-standard spelling, such as Stevan or Stevon. A common variant of the name used in English is Stephan (given name), Stephan ( ); related names that have found some currency or significance in English include Stefan (given name), Stefan (pronounced or in English) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Society For Industrial And Applied Mathematics
Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific society devoted to applied mathematics, and roughly two-thirds of its membership resides within the United States. Founded in 1951, the organization began holding annual national meetings in 1954, and now hosts conferences, publishes books and scholarly journals, and engages in advocacy in issues of interest to its membership. Members include engineers, scientists, and mathematicians, both those employed in academia and those working in industry. The society supports educational institutions promoting applied mathematics. SIAM is one of the four member organizations of the Joint Policy Board for Mathematics. Membership Membership is open to both individuals and organizations. By the end of its first full year of operation, SIAM had 130 me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Optimization
Bayesian optimization is a sequential design strategy for global optimization of black-box functions, that does not assume any functional forms. It is usually employed to optimize expensive-to-evaluate functions. With the rise of artificial intelligence innovation in the 21st century, Bayesian optimizations have found prominent use in machine learning problems for optimizing hyperparameter values. History The term is generally attributed to and is coined in his work from a series of publications on global optimization in the 1970s and 1980s. Early mathematics foundations From 1960s to 1980s The earliest idea of Bayesian optimization sprang in 1964, from a paper by American applied mathematician Harold J. Kushner“A New Method of Locating the Maximum Point of an Arbitrary Multipeak Curve in the Presence of Noise” Although not directly proposing Bayesian optimization, in this paper, he first proposed a new method of locating the maximum point of an arbitrary multipeak curv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surrogate Model
A surrogate model is an engineering method used when an outcome of interest cannot be easily measured or computed, so an approximate mathematical model of the outcome is used instead. Most engineering design problems require experiments and/or simulations to evaluate design objective and constraint functions as a function of design variables. For example, in order to find the optimal airfoil shape for an aircraft wing, an engineer simulates the airflow around the wing for different shape variables (e.g., length, curvature, material, etc.). For many real-world problems, however, a single simulation can take many minutes, hours, or even days to complete. As a result, routine tasks such as design optimization, design space exploration, sensitivity analysis and "what-if" analysis become impossible since they require thousands or even millions of simulation evaluations. One way of alleviating this burden is by constructing approximation models, known as surrogate models, ''metamodels' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic Design
Probabilistic design is a discipline within engineering design. It deals primarily with the consideration and minimization of the effects of random variability upon the performance of an engineering system during the design phase. Typically, these effects studied and optimized are related to quality and reliability. It differs from the classical approach to design by assuming a small probability of failure instead of using the safety factor. Probabilistic design is used in a variety of different applications to assess the likelihood of failure. Disciplines which extensively use probabilistic design principles include product design, quality control, systems engineering, machine design, civil engineering (particularly useful in limit state design) and manufacturing. Objective and motivations When using a probabilistic approach to design, the designer no longer thinks of each variable as a single value or number. Instead, each variable is viewed as a continuous random variable wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
