Aging-Intensity-Based Model Selection and Parameter Estimation on Heavily Censored Data

Abstract

The life distributions of product's components should be built as early as possible since many applications need them. The data for modelling are often heavily censored. In this case, it is a challenging issue to estimate the parameters. This paper proposes a new estimation method to address this issue. The proposed method estimates the shape parameter of a two-parameter life distribution through combining the concept of aging intensity with a semi-parametric smoothing TTT approach. The aging intensity of the Weibull distribution equals to its shape parameter; the smoothing TTT approach can be used to estimate the empirical aging intensity function, from which three representative values of the shape parameter are defined. Fixing each of them, the scale parameter is estimated using a singleparameter maximum likelihood method. In such a way, three distributions are fitted, from which a regression model is built to approximate the non-parametric estimates of the distribution function. The best model is selected based on the values of regression coefficients. Two examples are included to illustrate the appropriateness of the proposed approach.