Abstract
In this paper we defined a new lifetime model called the the Exponentiated additive Weibull (EAW) distribution. The proposed distribution has a number of well-known lifetime distributions as special sub-models, such as the additive Weibull, exponentiated modified Weibull, exponentiated Weibull and generalized linear failure rate distributions among others. We obtain quantile, moments, moment generating functions, incomplete moment, residual life and reversed Failure Rate Functions, mean deviations, Bonferroni and Lorenz curves. The method of maximum likelihood is used for estimating the model parameters. Applications illustrate the potentiality of the proposed distribution.
Highlights
In reliability engineering and lifetime analysis many applications require a bathtub shaped hazard rate function
In many applications in reliability, mechanical and electronic components and survival analysis, the hazard rate function can be of bathtub shape
Despite the fact that this phenomenon has been presented in many reliability engineering texts few practical models possessing this property have appeared in the literatures twoparameter flexible Weibull extension of Bebbington et al (2007) has a hazard function that can be increasing, decreasing or bathtub shaped
Summary
In reliability engineering and lifetime analysis many applications require a bathtub shaped hazard rate function. Weibull distribution is one of the most commonly used lifetime distributions in reliability and lifetime data analysis It is flexible in modeling failure time data, as the corresponding hazard rate function can be increasing,constant or decreasing. The new distribution due to its flexibility in accommodating all the forms of the hazard rate function can be used in a variety of problems for modeling lifetime data Another important characteristic of the distribution is that it contains, as special sub-models, the Weibull, exponentiated exponential (Gupta and Kundu, 1999, 2001), exponentiated modified Weibull distribution (Elbatal, 2009), exponentiated Weibull distribution (Mudholkar et al, 1995, 1996), generalized linear failure rate distribution, (Sarhan and Kundu, 2009), Modified Weibull distribution (Lai et al, 2003), among some other distributions.
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