Relation between aging intensity function and WPP plot and its application in reliability modelling

Parameter estimation on heavily censored data is a challenging problem, and new methods are needed. This paper aims to address this issue. It is based on a relation between the Weibull probability paper (WPP) plot and the aging intensity function (AIF): the slope of tangent line of the WPP plot is equal to the AIF. Based on this property, a WPP-based local regression method is developed to obtain the empirical AIF, which can aid model selection; and a WPP-based global regression method is proposed to obtain a sample of the shape parameter of a distribution, from which the shape parameter is estimated. Once this is done, the point estimate of the shape parameter is fixed and a single-parameter maximum likelihood method is used to estimate the scale parameter. The proposed method is applicable for both the Weibull and non-Weibull distributions. Two examples are included to illustrate the proposed method and its appropriateness. The results show that the proposed method outperforms the existing methods in terms of applicability, simplicity, accuracy, robustness and unbiasness.

Automated summary

This paper introduces a parameter estimation method based on the Weibull probability paper plot, which can obtain a sample of the shape parameter and estimate the scale parameter through a maximum likelihood method. Experimental results show that this method outperforms existing methods in various aspects.