The Beta Reduced Modified Weibull Distribution with Applications to Reliability Data

  • Lazhar Benkhelifa Department of Mathematics and Informatics, Larbi Ben M’Hidi University, Oum El Bouaghi, 04000, Algeria
Keywords: Beta distribution, Hazard rate function, Modified Weibull distribution, Maximum likelihood estimation.

Abstract

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

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

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

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

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

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

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

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

[9] 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.

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

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

[12] 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.

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

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

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

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

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

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

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

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

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

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

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

Downloads

Download data is not yet available.

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.

Published
2021-06-30
Section
Articles