Among all of the distributions available for reliability calculations, the Weibull distribution is the only one unique to the engineering field. 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 analysed.

A Swedish engineer and mathematician studying metallurgical failures, Professor Weibull pointed out that normal distributions require that initial metallurgical strengths be normally distributed, which is not necessarily the case. He noted the need for a function that could embrace a great variety of distributions, including the normal.

When delivering his hallmark American paper in 1951, A Statistical Distribution Function of Wide Applicability, Professor Weibull claimed that life data could select the most appropriate distribution from the broad family of Weibull distributions and then fit the parameters to provide reasonably accurate failure analysis. He used seven vastly different problems to prove that the Weibull distribution could easily be applied to a wide range of problems.

The initial reaction to the Weibull distribution was generally that it was too good to be true. However, pioneers in the field of failure data analysis began applying and improving the technique, which resulted in the U.S. Air Force recognising its merit and funding Professor Weibull’s research until 1975.

Today, Weibull analysis refers to graphically analysing probability plots to find the distribution that best represents a set of life data for a given failure mode. 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. By “fitting” a statistical distribution to life data, Weibull analysis provides for making predictions about the life of the products in the population. The parameterised distribution for this representative sample is then used to estimate such important life characteristics of the product as reliability, probability of failure at a specific time, mean life for the product and the failure rate.