Weibull Distribution

The Weibull distribution is a continuous probability distribution commonly used to model the time until failure of a component or system, or more generally the size of extreme values in a sample, defined by a shape parameter and a scale parameter that together determine the form of the distribution's density curve. The distribution was first identified by the French mathematician Maurice Frechet in 1927 in his foundational work on the theory of extreme values, but it takes its common name from the Swedish engineer Waloddi Weibull, who independently applied and popularized it in a widely cited 1951 paper on the statistical distribution of the breaking strength of materials. A key feature of the distribution is that its shape parameter controls whether the modeled failure rate increases, decreases, or stays constant over time, allowing a single family of curves to represent wear-out failure, infant mortality failure, and the constant failure rate of the exponential distribution as special cases, which is why the Weibull distribution remains one of the most widely used tools in reliability engineering and survival analysis.