THE BURR-XII DISTRIBUTION IN RELIABILITY-ANALYSIS

The Burr XII distribution is similar to the log-normal distribution in that it has a non-monotone hazard function which can accommodate many shapes of hazard. However, the Burr distribution has the advantages t hat: a) the Burr cumulative distribution function and reliability func tion can be written in closed form; thus, it simplifies the computatio n of the percentiles and the likelihood function for censored data; an d b) the Burr XII distribution has algebraic tails which are effective for modeling failures that occur with lesser frequency than with corr esponding models based on exponential tails. The Burr XII distribution gives the reliability practitioner another model for representing fai lure data. In this paper, the statistical and probabilistic properties of the Burr XII distribution are presented, and its relationship to o ther distributions used in reliability analyses is described. Its use as a model for failure data is outlined, methods for graphical estimat ion on probability paper are illustrated, and examples of its usage ar e presented.