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Tolerance Interval
A tolerance interval (TI) is a statistical interval within which, with some confidence level, a specified sampling (statistics), sampled proportion of a population falls. "More specifically, a 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." Definition Assume observation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Interval
In statistics, interval estimation is the use of Sample (statistics), sample data to estimation, estimate an ''interval (mathematics), interval'' of possible values of a Statistical parameter, 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 frequentism, frequentist method) and ''credible intervals'' (a Bayesian method). Less common forms include ''likelihood intervals,'' ''fiducial intervals,'' ''tolerance intervals,'' and ''prediction intervals''. For a non-statistical method, interval estimates can be deduced from fuzzy logic. Types Confidence intervals Confidence intervals are used to estimate the parameter of interest from a sampled data set, commonly the mean or standard deviation. A confidence interval states there is a 100γ% confidence that the parameter of interest is within a lower and upper bound. A common misconception of confidence interva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sample Mean
The sample mean (sample average) or empirical mean (empirical average), and the sample covariance or empirical covariance are statistics computed from a sample of data on one or more random variables. The sample mean is the average value (or mean value) of a sample of numbers taken from a larger population of numbers, where "population" indicates not number of people but the entirety of relevant data, whether collected or not. A sample of 40 companies' sales from the Fortune 500 might be used for convenience instead of looking at the population, all 500 companies' sales. The sample mean is used as an estimator for the population mean, the average value in the entire population, where the estimate is more likely to be close to the population mean if the sample is large and representative. The reliability of the sample mean is estimated using the standard error, which in turn is calculated using the variance of the sample. If the sample is random, the standard error falls with th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Intervals
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 s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Engineering Concepts
Engineering is the practice of using natural science, mathematics, and the engineering design process to solve problems within technology, increase efficiency and productivity, and improve systems. Modern engineering comprises many subfields which include designing and improving infrastructure, machinery, vehicles, electronics, materials, and energy systems. The discipline of engineering encompasses a broad range of more specialized fields of engineering, each with a more specific emphasis for applications of mathematics and science. See glossary of engineering. The word ''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: History Engineering has existed since ancient times, when humans devised inventions such as the wedge, lever, wheel and pulley, etc. The term ''engineering'' is derived ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factor Of Safety
In engineering, a factor of safety (FoS) or safety factor (SF) expresses how much stronger a system is than it needs to be for its specified maximum 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). Margin of safety (MoS or MS) is a related measure, expressed as a relative change. 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 sa ... [...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] |
Student's T-distribution
In probability theory and statistics, Student's distribution (or simply the distribution) t_\nu is a continuous probability distribution that generalizes the Normal distribution#Standard normal distribution, standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped. However, t_\nu has Heavy-tailed distribution, heavier tails, and the amount of probability mass in the tails is controlled by the parameter \nu. For \nu = 1 the Student's distribution t_\nu becomes the standard Cauchy distribution, which has very fat-tailed distribution, "fat" tails; whereas for \nu \to \infty it becomes the standard normal distribution \mathcal(0, 1), which has very "thin" tails. The name "Student" is a pseudonym used by William Sealy Gosset in his scientific paper publications during his work at the Guinness Brewery in Dublin, Ireland. The Student's distribution plays a role in a number of widely used statistical analyses, including Student's t- ... [...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 normal distribution, 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 Donald MacAlister#log-normal, McAlister, Gibrat's law, Gibrat and Cobb–Douglas. A l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fuel Economy In Automobiles
The fuel economy of an automobile relates to the distance traveled by a vehicle and the amount of fuel consumed. Consumption can be expressed in terms of the 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 the 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 s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States Environmental Protection Agency
The Environmental Protection Agency (EPA) is an independent agency of the United States 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 Lee Zeldin. The EPA is not a Cabinet department, but the administrator is normally given cabinet rank. The EPA has its headquarters in Washington, D.C. There are regional offices for each of the agency's ten regions, as well as 27 laboratories around the country. 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 consultat ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variance
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. It is the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by \sigma^2, s^2, \operatorname(X), V(X), or \mathbb(X). An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviation; for example, the variance of a sum of uncorrelated random variables is equal to the sum of their variances. A disadvantage of the variance for practical applications is that, unlike the standard deviation, its units differ from the random variable, which is why the standard devi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
