|
Factorial Design
In statistics, a factorial experiment (also known as full factorial experiment) investigates how multiple factors influence a specific outcome, called the response variable. Each factor is tested at distinct values, or levels, and the Experimental unit, experiment includes every possible combination of these levels across all factors. This comprehensive approach lets researchers see not only how each factor individually affects the response, but also how the factors interaction (statistics), interact and influence each other. Often, factorial experiments simplify things by using just two levels for each factor. A 2x2 factorial design, for instance, has two factors, each with two levels, leading to four unique combinations to test. The interaction between these factors is often the most crucial finding, even when the individual factors also have an effect. If a full factorial design becomes too complex due to the sheer number of combinations, researchers can use a fractional fact ... [...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] |
One-factor-at-a-time Method
The one-factor-at-a-time method, also known as one-variable-at-a-time, OFAT, OF@T, OFaaT, OVAT, OV@T, OVaaT, or monothetic analysis is a method of designing experiments involving the testing of factors, or causes, one at a time instead of multiple factors simultaneously. Advantages OFAT is favored by non-experts, especially in situations where the data is cheap and abundant. There exist cases where the mental effort required to conduct a complex multi-factor analysis exceeds the effort required to acquire extra data, in which case OFAT might make sense. Furthermore, some researchers have shown that OFAT can be more effective than fractional factorials under certain conditions (number of runs is limited, primary goal is to attain improvements in the system, and experimental error is not large compared to factor effects, which must be additive and independent of each other).Friedman, M., and Savage, L. J. (1947), “Planning Experiments Seeking Maxima,” in Techniques of Statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Value
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first Moment (mathematics), moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean, mean of the possible values a random variable can take, weighted by the probability of those outcomes. Since it is obtained through arithmetic, the expected value sometimes may not even be included in the sample data set; it is not the value you would expect to get in reality. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by Integral, integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field (mathematics), field that contains a finite number of Element (mathematics), elements. As with any field, a finite field is a Set (mathematics), set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are the integers mod n, integers mod p when p is a prime number. The ''order'' of a finite field is its number of elements, which is either a prime number or a prime power. For every prime number p and every positive integer k there are fields of order p^k. All finite fields of a given order are isomorphism, isomorphic. Finite fields are fundamental in a number of areas of mathematics and computer science, including number theory, algebraic geometry, Galois theory, finite geometry, cryptography and coding theory. Properties A finite field is a finite set that is a fiel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Arithmetic
In mathematics, modular arithmetic is a system of arithmetic operations for integers, other than the usual ones from elementary arithmetic, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book '' Disquisitiones Arithmeticae'', published in 1801. A familiar example of modular arithmetic is the hour hand on a 12-hour clock. If the hour hand points to 7 now, then 8 hours later it will point to 3. Ordinary addition would result in , but 15 reads as 3 on the clock face. This is because the hour hand makes one rotation every 12 hours and the hour number starts over when the hour hand passes 12. We say that 15 is ''congruent'' to 3 modulo 12, written 15 ≡ 3 (mod 12), so that 7 + 8 ≡ 3 (mod 12). Similarly, if one starts at 12 and waits 8 hours, the hour hand will be at 8. If one instead waited twice as long, 16 hours, the hour hand would be on 4. This ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2x2x2-ex
X, or x, is the twenty-fourth letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''ex'' (pronounced ), plural ''exes''."X", ''Oxford English Dictionary'', 2nd edition (1989); ''Merriam-Webster's Third New International Dictionary of the English Language, Unabridged'' (1993); "ex", ''op. cit''. History The letter , representing , was inherited from the Etruscan alphabet. It perhaps originated in the of the Euboean alphabet or another Western Greek alphabet, which also represented . Its relationship with the of the Eastern Greek alphabets, which represented , is uncertain. The pronunciation of in the Romance languages underwent sound changes, with various outcomes: * French: (e.g. ''laisser'' from ''laxare'') * Italian: (e.g. ''asse'' from ''axem'') and, in some cases, (e.g. ''lasciare'' from ''laxare'') * Portuguese: (e.g. ''eixo'' from ''axem'') * Rom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tuple
