BAYESIAN ESTIMATION OF FOUR PARAMETERS ADDITIVE CHEN-WEIBULL DISTRIBUTION

  • Umar Farouk Abbas
  • Abdulkadir Ahmed
  • Usman Mukhtar
Keywords: Bayes estimators, prior distribution, square error loss function, Chen Distribution, Weibull distribution

Abstract

Models with bathtub-shaped failure rate function have been widely accepted in the field of reliability and medicine and are particularly useful in reliability related decision making and cost analysis. In this study, the additive Chen-Weibull (ACW) distribution with increasing and bathtub-shaped failure rates function is studied using Bayesian and non-Bayesian approach using two real data set. The Bayes estimator were obtained by assuming non-informative prior (Half-Cauchy) under square error loss function (SELF), the Laplace Approximation and Monte Carlo Markov Chain (MCMC) techniques conducted in R were used to approximate the posterior distribution of ACW model. In addition, the maximum product of spacing method (MPS) of estimation is also considered using mpsedist function in BMT package in R with good set of initial values of parameters. We compared the performance of the two difference estimation methods by using Kolmogorov-Smirnov test. And the result showed that MPSEs method outperformed Bayesian approach

References

Ahmad, S. P and Ahmad, K. “Bayesian analysis of weibull distribution Using R Software” Australian Journal of Basic and Applied Sciences, 7(9): 156-164. ISSN 1991- 8178, (2013).

Almaliki, J. Saad and Y. Jingson, “A new modified weibull distribution”. Reliab Eng Syst Safe. 2013; Vol. 111(C):164-170. DOI: 10.1016/j.ress.2013.10.018 (2013).

Al Omari, M. A. (2016). Bayesian study using MCMC of Gompertz distribution based on interval censored data with three loss functions. Journal of applied science, ISSN 1812-5654

Bo H., W. C., Xiofeng, D. “Additive modify weibull distribution”. Reliability engineering system safety 145:28-37(2016)

Chen, R., and Amin, N.“Maximum product of spacing estimation with application to the lognormal distribution”. Mathematical Report 79-1 Cardiff Department of mathematics, UWIST. (1979)

Chen, Z. “A new two parameter lifetime distribution with bathtub-shaped or increasing failure rate function”. Statt probabil Lett. 49:155-161(2000)

Chris. B. G and Noor, A. I. (2012). “Bayesian Analysis of the survival function and failure rate of weibull distribution with censored data”. Mathematical problem in engineering volume 2012, Article ID 329489, doi:10.115/2012/329489 (2012)

Eisa, M., Rahmat, S., Batool, K. and Debasis, K.” Extended exponentaited Weibull (EEW) distribution”. Statistica, department of statistics, University of Bologna, Vol. 78(4), pages 365-396 (2018).

Elgarhy, M., shakil, M. and Elgarhy, K. B. “Exponentiated weibull-Exponential distribution (EWED) with applications”. An international journal of applications and applied mathematics (AAM) Vol. 12 Issue pp. 710-723 (2017).

Govind, S. Mudholkar and Srivastava, D. K. “Exponentiated Weibull family for analyzing Bathtub failure rate”. IEEE T Reliab. 1993; 42:299-302. (1993).

Hastings, W. K “Monte Carlo sampling methods using Markov Chains and their applications”. Biometrika 57, 97-109 (1970).

Hongtao, Z., Tian L. and Qiming C. “Five and four parameter lifetime distribution for bathtub-shaped failure rate using perks mortality equation”. Reliability engineering and system Safety Vol 152, August 2016 https://doi.org/10.1016/j.ress.2016.03.014

Kamram, A., Noshen, Y. A., Amjad, A., Sajjad, A. K., Sadaf, M., Alamgir, K., Umar, K., Dost, M. k., and Zamir, H. “Bayesian analysis of three-parameter Frechet distribution with medical application”. Computational and mathematical methods in medicine Article ID 9089856 (2019)

Lai, C. D, Xie, M and Murthy, D. N. P. “A Modified Weibull distribution”. IEEE T Reliab.2003; 52:33-37

Mohammed, K. S., Atur J. L. and Gauss, M.C. “On the generalized extended exponenetiated weibull (GExEW) distribution”. An international journal of computer mathematics 97:5, 1029-1057 (2019).

Neetu, S., Kanchan, J., and Suresh, S. “The generalized Weibull distribution: properties, estimation and applications”. Reliability engineering, system safety (2012), 102:5-15

Romana, S. and Athar, A. K. “Reliability analysis using exponential power model with bathtub-shaped failure rate function”. A Bayes study. Shehla and Khan springerplus (2016) 5:1079

Sarhan, A. M and Joseph, A. “Exponentiated Modified weibull extension distribution”. Reliab Eng Syst Safe. 2013; 112:137-144

Sarhan, A.M and Zaindin, M. “Modified weibull (MW) distribution” Applied Science 46N30, 47N30, 65C60, (2000)

Tien, T. T and Radim, B. “An Additive Chen-Weibull distribution and its applications in reliability modeling”. A research article (2020). DOI: 10.1002/qre.2740

Vikas, K S., Sanjay, K. S. and Umesh, S. “Classical and Bayesian methods of estimation for power Lindley distribution with application to waiting time data”. Article in communication for statistical application and methods Vol.24, No.3 (2017).

Weibull, W. Investigate in to strength properties of brittle material. Proc. The royal Sweedish for Engr. #149 (1938)

Xie, M and Lai C.D. “Reliability analysis using an additive Weibull model with bathtub shaped failure Rate function”. Reliability engineering (2019).
Published
2022-04-01
How to Cite
AbbasU. F., AhmedA., & MukhtarU. (2022). BAYESIAN ESTIMATION OF FOUR PARAMETERS ADDITIVE CHEN-WEIBULL DISTRIBUTION. FUDMA JOURNAL OF SCIENCES, 6(1), 181 - 190. https://doi.org/10.33003/fjs-2022-0601-891