Robust survival model as an optimization problem

Abstract

A new approach to the identification of a nonlinear multidimensional analytical survival model has been developed based on the gnostical theory of uncertain data. No a-priori statistical model of random data components is assumed; on the contrary: the estimate of the most important characteristic of data uncertainty, its distribution function, is a result of the analysis. This estimation process represents a multidimensional constrained optimization problem. The form of the distribution function is thus determined by the data and may differ from all standard statistical distributions. The estimation of deterministic model parameters can be performed simultaneously with estimation of the distribution of indeterministic data components. All results are robust not only with respect to a-priori statistical assumptions (there are none applied) but also to outliers and peripheral data clusters. Both uncensored and censored data are taken in account for estimation. The method has been successfully implemented and applied to practical problems connected with the evaluation of the reliability of truck components.