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# Topic: Weibull distribution

 Weibull distribution - Wikipedia, the free encyclopedia The Weibull distribution is often used in place of the Normal distribution due to the fact that a Weibull variate can be generated through inversion, while Normal variates are typically generated using the more complicated Box-Muller Method, which requires two uniform random variates. Weibull distributions may also be used to represent manufacturing and delivery times in industrial engineering problems, while it is very important in extreme value theory and weather forecasting. Furthermore, concerning wireless communications, the Weibull distribution may be used for fading channel modelling, since the Weibull fading model seems to exhibit good fit to experimental fading channel measurements. en.wikipedia.org /wiki/Weibull_distribution   (492 words)

 1.3.6.6.8. Weibull Distribution The formula for the inverse survival function of the Weibull distribution is Maximum likelihood estimation for the Weibull distribution is discussed in the Reliability chapter (Chapter 8). The Weibull distribution is used extensively in reliability applications to model failure times. www.itl.nist.gov /div898/handbook/eda/section3/eda3668.htm   (322 words)

 Relex Weibull Analysis - Relex Feature Article Originally proposed in 1937 by Professor Waloddi Weibull (1887-1979), the Weibull distribution is one of the most widely used distributions for failure data analysis, which is also known as life data analysis because life span measurements of a component or system are analyzed. Although the Weibull distribution is the leading method worldwide for examining life data to determine best-fit distributions, other distributions occasionally used for life data analysis include the exponential, lognormal, and normal. Weibull analysis studies the relationship between the life span of a component and its reliability by graphing life data for an individual failure mode on a Weibull probability plot. www.relexsoftware.com /resources/art/art_weibull2.asp   (1149 words)

 Weibull Analysis The corresponding density distribution f(t) is the derivative of this, i.e., Interestingly, the "Weibull distribution" had already been studied in the 1920's by the statistician Emil Gumbel (1891-1966), who is best remembered today for his confrontation with the Nazis in 1931 when they organized a campaign to force him out of his professorship at Heidelberg University for his outspoken pacifist and anti-Nazi views. However, for the Weibull distribution it is not so easy, because the failure rate of each widget is a function of the age of that particular widget. www.mathpages.com /home/kmath122/kmath122.htm   (1842 words)

 Weibull Reliability Model, Distribution, Weibull Analysis - Relex Feature Article The Weibull distribution is one of the most widely used probability distributions in the reliability engineering discipline. Developed in 1937 by Dr. Waloddi Weibull, it was first introduced to the greater population in 1951 in Dr. Waloddi's famous paper "A Statistical Distribution Function of Wide Applicability." Although it was initially received with much skepticism, the Weibull distribution has since become a standard in reliability textbooks for modeling time-dependent failure data. The failure distribution of the system load was previously determined to be exponential with a MTTF of 10 years, and the entire system is required to maintain a reliability of 0.60 throughout its required operational life of 2.5 years. www.relexsoftware.com /resources/art/art_weibull3.asp   (1145 words)

 Weibull vs. Geometric Distribution   (Site not responding. Last check: 2007-11-06) The geometric distribution describes the number of trials it takes for a success (heads) to occur, where each trial is independent of the others and each has a success probability of "p". The geometric distribution is analogous to the exponential distribution. So, the relationship between the geometric and the Weibull distributions is as follows: the geometric distribution is the discrete analog to the special case of the Weibull distribution with the Weibull parameter a=1. www.mathoptions.com /weibull1.htm   (544 words)

 Generalized extreme value distribution - Wikipedia, the free encyclopedia In probability theory and statistics, the generalized extreme value distribution (GEV) is a family of continuous probability distributions developed within extreme value theory to combine the Gumbel, Fréchet and Weibull families also known as type I, II and III extreme value distributions. Its importance arises from the fact that it is the limit distribution of the maxima of a sequence of independent and identically distributed random variables. Because of this, the GEV is used as an approximation to model the maxima of long (finite) sequences of random variables. en.wikipedia.org /wiki/Generalized_extreme_value_distribution   (550 words)

 Classic Case Studies in Reliability Analysis: The Weibull Distribution Three of the case studies were modeled using a three parameter Weibull distribution and four were modeled using a two population mixed Weibull. As modern day analysts, we enter this data set into Weibull++ 6 and our first point of interest is the goodness of fit of the three-parameter Weibull distribution. Using Weibull++ 6, we are able to quickly learn that the median yield strength is 45.45, the mean yield strength is 45.52 and that only 0.68% of the units in the population are expected to have a yield strength of 40 or lower. www.reliasoft.com /newsletter/2q2001/classic_weibull.htm   (696 words)

