The Burr XII Distribution in Reliability Analysis

Abstract

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 that: a) the Burr cumulative distribution function and reliability function can be written in closed form; thus, it simplifies the computation of the percentiles and the likelihood function for censored data; and b) the Burr XII distribution has algebraic tails which are effective for modeling failures that occur with lesser frequency than with corresponding models based on exponential tails. The Burr XII distribution gives the reliability practitioner another model for representing failure data. In this paper, the statistical and probabilistic properties of the Burr XII distribution are presented, and its relationship to other distributions used in reliability analyses is described. Its use as a model for failure data is outlined, methods for graphical estimation on probability paper are illustrated, and examples of its usage are presented.

• Goodness-of-Fit Methods
• Hazard Function
• Maximum Likelihood
• Probability Plots

Additional information

Notes on contributors

William J. Zimmer

Dr. Zimmer is a Professor of Mathematics and Statistics. He is a Member of ASQ.

J. Bert Keats

Dr. Keats is Professor of Engineering. He is a Senior Member of ASQ.

F. K. Wang

Dr. Wang is Associate Professor of Business Administration. He is a Member of ASQ.