WEIBULL DISTRIBUTION

Weibull distribution

Weibull distribution

Introduction

One important distribution in statistics is Weibull distribution which is distributed normally and also it is continuous. It is also defined over the set of positive real numbers , for example, to describe lifetimes and failure frequencies of electronic components or (brittle) materials (such as in quality ), but also for the statistical study of wind speeds is used. It is named after the Swedish engineer and mathematician Waloddi Weibull . Waloddi Weibull was a Swedish Physicist who has credited with being accurate in his description of the Weibull Distribution. The Weibull distribution can be used to describe increasing, constant and decreasing failure rates of technical systems. In practice, the Weibull distribution in addition to the exponential distribution, which is a special case of the more general Weibull distribution, the most commonly used life distribution.

The Weibull distribution was developed in 1951 by Swedish professor Waladdi Weibull. Despite being a distribution function discovery four decades ago, its applicability in the field of engineering is very recent. This function has three continuous parameters: shape parameter (b), scale parameter (q) and location parameter (d). The scale parameter is a parameter whose values ??are discrete, as the number of cycles until failure of a component requested cyclically. The shape parameter varies between five and eight, and when this value equals one. Also the shape of Weibull distribution is very much similar to that of exponential distribution and because of this when it equal to 3.5, the Weibull distribution approximately behaves as the normal distribution.

The scale parameter is known as life characteristic (q + d) when the location parameter is zero. This parameter is zero when the fault does not occur when the variable time also equals zero. Imagine, for example, an airplane landing gear that needs to be tested for fatigue, in their most critical regions, ie, where the level of cyclic request is more intense. For the tests, a few specimens can be made for lack of material. Therefore, the Weibull distribution may aid in processing of the results in order to evaluate the reliability of the results. In this work we investigated ten results of cycles to fatigue fracture of a low carbon steel with 400MPa request level. Results Of the ten were selected repeatedly at random, three results for the implementation of the Weibull distribution. The main purpose of this choice was to check if three specimens are sufficient to provide reliable results. From all the results were evaluated, all had reliability of ninety percent. Therefore, the lifting of a fatigue curve for each request level, it is possible that three specimens for each voltage level, can ensure a fatigue curve with ninety percent reliability. The Weibull distribution is widely used for various assumed values ??of the slope parameter. However we can model a wide variety of data and life characteristics.

Background and History

The statistics of probability distribution also contains weibull distribution which is included under the continuous probability ...