The Beta Reduced Modified Weibull Distribution with Applications to Reliability Data

Authors

  • Lazhar Benkhelifa Department of Mathematics and Informatics, Larbi Ben M’Hidi University, Oum El Bouaghi, 04000, Algeria

DOI:

https://doi.org/10.13052/jrss0974-8024.14116

Keywords:

Beta distribution, Hazard rate function, Modified Weibull distribution, Maximum likelihood estimation

Abstract

In this paper, we introduce a new probability distribution with application in reliability called the beta reduced modified Weibull distribution. The proposed distribution presents a more flexible model and has the capability to capture decreasing, increasing, bathtub, unimodal (upside-down bathtub) and modified unimodal shaped hazard rates. Also, this distribution has a bathtub-shaped hazard rate function with a long useful life period, which is desirable property in reliability analysis. We obtain the expansions for the moments, quantile function, stress-strength reliability, density function of the order statistics and their moments. We use the method of maximum likelihood to estimate the model parameters for complete and right-censored data. We evaluate the performance of the maximum likelihood estimators in a simulation study. We analyze three reliability data sets, complete and censored, to examine the flexibility of the proposed model.

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Author Biography

Lazhar Benkhelifa, Department of Mathematics and Informatics, Larbi Ben M’Hidi University, Oum El Bouaghi, 04000, Algeria

Lazhar Benkhelifa received the engineer degree in statistics from university of Biskra (Algeria), the Magister degree in probability and statistics from university of Biskra (Algeria), the doctorate degree in statistics from university of Biskra (Algeria) in 2015 and the habilitation (Habilitation Universitaire) from university of Oum El Bouaghi (Algeria) in 2018. He works as a teacher at the department of Mathematics and Informatics, Larbi Ben M’Hidi University, Oum El Bouaghi, Algeria. His current research activities are focused in the following aspects: statistical computing, Life time data analysis, distribution theory and statistical software.

References

C.D. Lai, M. Xie and D.N.P. Murthy. A modified Weibull distribution. EEE Transactions on Reliability, 52(1):33-37, 2003.

M. Bebbington, C.D. Lai, and R. Zitikis. A flexible Weibull extension. Reliability Engineering and System Safety, 92:719-726, 2007.

A.M. Sarhan and J. Apaloo. Exponentiated modified weibull extension distribution. Reliability Engineering and System Safety, 112:137-144, 2013.

F. Famoye, C. Lee and O. Olumolade. The beta-Weibull distribution. Journal of Statistical Theory and Applications, 4(2):121-136, 2005.

L. Benkhelifa. The Weibull Birnbaum-Saunders distribution and its applications. Statistics, Optimization and Information Computing, 9(1):61-81, 2021.

W. Nelson. Accelerated life testing: statistical models. data analysis and test plans. New York: Wiley; 1990.

G.O. Silva, E.M. Ortega and G.M. Cordeiro. The beta modified Weibull distribution. Lifetime Data Analysis, 16(3):409-430, 2010.

G.M. Cordeiro, E.M. Hashimoto and E.M. Ortega and . The McDonald Weibull model. Statistics, 48(2):256-278, 2014.

N. Singla, K. Jain and S. Kumar Sharma. The beta generalized Weibull distribution: properties and applications. Reliability Engineering and System Safety, 102:5-15, 2012.

A. Saboor, H.S. Bakouch and M.N. Khan. Beta Sarhan–Zaindin modified Weibull distribution. Applied Mathematical Modelling, 40: 6604, 2016.

B. He and W. Cui. An additive modified Weibull distribution. Reliability Engineering and System Safety, 145:28-37, 2016.

F. Prataviera E.M. Ortega, G.M. Cordeiro, R.R. Pescim and B.A.W. Verssania. A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems. Reliability Engineering and System Safety, 176:13–26, 2018.

A.A. Ahmad and M.G.M. Ghazal. Exponentiated additive Weibull distribution. Reliability Engineering and System Safety, 193:106663, 2020.

S.J. Almalki and J. Yuan. The new modified Weibull distribution. Reliability Engineering and System Safety, 111:164-170, 2013.

S.J. Almalki. Reduced new modified Weibull distribution. Communications in Statistics - Theory and Methods, 47:2297-2313, 2018.

W. Kuo and M.J. Zuo. Reduced new modified Weibull distribution. Optimal reliability modeling: principles and applications. Wiley; 2001.

N. Eugene and F. Famoye. Beta-normal distribution and its applications. Communications in Statistics - Theory and Methods, 31:497-512, 2002.

B.C. Arnold and H.N. Nagarajah. A first course in order statistics. New York: John Wiley, 2008.

I.S. Gradshteyn and I.M. Ryzhik. Table of integrals, Series and Products. Academic Press, New York; 2000.

R.G. Miller, G. Gong and A. Muñoz. Survival analysis. New York: John Wiley and Sons; 1981.

M.V. Aarset. How to identify a bathtub hazard rate. EEE Transactions on Reliability, 36(1):106-108, 1987.

W.Q. Meeker and L.A. Escobar. Statistical methods for reliability data. New York: Wiley; 1998.

Y. Liu and A.I. Abeyratne. Practical applications of bayesian reliability. New York: John Wiley and Sons; 2019.

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Published

2021-06-22

How to Cite

Benkhelifa, L. . (2021). The Beta Reduced Modified Weibull Distribution with Applications to Reliability Data. Journal of Reliability and Statistical Studies, 14(01), 311–322. https://doi.org/10.13052/jrss0974-8024.14116

Issue

2021: Vol 14 Iss 1

Section

Articles