In mathematics, a tuple is a finite sequence or ''ordered list'' of numbers or, more generally, mathematical objects, which are called the ''elements'' of the tuple. An -tuple is a tuple of elements, where is a non-negative integer. There is only one 0-tuple, called the ''empty tuple''. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term ''"infinite tuple"'' is occasionally used for ''"infinite sequences"''. Tuples are usually written by listing the elements within parentheses "" and separated by commas; for example, denotes a 5-tuple. Other types of brackets are sometimes used, although they may have a different meaning. An -tuple can be formally defined as the image of a function that has the set of the first natural numbers as its domain. Tuples may be also defined from ordered pairs by a recurrence starting from an ordered pair; indeed, an -tuple can be identified with the ordered pair of its first elements and its t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorial Design
In statistics, a factorial experiment (also known as full factorial experiment) investigates how multiple factors influence a specific outcome, called the response variable. Each factor is tested at distinct values, or levels, and the experiment includes every possible combination of these levels across all factors. This comprehensive approach lets researchers see not only how each factor individually affects the response, but also how the factors interact and influence each other. Often, factorial experiments simplify things by using just two levels for each factor. A 2x2 factorial design, for instance, has two factors, each with two levels, leading to four unique combinations to test. The interaction between these factors is often the most crucial finding, even when the individual factors also have an effect. If a full factorial design becomes too complex due to the sheer number of combinations, researchers can use a fractional factorial design. This method strategically omit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cube Plot For Bearing Life
A cube or regular hexahedron is a three-dimensional solid object in geometry, which is bounded by six congruent square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It is a type of parallelepiped, with pairs of parallel opposite faces, and more specifically a rhombohedron, with congruent edges, and a rectangular cuboid, with right angles between pairs of intersecting faces and pairs of intersecting edges. It is an example of many classes of polyhedra: Platonic solid, regular polyhedron, parallelohedron, zonohedron, and plesiohedron. The dual polyhedron of a cube is the regular octahedron. The cube can be represented in many ways, one of which is the graph known as the cubical graph. It can be constructed by using the Cartesian product of graphs. The cube is the three-dimensional hypercube, a family of polytopes also including the two-dimensional square and four-dimensional tesseract. A cube with unit side length is the canonical unit of volume in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bearing (mechanical)
A ball bearing A bearing is a machine element that constrains relative motion to only the desired motion and reduces friction between moving parts. The design of the bearing may, for example, provide for free linear movement of the moving part or for free rotation around a fixed axis; or, it may prevent a motion by controlling the vectors of normal forces that bear on the moving parts. Most bearings facilitate the desired motion by minimizing friction. Bearings are classified broadly according to the type of operation, the motions allowed, or the directions of the loads (forces) applied to the parts. The term "bearing" is derived from the verb " to bear"; a bearing being a machine element that allows one part to bear (i.e., to support) another. The simplest bearings are bearing surfaces, cut or formed into a part, with varying degrees of control over the form, size, roughness, and location of the surface. Other bearings are separate devices installed into a machine or mach ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George E
George may refer to: Names * George (given name) * George (surname) People * George (singer), American-Canadian singer George Nozuka, known by the mononym George * George Papagheorghe, also known as Jorge / GEØRGE * George, stage name of Giorgio Moroder * George, son of Andrew I of Hungary Places South Africa * George, South Africa, a city ** George Airport United States * George, Iowa, a city * George, Missouri, a ghost town * George, Washington, a city * George County, Mississippi * George Air Force Base, a former U.S. Air Force base located in California Computing * George (algebraic compiler) also known as 'Laning and Zierler system', an algebraic compiler by Laning and Zierler in 1952 * GEORGE (computer), early computer built by Argonne National Laboratory in 1957 * GEORGE (operating system), a range of operating systems (George 1–4) for the ICT 1900 range of computers in the 1960s * GEORGE (programming language), an autocode system invented by Charles Le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasi-Monte Carlo Method
In numerical analysis, the quasi-Monte Carlo method is a method for numerical integration and solving some other problems using low-discrepancy sequences (also called quasi-random sequences or sub-random sequences) to achieve variance reduction. This is in contrast to the regular Monte Carlo method or Monte Carlo integration, which are based on sequences of pseudorandom numbers. Monte Carlo and quasi-Monte Carlo methods are stated in a similar way. The problem is to approximate the integral of a function ''f'' as the average of the function evaluated at a set of points ''x''1, ..., ''x''''N'': : \int_ f(u)\,u \approx \frac\,\sum_^N f(x_i). Since we are integrating over the ''s''-dimensional unit cube, each ''x''''i'' is a vector of ''s'' elements. The difference between quasi-Monte Carlo and Monte Carlo is the way the ''x''''i'' are chosen. Quasi-Monte Carlo uses a low-discrepancy sequence such as the Halton sequence, the Sobol sequence, or the Faure sequence, whereas Mont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
