Once these have been 'ironed out,' a (hopefully) long relatively trouble-free period of operation will follow. Then, after some time of operation, the failure rate again begins to increase (so-called Wear-out Failures), until all components or devices will have failed.įor example, new automobiles often suffer several small failures right after they were purchased. The hazard (conditional failure) function for most machines (components, devices) can best be described in terms of the 'bathtub' curve: Very early during the life of a machine, the rate of failure is relatively high (so-called Infant Mortality Failures) after all components settle, and the electronic parts are burned in, the failure rate is relatively constant and low.

H(t) stands for the hazard function (of timeį(t) are the probability density and cumulative distribution functions, respectively. This function is called the hazard function (or, sometimes, also the conditional failure, intensity, or force of mortality function), and is generally defined as: It is often meaningful to consider the function that describes the probability of failure during a very small time increment (assuming that no failures have occurred prior to that time).

The distribution is named after the Swedish professor Waloddi Weibull, who demonstrated the appropriateness of this distribution for modeling a wide variety of different data sets (see also Hahn and Shapiro, 1967 for example, the Weibull distribution has been used to model the life times of electronic components, relays, ball bearings, or even some businesses). A useful general distribution for describing failure time data is the Weibull distribution (see also Weibull CDF, reliability, and hazard functions).

Reliability weibull