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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 Niels 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 * Fast probability integration * Stress–strength analysis References Probabilistic models Reliability engineering {{engineering-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th ed., (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', vol. 1, 3rd ed., (1968), Wiley, . This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These concepts have been given an axiomatic mathematical formaliza ... [...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 is defined as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, OR will operate in a defined environment without failure. 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. In practice, it is calculated using different techniques, and its value ranges between 0 and 1, where 0 indicates no probability of success while 1 indicates definite success. This probability is estimated from detailed (physics of failure) analysis, previous data sets, or through reliability testing and reliability modeling. Availability, testability, maintainability, and maintenance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Sampling
Line sampling is a method used in reliability engineering to compute small (i.e., rare event) failure probabilities encountered in engineering systems. The method is particularly suitable for Curse of dimensionality, high-dimensional reliability problems, in which the performance function exhibits moderate non-linearity with respect to the uncertain parameters The method is suitable for analyzing black box systems, and unlike the importance sampling method of variance reduction, does not require detailed knowledge of the system. The basic idea behind line sampling is to refine estimates obtained from the first-order reliability method (FORM), which may be incorrect due to the non-linearity of the Limit_state_design, limit state function. Conceptually, this is achieved by averaging the result of different FORM simulations. In practice, this is made possible by identifying the importance direction \boldsymbol \alpha in the input parameter space, which points towards the region w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Hasofer
Abraham Michael Hasofer (1927–2010) was an Australian statistician. He was a professor and the Chair of Statistics within the Mathematics Department in the University of New South Wales from 1969 to 1991. He subsequently held a position at the La Trobe University in Melbourne. He authored a number of publications in the field of applied mathematics and civil engineering, including his formulation of the Hasofer-Lind Reliability Index. Biography Abraham Hasofer was born in Alexandria, Egypt, on 2 October 1927 to an Ashkenazi Jewish family. He migrated to Israel after the state's independence but subsequently migrated to Australia in 1955. In the 1960s, Hasofer joined the Chabad Hasidic movement. Education and career In 1948, Hasofer earned a bachelor's degree in Electrical Engineering from the University of Alexandria in Egypt. In 1960, he earned a Bachelor of Science from the University of Tasmania, and in 1964, Hasofer earned his PhD in Mathematical Statistics from the Uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Niels Lind
Niels is a male given name, equivalent to Nicholas, which is common in Denmark, Belgium, Norway (formerly) and the Netherlands. The Norwegian and Swedish variant is Nils. The name is a developed short form of Nicholas or Greek Nikolaos, after Saint Nicholas. Its pet form is Nisse, and female variants are Nielsine, Nielsina, and Nielsa. Notable people with the name include: * Niels, King of Denmark (1065–1134) * Niels, Count of Halland (died 1218) *Niels Aagaard (1612–1657), Danish poet *Niels Aall (1769–1854), Norwegian businessman and politician *Niels Henrik Abel (1802–1829), Norwegian mathematician *Niels Arestrup (1949–2024), French-Danish actor and director * Niels Viggo Bentzon (1919–2000), Danish composer and pianist *Niels Bohr (1885–1962), Danish physicist and Nobel Prize recipient * Niels Busk (born 1942), Danish politician *Niels Ebbesen (died 1340), Danish squire and national hero * Niels Nikolaus Falck (1784–1850), Danish jurist and historian *Niels ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
EN 1990
EN or En or en may refer to: Businesses * Bouygues (stock symbol EN) * Island Rail Corridor, formerly known as the Esquimalt and Nanaimo Railway (reporting mark EN) * Euronews, a news television and internet channel Language and writing * N, 14th letter of the Roman alphabet * EN, a mark in Sumerian cuneiform script for a High priest or Priestess (meaning "lord", or "priest") *En (digraph) /‹en›/, a phoneme *En (Cyrillic), 15th letter of the Cyrillic alphabet *En (typography), a unit of typographical width ** Dash#En dash /en dash/, a dash of length 1 en * En language, a language spoken in northern Vietnam *English language (ISO language code: en) Organisations * Eastern National, a US organization providing educational products to National Park visitors * English Nature, a former UK government conservation agency * Envirolink Northwest, an environmental organization in England Religion * En (deity) in Albanian mythology Science and technology * Engineer * E''n'' (Lie a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fast Probability Integration
Fast probability integration (FPI) is a method of determining the probability of a class of events, particularly a failure event, that is faster to execute than Monte Carlo analysis. It is used where large numbers of time-variant variables contribute to the reliability of a system. The method was proposed by Wen and Chen in 1987. For a simple failure analysis with one stress variable, there will be a time-variant failure barrier, r(t), beyond which the system will fail. This simple case may have a deterministic solution, but for more complex systems, such as crack analysis of a large structure, there can be a very large number of variables, for instance, because of the large number of ways a crack can propagate. In many cases, it is infeasible to produce a deterministic solution even when the individual variables are all individually deterministic. In this case, one defines a probabilistic failure barrier surface, \mathbf R (t), over the vector space of the stress variables. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 (mathematics), 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 Standard normal table, Z table or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic Models
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th ed., (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', vol. 1, 3rd ed., (1968), Wiley, . This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These concepts have been given an axiomatic mathematical formaliza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
