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Stress–strength Analysis
Stress–strength analysis is the analysis of the strength of the materials and the interference of the stresses placed on the materials, where "materials" is not necessarily the raw goods or parts, but can be an entire system. Stress-Strength Analysis is a tool used in reliability engineering. Environmental stresses have a distribution with a mean \left(\mu_x\right) and a standard deviation \left(s_x\right) and component strengths have a distribution with a mean \left(\mu_y\right) and a standard deviation \left(s_y\right). The overlap of these distributions is the probability of failure \left(Z\right). This overlap is also referred to stress-strength interference. Reliability If the distributions for both the stress and the strength both follow a Normal distribution, then the reliability (R) of a component can be determined by the following equation: R = 1 - P(Z), where Z = -\frac P(Z) can be determined from a Z table or a statistical software package. See also * Fir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reliability Engineering
Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability describes the ability of a system or component to function under stated conditions for a specified period of time. Reliability is closely related to availability, which is typically described as the ability of a component or system to function at a specified moment or interval of time. The reliability function is theoretically defined as the probability of success at time t, which is denoted R(t). This probability is estimated from detailed (physics of failure) analysis, previous data sets or through reliability testing and reliability modelling. Availability, testability, maintainability and maintenance, repair and operations, maintenance are often defined as a part of "reliability engineering" in reliability programs. Reliability often plays the key role in the cost-effectiveness of systems. Reliability engineering deals with the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distribution (mathematics)
Distributions, also known as Schwartz distributions or generalized functions, are objects that generalize the classical notion of functions in mathematical analysis. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative. Distributions are widely used in the theory of partial differential equations, where it may be easier to establish the existence of distributional solutions than classical solutions, or where appropriate classical solutions may not exist. Distributions are also important in physics and engineering where many problems naturally lead to differential equations whose solutions or initial conditions are singular, such as the Dirac delta function. A function f is normally thought of as on the in the function domain by "sending" a point x in its domain to the point f(x). Instead of acting on points, distribution theory reinterpr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the ''arithmetic mean'', also known as "arithmetic average", is a measure of central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values. The arithmetic mean of a set of numbers ''x''1, ''x''2, ..., x''n'' is typically denoted using an overhead bar, \bar. If the data set were based on a series of observations obtained by sampling from a statistical population, the arithmetic mean is the ''sample mean'' (\bar) to distinguish it from the mean, or expected value, of the underlying distribution, the ''population mean'' (denoted \mu or \mu_x).Underhill, L.G.; Bradfield d. (1998) ''Introstat'', Juta and Company Ltd.p. 181/ref> Outside probability and statistics, a wide range of other notions of mean are o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. Standard deviation may be abbreviated SD, and is most commonly represented in mathematical texts and equations by the lower case Greek letter σ (sigma), for the population standard deviation, or the Latin letter '' s'', for the sample standard deviation. The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same unit as the data. The standard deviation of a popu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Normal Table
A standard normal table, also called the unit normal table or Z table, is a mathematical table for the values of Φ, which are the values of the cumulative distribution function of the normal distribution. It is used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution, and by extension, any normal distribution. Since probability tables cannot be printed for every normal distribution, as there are an infinite variety of normal distributions, it is common practice to convert a normal to a standard normal and then use the standard normal table to find probabilities. Normal and standard normal distribution Normal distributions are symmetrical, bell-shaped distributions that are useful in describing real-world data. The ''standard'' normal distribution, represented by the letter Z, is the normal distribution having a mean of 0 and a standard deviation of 1. Conversion If ''X'' is a random variable from a normal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-order Reliability Method
The first-order reliability method, (FORM), is a semi- probabilistic reliability analysis method devised to evaluate the reliability of a system. The accuracy of the method can be improved by averaging over many samples, which is known as Line Sampling. The method is also known as the Hasofer-Lind Reliability Index, developed by Professor Michael Hasofer and Professor Neil Lind in 1974. The index has been recognized as an important step towards the development of contemporary methods to effectively and accurately estimate structural safety. The analysis method depends on a "Most Probable Point" on the limit state C Annis"How FORM/SORM is Supposed to Work"/ref> See also * EN 1990 En or EN may refer to: Businesses * Bouygues (stock symbol EN) * Esquimalt and Nanaimo Railway (reporting mark EN, but now known as Southern Railway of Vancouver Island) * Euronews, a news television and internet channel Language and writing * E ... * Fast probability integration * Stress–streng ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanical Failure
Structural integrity and failure is an aspect of engineering that deals with the ability of a structure to support a designed structural load (weight, force, etc.) without breaking and includes the study of past structural failures in order to prevent failures in future designs. Structural integrity is the ability of an item—either a structural component or a structure consisting of many components—to hold together under a load, including its own weight, without breaking or deforming excessively. It assures that the construction will perform its designed function during reasonable use, for as long as its intended life span. Items are constructed with structural integrity to prevent catastrophic failure, which can result in injuries, severe damage, death, and/or monetary losses. ''Structural failure'' refers to the loss of structural integrity, or the loss of load-carrying capacity in either a structural component or the structure itself. Structural failure is initiated whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reliability Engineering
Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability describes the ability of a system or component to function under stated conditions for a specified period of time. Reliability is closely related to availability, which is typically described as the ability of a component or system to function at a specified moment or interval of time. The reliability function is theoretically defined as the probability of success at time t, which is denoted R(t). This probability is estimated from detailed (physics of failure) analysis, previous data sets or through reliability testing and reliability modelling. Availability, testability, maintainability and maintenance, repair and operations, maintenance are often defined as a part of "reliability engineering" in reliability programs. Reliability often plays the key role in the cost-effectiveness of systems. Reliability engineering deals with the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