 Wallodi Weibull Biography written by Dr. Robert B. Abernethy The Weibull distribution is by far the world’s most popular statistical model for life data. Weibull was a member of many technical societies and worked to the last day of his remarkable life. The Weibull Distribution was first published in 1939, over 60 years ago and has proven to be invaluable for life data analysis in aerospace, automotive, electric power, nuclear power, medical, dental, electronics, every industry. www.barringer1.com /weibull_bio.htm   (1277 words)

 Distribution Fitting To determine this underlying distribution, it is common to fit the observed distribution to a theoretical distribution by comparing the frequencies observed in the data to the expected frequencies of the theoretical distribution (i.e., a Chi-square goodness of fit test). The major distributions that have been proposed for modeling survival or failure times are the exponential (and linear exponential) distribution, the Weibull distribution of extreme events, and the Gompertz distribution. The logistic distribution is used to model binary responses (e.g., Gender) and is commonly used in logistic regression. www.statsoft.com /textbook/stdisfit.html   (1769 words)

 Weibull Distribution   (Site not responding. Last check: 2007-11-06) The Weibull distribution (continuous) could be used to model the time required to perform some task. A Weibull distribution with parameters shape = 1 and scale = b is an exponential distribution with mean = b. The Weibull distribution is skewed to the left when shape > 3.6. www.caciasl.com /docs/sp412/webhelp/SPHelp/weibull_distribution.html   (98 words)

 Internet Topology - 11. Weibull approximations (AB) Every data point (outdegree value) is assigned two coordinates: x, the Weibul distribution value at that argument; and y, the value of the ccdf of outdegree frequencies in the graph. Inspection of the data shows that Weibull is a very good approximation with relative error less than 7% for outdegrees between 8 and 295, even though it changes sign from a slight underestimation to a slight overestimation of outdegree probabilities between outdegrees 113 and 114. Discrete Weibull distribution can also result from growth process in which each member of a population starts from a small size and grows to some limiting size k where its growth stops. www.caida.org /~broido/ipt/ipt.weib.html   (1075 words)

 8.1.6.2. Weibull The Weibull is a very flexible life distribution model with two parameters. Another special case of the Weibull occurs when the shape parameter is 2. The distribution is called the Rayleigh Distribution and it turns out to be the theoretical probability model for the magnitude of radial error when the x and y coordinate errors are independent normals with 0 mean and the same standard deviation. www.itl.nist.gov /div898/handbook/apr/section1/apr162.htm   (632 words)

 Supported Distributions These distributions apply when the log of the response is modeled (this is the default analysis). The corresponding survival distribution function (G) and its density function (g) are given for the untransformed baseline distribution. For example, for the WEIBULL distribution, S(w) and f(w) are the baseline survival distribution function and the probability density function for the extreme value distribution (the log of the response) while G(t) and g(t) are the survival distribution function and probability distribution function of a Weibull distribution (using the untransformed response). www.asu.edu /sas/sasdoc/sashtml/stat/chap36/sect16.htm   (362 words)

 Probability Distributions   (Site not responding. Last check: 2007-11-06) The Weibull Distribution is typically used in reliability modeling. The Log-Normal Distribution is useful when the raw data are highly skewed whereas the natural log of the data are normally distributed. The Beta Distribution is a continuous distribution bounded between 0 and 1. www.stat.vt.edu /~sundar/java/applets/Distributions.html   (494 words)

 [No title] An example is the Weibull distribution, a flexible univariate distribution that is often used in survival analysis. The beta distribution is a two-parameter family of distributions for random variables which are restricted to the interval [0, 1]. Let B(x; a, b) be the CDF for the beta distribution, in which x is the random variate and a and b are the parameters. www.biostat.umn.edu /~john-c/5421/notes.012   (681 words)

 Using Excel for Weibull Analysis For the uninitiated, Weibull analysis is a method for modeling data sets containing values greater than zero, such as failure data. Weibull analysis can make predictions about a product's life, compare the reliability of competing product designs, statistically establish warranty policies or proactively manage spare parts inventories, to name just a few common industrial applications. Moreover, the universal convention for displaying a Weibull probability plot is to depict "ln(lifetime)" on the horizontal axis. www.qualitydigest.com /jan99/html/body_weibull.html   (2636 words)

 Weibull Discussion The Weibull distribution is unique in that it takes on the shape which best fits the data. In other words, the Weibull distribution has the ability to reveal, rather than mask, the correct distribution of the data. In addition, use of any of the Weibull analysis routines to accomplish estimates of population characteristics, is simply a recognition of the fact that populations are rarely 100% normal, binomial, or exponential and so on. www.applicationsresearch.com /WeibullDiscussion.htm   (515 words)

