Advanced Weibull Modelling with Outliers



Published Sep 4, 2023
Yipeng Pang Guoqiang Hu Sungin Cho


This paper presents a comprehensive process for the advanced Weibull modelling with potential outlier inclusions. In this process, an algorithm is designed to identify if there exist any outliers (i.e., failures with different failure modes from the majority) in the failure data of the equipment of interest. Depending on the conditions of the identified outliers, a suitable statistical model is developed. To validate the model, it is compared with the estimated empirical distribution function with the inclusion of new failure data. It is shown that the proposed advanced Weibull model outperforms the two-parameter Weibull model in terms of fitting, and hence a better accuracy is achieved in the failure statistical analysis. Case study in the application of power systems is conducted to illustrate its effectiveness.  

Abstract 189 | PDF Downloads 226



Statistical modelling, Weibull application, Outlier detection

Banerjee, S., & Iglewicz, B. (2007). A simple univariate outlier identification procedure designed for large samples. Communications in Statistics: Simulation and Computation, 36(2), 249–263.

Barnett, V., & Lewis, T. (1994). Outliers in statistical data. Wiley New York.

Dixit, U. J. (1994). Bayesian approach to prediction in the presence of outliers for Weibull distribution. Metrika, 41(1), 127–136.

Fung, K. Y., & Paul, S. R. (2007). Comparisons of outlier detection procedures in weibull or extreme-value distribution. Communications in Statistics Simulation and Computation, 14(4), 895–917.

Gupta, P. K., & Singh, A. K. (2017). Classical and Bayesian estimation of Weibull distribution in presence of outliers. Cogent Mathematics, 4(1).

Nasiri, P., & Pazira, H. (2011). Bayesian Approach on the Generalized Exponential Distribution in the Presence of Outliers. Journal of Statistical Theory and Practice, 4(3), 453–475.

Pettit, L. I. (1988). Bayes Methods for Outliers in Exponential Samples. Journal of the Royal Statistical Society: Series B (Methodological), 50(3), 371–380.

Shu, C., Qin, T., Chen, X., & Yin, P. (2018). Study on Outlier Detection Method in Survival Analysis: Weibull Regression Outlier Model. Journal of Biometrics & Biostatistics, 9(4).

Zhang, H., Gao, Z., Du, C., Bi, S., Fang, Y., Yun, F., . . . Shen, X. (2022). Parameter estimation of three-parameter Weibull probability model based on outlier detection. RSC Advances, 12(53), 34154–34164.
Regular Session Papers