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Robustify
Robustification is a form of optimisation whereby a system is made less sensitive to the effects of random variability, or noise, that is present in that system's input variables and parameters. The process is typically associated with engineering systems, but the process can also be applied to a political policy, a business strategy or any other system that is subject to the effects of random variability. Clarification on definition Robustification as it is defined here is sometimes referred to as parameter design or robust parameter design (RPD) and is often associated with Taguchi methods. Within that context, robustification can include the process of finding the inputs that contribute most to the random variability in the output and controlling them, or tolerance design. At times the terms design for quality or Design for Six Sigma (DFFS) might also be used as synonyms Principles Robustification works by taking advantage of two different principles. Non-linearities Consid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimisation
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts 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 maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robustification
Robustification is a form of optimisation whereby a system is made less sensitive to the effects of random variability, or noise, that is present in that system's input variables and parameters. The process is typically associated with engineering systems, but the process can also be applied to a political policy, a business strategy or any other system that is subject to the effects of random variability. Clarification on definition Robustification as it is defined here is sometimes referred to as parameter design or robust parameter design (RPD) and is often associated with Taguchi methods. Within that context, robustification can include the process of finding the inputs that contribute most to the random variability in the output and controlling them, or tolerance design. At times the terms design for quality or Design for Six Sigma (DFFS) might also be used as synonyms Principles Robustification works by taking advantage of two different principles. Non-linearities Consi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sensitivity Analysis
Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty; ideally, uncertainty and sensitivity analysis should be run in tandem. The process of recalculating outcomes under alternative assumptions to determine the impact of a variable under sensitivity analysis can be useful for a range of purposes, including: * Testing the robustness of the results of a model or system in the presence of uncertainty. * Increased understanding of the relationships between input and output variables in a system or model. * Uncertainty reduction, through the identification of model input that cause significant uncertainty in the output and should therefore be the focus of attention in order to increase robustness (perhap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution. In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases). Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of ris ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propagation Of Error
In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have uncertainties due to measurement limitations (e.g., instrument precision) which propagate due to the combination of variables in the function. The uncertainty ''u'' can be expressed in a number of ways. It may be defined by the absolute error . Uncertainties can also be defined by the relative error , which is usually written as a percentage. Most commonly, the uncertainty on a quantity is quantified in terms of the standard deviation, , which is the positive square root of the variance. The value of a quantity and its error are then expressed as an interval . If the statistical probability distribution of the variable is known or can be assumed, it is possible to derive confidence limits to describe t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Western World
The Western world, also known as the West, primarily refers to the various nations and state (polity), states in the regions of Europe, North America, and Oceania.Western Civilization Our Tradition; James Kurth; accessed 30 August 2011 The Western world is also known as the Occident (from the Latin word ''occidēns'' "setting down, sunset, west") in contrast to the Eastern world known as the Orient (from the Latin word ''oriēns'' "origin, sunrise, east"). Following the Discovery of America in 1492, the West came to be known as the "world of business" and trade; and might also mean the Northern half of the North–South divide, the countries of the ''Global North'' (often equated with capitalist Developed country, developed countries). [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Japan
Japan ( ja, 日本, or , and formally , ''Nihonkoku'') is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by the Sea of Japan, while extending from the Sea of Okhotsk in the north toward the East China Sea, Philippine Sea, and Taiwan in the south. Japan is a part of the Ring of Fire, and spans Japanese archipelago, an archipelago of List of islands of Japan, 6852 islands covering ; the five main islands are Hokkaido, Honshu (the "mainland"), Shikoku, Kyushu, and Okinawa Island, Okinawa. Tokyo is the Capital of Japan, nation's capital and largest city, followed by Yokohama, Osaka, Nagoya, Sapporo, Fukuoka, Kobe, and Kyoto. Japan is the List of countries and dependencies by population, eleventh most populous country in the world, as well as one of the List of countries and dependencies by population density, most densely populated and Urbanization by country, urbanized. About three-fourths of Geography of Japan, the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States
The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territories, nine Minor Outlying Islands, and 326 Indian reservations. The United States is also in free association with three Pacific Island sovereign states: the Federated States of Micronesia, the Marshall Islands, and the Republic of Palau. It is the world's third-largest country by both land and total area. It shares land borders with Canada to its north and with Mexico to its south and has maritime borders with the Bahamas, Cuba, Russia, and other nations. With a population of over 333 million, it is the most populous country in the Americas and the third most populous in the world. The national capital of the United States is Washington, D.C. and its most populous city and principal financial center is New York City. Paleo-Americ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genichi Taguchi
was an engineer and statistician. From the 1950s onwards, Taguchi developed a methodology for applying statistics to improve the quality of manufactured goods. Taguchi methods have been controversial among some conventional Western statisticians, but others have accepted many of the concepts introduced by him as valid extensions to the body of knowledge. Biography Taguchi was born and raised in the textile town of Tokamachi, in Niigata prefecture. He initially studied textile engineering at Kiryu Technical College with the intention of entering the family kimono business. However, with the escalation of World War II in 1942, he was drafted into the Astronomical Department of the Navigation Institute of the Imperial Japanese Navy. After the war, in 1948 he joined the Ministry of Public Health and Welfare, where he came under the influence of eminent statistician Matosaburo Masuyama, who kindled his interest in the design of experiments. He also worked at the Institute of Stati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Noise
In statistics, the fraction of variance unexplained (FVU) in the context of a regression task is the fraction of variance of the regressand (dependent variable) ''Y'' which cannot be explained, i.e., which is not correctly predicted, by the explanatory variables ''X''. Formal definition Suppose we are given a regression function f yielding for each y_i an estimate \widehat_i = f(x_i) where x_i is the vector of the ''i''th observations on all the explanatory variables. We define the fraction of variance unexplained (FVU) as: :\begin \text & = = = \left( = 1- , \text\right) \\ pt & = 1 - R^2 \end where ''R''2 is the coefficient of determination and ''VAR''err and ''VAR''tot are the variance of the residuals and the sample variance of the dependent variable. ''SS''''err'' (the sum of squared predictions errors, equivalently the residual sum of squares), ''SS''''tot'' (the total sum of squares), and ''SS''''reg'' (the sum of squares of the regression, equivalently the explai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Practitioner
Practitioner may refer to: *Health practitioner *Justice and public safety practitioner *Legal practitioner *Medical practitioner *Mental health professional or practitioner *Theatre practitioner Spiritual Practitioner *Solitary practitioner in Wicca and Paganism *Zen Zen ( zh, t=禪, p=Chán; ja, text= 禅, translit=zen; ko, text=선, translit=Seon; vi, text=Thiền) is a school of Mahayana Buddhism that originated in China during the Tang dynasty, known as the Chan School (''Chánzong'' 禪宗), and ... practitioner in Buddhism ;Other *'' The Practitioner'', a medical journal See also * {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph (discrete Mathematics)
In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a Set (mathematics), set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
