Lifetime Distribution Terms
A mathematical model that describes the probability of failures occurring over time. Also known as the probability density function (pdf), this function is integrated to obtain the probability that the failure time takes a value in a given time interval. This function is the basis for other important reliability functions, including the reliability function, the failure rate function, and the mean life.
see Normal distribution
Generalized gamma distribution
While not as frequently used for modeling life data as other life distributions, the generalized gamma distribution does have the ability to mimic the attributes of other distributions such as the Weibull or lognormal, based on the values of the distribution's parameters. While the generalized gamma distribution is not often used to model life data by itself, its ability to behave like other more commonly-used life distributions is sometimes used to determine which of those life distributions should be used to model a particular set of data.
see Failure distribution
Mixed Weibull distribution
A variation of the Weibull distribution used to model data with distinct subpopulations that may represent different failure characteristics over the lifetime of a product. Each subpopulation has separate Weibull parameters calculated, and the results are combined in a mixed Weibull distribution to represent all of the subpopulations in one function.
A common lifetime statistical distribution that was developed by mathematician C. F. Gauss. The distribution is a continuous, bell-shaped distribution that is symmetric about its mean and can take on values from negative infinity to positive infinity.
Probability density function (pdf)
A mathematical model that describes the probability of events occurring over time. This function is integrated to obtain the probability that the event time takes a value in a given time interval. In life data analysis, the event in question is a failure, and the pdf is the basis for other important reliability functions, including the reliability function, the failure rate function, and the mean life.
A statistical distribution frequently used in life data analysis. Developed by Swedish mathematician Waloddi Weibull, this distribution is widely used due to its versatility and the fact that the Weibull pdf can assume different shapes based on the parameter values.