SOME SIMULATION RESULTS OF WEIBULL AND MIXED WEIBULL DISTRIBUTIONS

Ahmad Mahir Razali (Malaysia), Ali A. Salih Al-Wakeel (Malaysia) and Asaad A. Mahdi (Malaysia)

Received January 13, 2009

Abstract

The Weibull variate is commonly used as a lifetime distribution in reliability applications. The two-parameter (shape and scale) Weibull distribution can represent a decreasing, constant or increasing failure rate. Further, flexibility can be introduced into the Weibull distribution by adding the third parameter which is a location parameter. In this paper, we discuss the idea of Weibull distribution which is one of the continuous distributions with two and three parameters. We also try to explain the idea of a mixed Weibull distribution which can be generated from two or more Weibull distributions. This idea has been suggested and used recently in statistical distributions as it gives a number of parameters more than Weibull distribution. We also mention the idea of how to combine two or more Weibull distributions to obtain a mixed Weibull distribution using a mixing parameter. This distribution is more flexible in reliability studies. We have several versions of mixed Weibull distributions that are used in the field of statistics and engineering.

Keywords and phrases: two-parameter Weibull distribution, three-parameter Weibull distribution, mixed Weibull distribution.