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Tolerance Interval
A tolerance interval is a statistical interval within which, with some confidence level, a specified proportion of a sampled population falls. "More specifically, a 100×p%/100×(1−α) tolerance interval provides limits within which at least a certain proportion (p) of the population falls with a given level of confidence (1−α)." "A (p, 1−α) tolerance interval (TI) based on a sample is constructed so that it would include at least a proportion p of the sampled population with confidence 1−α; such a TI is usually referred to as p-content − (1−α) coverage TI."Krishnamoorthy, K. and Lian, Xiaodong(2011) 'Closed-form approximate tolerance intervals for some general linear models and comparison studies', Journal of Statistical Computation and Simulation, First published on: 13 June 2011 "A (p, 1−α) upper tolerance limit (TL) is simply a 1−α upper confidence limit for the 100 p percentile of the population." A tolerance interval can be seen as a statistical vers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Interval
In statistics, interval estimation is the use of sample data to estimate an '' interval'' of plausible values of a parameter of interest. This is in contrast to point estimation, which gives a single value. The most prevalent forms of interval estimation are ''confidence intervals'' (a frequentist method) and ''credible intervals'' (a Bayesian method); less common forms include '' likelihood intervals'' and '' fiducial intervals''. Other forms of statistical intervals include ''tolerance intervals'' (covering a proportion of a sampled population) and '' prediction intervals'' (an estimate of a future observation, used mainly in regression analysis). Non-statistical methods that can lead to interval estimates include fuzzy logic. Discussion The scientific problems associated with interval estimation may be summarised as follows: :*When interval estimates are reported, they should have a commonly held interpretation in the scientific community and more widely. In this regard, cre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States Environmental Protection Agency
The Environmental Protection Agency (EPA) is an independent executive agency of the United States federal government tasked with environmental protection matters. President Richard Nixon proposed the establishment of EPA on July 9, 1970; it began operation on December 2, 1970, after Nixon signed an executive order. The order establishing the EPA was ratified by committee hearings in the House and Senate. The agency is led by its administrator, who is appointed by the president and approved by the Senate. The current administrator is Michael S. Regan. The EPA is not a Cabinet department, but the administrator is normally given cabinet rank. The EPA has its headquarters in Washington, D.C., regional offices for each of the agency's ten regions and 27 laboratories. The agency conducts environmental assessment, research, and education. It has the responsibility of maintaining and enforcing national standards under a variety of environmental laws, in consultation with state, tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Intervals
Statistics (from German: ''Statistik'', "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.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data 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 experi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Engineering Concepts
Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more specialized fields of engineering, each with a more specific emphasis on particular areas of applied mathematics, applied science, and types of application. See glossary of engineering. The term ''engineering'' is derived from the Latin ''ingenium'', meaning "cleverness" and ''ingeniare'', meaning "to contrive, devise". Definition The American Engineers' Council for Professional Development (ECPD, the predecessor of ABET) has defined "engineering" as: The creative application of scientific principles to design or develop structures, machines, apparatus, or manufacturing processes, or works utilizing them singly or in combination; or to construct or operate the same with full cognizance of their design; or to forecast their behavior under specific ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factor Of Safety
In engineering, a factor of safety (FoS), also known as (and used interchangeably with) safety factor (SF), expresses how much stronger a system is than it needs to be for an intended load. Safety factors are often calculated using detailed analysis because comprehensive testing is impractical on many projects, such as bridges and buildings, but the structure's ability to carry a load must be determined to a reasonable accuracy. Many systems are intentionally built much stronger than needed for normal usage to allow for emergency situations, unexpected loads, misuse, or degradation (reliability). Definition There are two definitions for the factor of safety (FoS): * The ratio of a structure's absolute strength (structural capability) to actual applied load; this is a measure of the reliability of a particular design. This is a calculated value, and is sometimes referred to, for the sake of clarity, as a ''realized factor of safety''. * A constant required value, imposed by law, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Engineering Tolerance
Engineering tolerance is the permissible limit or limits of variation in: # a physical dimension; # a measured value or physical property of a material, manufactured object, system, or service; # other measured values (such as temperature, humidity, etc.); # in engineering and safety, a physical distance or space (tolerance), as in a truck (lorry), train or boat under a bridge as well as a train in a tunnel (see structure gauge and loading gauge); # in mechanical engineering, the space between a bolt and a nut or a hole, etc. Dimensions, properties, or conditions may have some variation without significantly affecting functioning of systems, machines, structures, etc. A variation beyond the tolerance (for example, a temperature that is too hot or too cold) is said to be noncompliant, rejected, or exceeding the tolerance. Considerations when setting tolerances A primary concern is to determine how wide the tolerances may be without affecting other factors or the outcome of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noncentral Chi-squared Distribution
