Engineering Statistics
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Engineering Statistics
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: # Design of Experiments (DOE) is a methodology for formulating scientific and engineering problems using statistical models. The protocol specifies a randomization procedure for the experiment and specifies the primary data-analysis, particularly in hypothesis testing. In a secondary analysis, the statistical analyst further examines the data to suggest other questions and to help plan future experiments. In engineering applications, the goal is often to optimize a process or product, rather than to subject a scientific hypothesis to t ...
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Engineering
Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, systems. Modern engineering comprises many subfields which include designing and improving infrastructure, machinery, vehicles, electronics, Materials engineering, materials, and energy systems. The Academic discipline, discipline of engineering encompasses a broad range of more Academic specialization, specialized fields of engineering, each with a more specific emphasis for applications of applied mathematics, mathematics and applied science, science. See glossary of engineering. The word '':wikt:engineering, engineering'' is derived from the Latin . Definition The American Engineers' Council for Professional Development (the predecessor of the Accreditation Board for Engineering and Technology aka ABET) has defined "engineering" as: ...
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Statistical Method
Statistics (from German: ', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the sy ...
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Interaction (statistics)
In statistics, an interaction may arise when considering the relationship among three or more Variable (statistics), variables, and describes a situation in which the effect of one causal variable on an outcome depends on the state of a second causal variable (that is, when effects of the two causes are not additive map, additive). Although commonly thought of in terms of Causality, causal relationships, the concept of an interaction can also describe non-causal associations (then also called Moderation (statistics), ''moderation'' or ''effect modification''). Interactions are often considered in the context of regression analysis, regression analyses or factorial experiments. The presence of interactions can have important implications for the interpretation of statistical models. If two variables of interest interact, the relationship between each of the interacting variables and a third "dependent variable" depends on the value of the other interacting variable. In practice, th ...
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Main Effect
In the design of experiments and analysis of variance, a main effect is the effect of an independent variable on a dependent variable averaged across the levels of any other independent variables. The term is frequently used in the context of factorial designs and regression models Regression or regressions may refer to: Arts and entertainment * ''Regression'' (film), a 2015 horror film by Alejandro Amenábar, starring Ethan Hawke and Emma Watson * ''Regression'' (magazine), an Australian punk rock fanzine (1982–1984) * ... to distinguish main effects from interaction effects. Relative to a factorial design, under an analysis of variance, a main effect test will test the hypotheses expected such as H0, the null hypothesis. Running a hypothesis for a main effect will test whether there is evidence of an effect of different treatments. However, a main effect test is nonspecific and will not allow for a localization of specific mean pairwise comparisons (simple effects). A mai ...
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Harvard Mark I
The Harvard Mark I, or IBM Automatic Sequence Controlled Calculator (ASCC), was one of the earliest general-purpose electromechanical computers used in the war effort during the last part of World War II. One of the first programs to run on the Mark I was initiated on 29 March 1944 by John von Neumann. At that time, von Neumann was working on the Manhattan Project, and needed to determine whether implosion was a viable choice to detonate the atomic bomb that would be used a year later. The Mark I also computed and printed mathematical tables, which had been the initial goal of British inventor Charles Babbage for his analytical engine in 1837. According to Edmund Berkeley, the operators of the Mark I often called the machine "Bessy, the Bessel engine", after Bessel functions. The Mark I was disassembled in 1959; part of it was given to IBM, part went to the Smithsonian Institution, and part entered the Harvard Collection of Historical Scientific Instruments. For decades, H ...
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Harvard University
Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyman John Harvard (clergyman), John Harvard, it is the oldest institution of higher learning in the United States. Its influence, wealth, and rankings have made it one of the most prestigious universities in the world. Harvard was founded and authorized by the Massachusetts General Court, the governing legislature of Colonial history of the United States, colonial-era Massachusetts Bay Colony. While never formally affiliated with any Religious denomination, denomination, Harvard trained Congregationalism in the United States, Congregational clergy until its curriculum and student body were gradually secularized in the 18th century. By the 19th century, Harvard emerged as the most prominent academic and cultural institution among the Boston B ...
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Charles Babbage
Charles Babbage (; 26 December 1791 – 18 October 1871) was an English polymath. A mathematician, philosopher, inventor and mechanical engineer, Babbage originated the concept of a digital programmable computer. Babbage is considered by some to be "List of pioneers in computer science, father of the computer". He is credited with inventing the first mechanical computer, the difference engine, that eventually led to more complex electronic designs, though all the essential ideas of modern computers are to be found in his analytical engine, programmed using a principle openly borrowed from the Jacquard loom. As part of his computer work, he also designed the first Printer (computing), computer printers. He had a broad range of interests in addition to his work on computers covered in his 1832 book ''Economy of Manufactures and Machinery''. He was an important figure in the social scene in London, and is credited with importing the "scientific soirée" from France with hi ...
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Slide Rule
A slide rule is a hand-operated mechanical calculator consisting of slidable rulers for conducting mathematical operations such as multiplication, division, exponents, roots, logarithms, and trigonometry. It is one of the simplest analog computers. Slide rules exist in a diverse range of styles and generally appear in a linear, circular or cylindrical form. Slide rules manufactured for specialized fields such as aviation or finance typically feature additional scales that aid in specialized calculations particular to those fields. The slide rule is closely related to nomograms used for application-specific computations. Though similar in name and appearance to a standard ruler, the slide rule is not meant to be used for measuring length or drawing straight lines. Maximum accuracy for standard linear slide rules is about three decimal significant digits, while scientific notation is used to keep track of the order of magnitude of results. English mathematician and clergy ...
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Abacus
An abacus ( abaci or abacuses), also called a counting frame, is a hand-operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoption of the Hindu–Arabic numeral system. An abacus consists of a two-dimensional array of Sliding (motion), slidable beads (or similar objects). In their earliest designs, the beads could be loose on a flat surface or sliding in grooves. Later the beads were made to slide on rods and built into a frame, allowing faster manipulation. Each rod typically represents one Numerical digit, digit of a multi-digit number laid out using a positional numeral system such as base ten (though some cultures used different numerical bases). Roman Empire, Roman and East Asian abacuses use a system resembling bi-quinary coded decimal, with a top deck (containing one or two beads) representing fives and a bottom deck (containing four or five beads) representing ones. Natural numbers are normally use ...
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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 ...
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Dynamical System
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, fluid dynamics, the flow of water in a pipe, the Brownian motion, random motion of particles in the air, and population dynamics, the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real number, real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a Set (mathematics), set, without the need of a Differentiability, smooth space-time structure defined on it. At any given time, ...
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