Comparing the parameter estimation methods of Weibull distribution with censored lifetime

##plugins.themes.bootstrap3.article.main##

##plugins.themes.bootstrap3.article.sidebar##

PDF
Published Jul 14, 2017
DOI https://doi.org/10.36001/phmap.2017.v1i1.1815
Jihyun Park
Department of Industrial and Management Engineering, Hanyang University, Seoul, 14763, South Korea
Juhyun Lee
Department of Industrial and Management Engineering, Hanyang University, Seoul, 14763, South Korea
Suneung Ahn
Department of Industrial and Management Engineering, Hanyang University, Ansan, Gyeonggi-do, 15588, South Korea

Abstract

Weibull distribution is widely used in reliability engineering and lifetime analysis because of its flexibility in modeling both increasing and decreasing failure rate. Weibull distribution has shape parameter and scale parameter, and it is difficult to estimate the parameters due to the no-closed form of likelihood function. In recent years, there has been studied on the approximating parameter estimation methods based on the simulation. In this study, we use the approximating parameter estimation of Weibull distribution with censored lifetime. The methods which are applied in numerical example are Bayesian estimation method, maximum likelihood estimation, and Markov chain Monte Carlo. Accuracy of estimation methods is performed by the mean square errors of parameter estimator in simulation reducing the experiment time. In addition, it can be helpful to set the design of experiment considering the characteristics of Weibull distribution with censored lifetime.

Abstract 53 | PDF Downloads 101

##plugins.themes.bootstrap3.article.details##

Keywords

PHM

References
An, D., & Choi, J.-H. (2013). Improved MCMC method for parameter estimation based on marginal probability density function. Journal of Mechanical Science and Technology, 27(6), 1771-1779.
Erto, P., & Giorgio, M. (2013). A note on using Bayes priors for Weibull distribution. arXiv preprint arXiv:1310.7056.
Jia, X., Wang, D., Jiang, P., & Guo, B. (2016). Inference on the reliability of Weibull distribution with multiply Type-I censored data. Reliability Engineering & System Safety, 150, 171-181.
Kelly, D., & Smith, C. (2011). Bayesian inference for probabilistic risk assessment: A practitioner's guidebook: Springer Science & Business Media.
Kundu, D., & Mitra, D. (2016). Bayesian inference of Weibull distribution based on left truncated and right censored data. Computational Statistics & Data Analysis, 99, 38-50.
Ntzoufras, I. (2011). Bayesian modeling using WinBUGS (Vol. 698): John Wiley & Sons.
Pradhan, B., & Kundu, D. (2014). Analysis of intervalcensored data with Weibull lifetime distribution. Sankhya B, 76(Part 1), 120-139.
Rinne, H. (2008). The Weibull distribution: a handbook: CRC Press.
Tan, Z. (2009). A new approach to MLE of Weibull distribution with interval data. Reliability Engineering & System Safety, 94(2), 394-403.
Wong, R. K. (1977). Weibull distribution, iterative likelihood techniques and hydrometeorological data. Journal of Applied Meteorology, 16(12), 1360-1364.
Zaidi, A., Ould Bouamama, B., & Tagina, M. (2012). Bayesian reliability models of Weibull systems: State of the art. International Journal of Applied Mathematics and Computer Science, 22(3), 585-600.
Issue
Vol. 1 No. 1 (2017): Proceedings of the Asia Pacific Conference of the PHM Society 2017
Section
Regular Session Papers