In probability theory and statistics, the noncentral chi-squared distribution (or noncentral chi-square distribution, noncentral \chi^2 distribution) is a noncentral generalization of the chi-squared distribution. It often arises in the power analysis of statistical tests in which the null distribution is (perhaps asymptotically) a chi-squared distribution; important examples of such tests are the likelihood-ratio tests. Definitions Background Let (X_1,X_2, \ldots, X_i, \ldots,X_k) be ''k'' independent, normally distributed random variables with means \mu_i and unit variances. Then the random variable : \sum_^k X_i^2 is distributed according to the noncentral chi-squared distribution. It has two parameters: k which specifies the number of degrees of freedom (i.e. the number of X_i), and \lambda which is related to the mean of the random variables X_i by: : \lambda=\sum_^k \mu_i^2. \lambda is sometimes called the noncentrality parameter. Note that some references def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noncentral T-distribution
The noncentral ''t''-distribution generalizes Student's ''t''-distribution using a noncentrality parameter. Whereas the central probability distribution describes how a test statistic ''t'' is distributed when the difference tested is null, the noncentral distribution describes how ''t'' is distributed when the null is false. This leads to its use in statistics, especially calculating statistical power. The noncentral ''t''-distribution is also known as the singly noncentral ''t''-distribution, and in addition to its primary use in statistical inference, is also used in robust modeling for data. Definitions If ''Z'' is a standard normal random variable, and ''V'' is a chi-squared distributed random variable with ν degrees of freedom that is independent of ''Z'', then :T=\frac is a noncentral ''t''-distributed random variable with ν degrees of freedom and noncentrality parameter μ ≠ 0. Note that the noncentrality parameter may be negative. Cumulative distribution fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Student's T-distribution
In probability and statistics, Student's ''t''-distribution (or simply the ''t''-distribution) is any member of a family of continuous probability distributions that arise when estimating the mean of a normally distributed population in situations where the sample size is small and the population's standard deviation is unknown. It was developed by English statistician William Sealy Gosset under the pseudonym "Student". The ''t''-distribution plays a role in a number of widely used statistical analyses, including Student's ''t''-test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis. Student's ''t''-distribution also arises in the Bayesian analysis of data from a normal family. If we take a sample of n observations from a normal distribution, then the ''t''-distribution with \nu=n-1 degrees of freedom can be de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lognormal Distribution
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable is log-normally distributed, then has a normal distribution. Equivalently, if has a normal distribution, then the exponential function of , , has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values. It is a convenient and useful model for measurements in exact and engineering sciences, as well as medicine, economics and other topics (e.g., energies, concentrations, lengths, prices of financial instruments, and other metrics). The distribution is occasionally referred to as the Galton distribution or Galton's distribution, after Francis Galton. The log-normal distribution has also been associated with other names, such as McAlister, Gibrat and Cobb–Douglas. A log-normal process is the statistical realization of the multi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fuel Economy In Automobiles
The fuel economy of an automobile relates distance traveled by a vehicle and the amount of fuel consumed. Consumption can be expressed in terms of volume of fuel to travel a distance, or the distance traveled per unit volume of fuel consumed. Since fuel consumption of vehicles is a significant factor in air pollution, and since importation of motor fuel can be a large part of a nation's foreign trade, many countries impose requirements for fuel economy. Different methods are used to approximate the actual performance of the vehicle. The energy in fuel is required to overcome various losses (wind resistance, tire drag, and others) encountered while propelling the vehicle, and in providing power to vehicle systems such as ignition or air conditioning. Various strategies can be employed to reduce losses at each of the conversions between the chemical energy in the fuel and the kinetic energy of the vehicle. Driver behavior can affect fuel economy; maneuvers such as sudden accelerat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sampling Error
In statistics, sampling errors are incurred when the statistical characteristics of a population are estimated from a subset, or sample, of that population. Since the sample does not include all members of the population, statistics of the sample (often known as estimators), such as means and quartiles, generally differ from the statistics of the entire population (known as parameters). The difference between the sample statistic and population parameter is considered the sampling error.Sarndal, Swenson, and Wretman (1992), Model Assisted Survey Sampling, Springer-Verlag, For example, if one measures the height of a thousand individuals from a population of one million, the average height of the thousand is typically not the same as the average height of all one million people in the country. Since sampling is almost always done to estimate population parameters that are unknown, by definition exact measurement of the sampling errors will not be possible; however they can often be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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