A New Flexible Bathtub-Shaped Modification of the Weibull Model: Properties and Applications

Many studies have suggested the modifications and generalizations of the Weibull distribution to model the nonmonotone hazards. In this paper, we combine the logarithms of two cumulative hazard rate functions and propose a new modified form of the Weibull distribution. The newly proposed distributio...

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Bibliographic Details
Published in:Mathematical problems in engineering 2020, Vol.2020 (2020), p.1-11
Main Authors: Hamedani, G. G, Muhmoudi, Eisa, Ahmad, Zubair, Liao, Qinghu
Format: Article
Language:English
Subjects:
Logarithms
Mathematical problems
Maximum likelihood estimates
Maximum likelihood estimation
Parameter estimation
Random variables
Reliability analysis
Reliability engineering
Weibull distribution
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Summary:Many studies have suggested the modifications and generalizations of the Weibull distribution to model the nonmonotone hazards. In this paper, we combine the logarithms of two cumulative hazard rate functions and propose a new modified form of the Weibull distribution. The newly proposed distribution may be called a new flexible extended Weibull distribution. Corresponding hazard rate function of the proposed distribution shows flexible (monotone and nonmonotone) shapes. Three different characterizations along with some mathematical properties are provided. We also consider the maximum likelihood estimation procedure to estimate the model parameters. For the illustrative purposes, two real applications from reliability engineering with bathtub-shaped hazard functions are analyzed. The practical applications show that the proposed model provides better fits than the other nonnested models.
ISSN:1024-123X
1563-5147
DOI:10.1155/2020/3206257