Discrete Weibull-geometric distribution

Abstract

The failure-time distribution is used to describe the life of a device, material, or structure. One of the most commonly used distributions to analyze failure-time data is Weibull distribution. The Weibull distribution is very flexible for modeling varying types of failure rates data with constant, increasing and decreasing shapes, but cannot be used for modeling data with unimodal failure rates. Because of this, we developed the Weibull distribution using compounding method to produce a Weibull-Geometric distribution. The Weibull-Geometric distribution is useful for modeling failure rates data with a unimodal shape. In studies of failure, time to failure is frequently measured in the number of cycles to failure or shocks to failure and become a discrete random variable. Hence, this paper discusses the formation of distribution that more appropriate to modeling discrete failure data. The discrete distribution is obtained by discretizing the continuous Weibull-Geometric distribution. The discretization is carried out by maintaining one of characteristics of the continuous distribution, that is, its survival function. The result distribution, called Discrete Weibull-Geometric distribution (DWG) has unimodal failure rates, right skew, and more appropriate at modeling discrete failure data. At the end of this paper, the Discrete Weibull-Geometric distribution is used to illustrate the real dataset and show that DWG distribution is the appropriate model.