 PlanetMath: Weibull random variable The resulting distribution is called the standard Weibull, or Rayleigh distribution: The Weibull distribution is often used to model reliability or lifetime of products such as light bulbs. This is version 3 of Weibull random variable, born on 2004-06-24, modified 2004-06-30. planetmath.org /encyclopedia/RayleighDistribution.html   (128 words)

 Multiple Failure Modes with the Weibull Distributions   (Site not responding. Last check: 2007-11-06) Several leading consultants have stated that the Weibull distribution cannot be used to model multiple failure modes. By definition the Weibull distribution is an extreme value distribution. If the Weibull distribution is used to model the time to fail for the system, the results will match the theoretical value, proving that it is possible to model multiple failure modes with the Weibull distribution. www.engineeredsoftware.com /weibull_mfm.asp   (311 words)

 Weibull Analysis of Interval Data with Common Inspection Schedule The DISTRIBUTION statement specifies that the Weibull distribution is used for parameter estimation and probability plotting. The confidence intervals for the cumulative probability are based on the binomial distribution for time intervals until right censoring occurs. For time intervals after right censoring occurs, the binomial distribution is not valid, and a normal approximation is used to compute confidence intervals. www.uni.edu /sasdoc/qc/chap30/sect6.htm   (648 words)

 The Weibull Distribution -- Ask Statman   (Site not responding. Last check: 2007-11-06) I have heard the term "Weibull distribution," but I don’t know what it means. The Weibull distribution is often used to describe the life times of parts. In the past, I have discussed the normal distribution, or bell curve. www.mathoptions.com /Weibull.htm   (658 words)

 Describing Wind Variations: Weibull Distribution The wind variation for a typical site is usually described using the so-called Weibull distribution, as shown in the image. The statistical distribution of wind speeds varies from place to place around the globe, depending upon local climate conditions, the landscape, and its surface. The Weibull distribution may thus vary, both in its shape, and in its mean value. www.windpower.org /en/tour/wres/weibull.htm   (547 words)

 Dr Bob Abernethy - Biographies - Wallodi Weibull   (Site not responding. Last check: 2007-11-06) Many including the author were skeptical that this method of allowing the data to select the most appropriate distribution from the broad family of Weibull distributions would work. Robert Heller (3) spoke at the 1984 Symposium to the Memory of Wallodi Weibull in Stockholm, Sweden and said, in 1963, at the invitation of the Professor Freudenthal, he became a Visiting Professor at Columbia University's Institute for the Study of Fatigue and Reliability. Professor Weibull's proudest moment came in 1978 when he received the Great Gold medal from the Royal Swedish Academy of Engineering Sciences which was personally presented to him by King Carl XVI Gustav of Sweden. www.bobabernethy.com /bios_weibull.htm   (1737 words)

 The Weibull Distribution The Weibull distribution is one of the most widely used lifetime distributions in reliability engineering. It is a versatile distribution that can take on the characteristics of other types of distributions, based on the value of the shape parameter, This chapter provides a brief background on the Weibull distribution, presents and derives most of the applicable equations and presents examples calculated both manually and by using Weibull++. www.weibull.com /LifeDataWeb/the_weibull_distribution.htm   (92 words)

 Generating Weibull Distributed Random Numbers This is a step-by-step explaination of how to calculate a transformation function that converts a random variable of one distribution to another distribution. This example uses the Weibull distribution as the intended target distribution. We start with the random number, x, which comes from a uniform distribution (in the range from 0 to 1). www.taygeta.com /random/weibull.xml   (323 words)

 Weibull Distribution The Weibull distribution is one of the most commonly used distributions in reliability engineering because of the many shapes it attains for various values of The cdf of the 2-parameter Weibull distribution is given by: The Weibull conditional reliability function is given by: www.weibull.com /AccelTestWeb/weibull_distribution.htm   (207 words)

 Beyond the Box Score :: Downloadable Run Distribution Fun! My conclusion was that the way a team distributes its runs scored and allowed can have consequences on its wins and losses in a way that manifests itself as deviations from projected Pythagorean wins. The real magic of the Weibull distribution is that it can be used to derive the Pythagorean theorem - and the parameter andgamma is the same as the exponent in the Pythagorean theorem. For each team, the actual run distribution and Weibull distribution are shown, as well as α for runs scored and allowed (shown as "a_RS" and "a_RA," respectively). www.beyondtheboxscore.com /story/2006/2/23/164417/484   (981 words)

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