Time-Dependent Reliability Analysis of Deteriorating Structures Based on Phase-Type Distributions

Abstract

This paper develops a method for the time-dependent reliability analysis of deteriorating structures using phase-type (PH) distributions. The deteriorating model consists of two aspects: the progressive deterioration posed by aging effects, and the shock deterioration caused by random shocks. Evaluating the distribution of the sum of random variables is a tough work in the model. For simplified problems that random variables follow specific distributions with the convolutions being derived analytically, it is effective to utilize semianalytical methods for the time-dependent reliability analysis. For other general problems (the distribution does not have additivity or is even unknown, only with limited datasets), the semianalytical method will no longer be applicable. In dealing with such problems, PH fitting is utilized in the proposed model, i.e., any distribution or general datasets are approximated as PH distributions using Expectation Maximization algorithms. Owing to the good properties in convolution of PH distributions, the time-dependent reliability can be evaluated conveniently. Numerical examples are given to demonstrate the efficiency of the model proposed, and its accuracy is verified by comparing the model results with those of Monte Carlo simulation. The interaction between the degradation process and the shock process is also modeled and displayed with an example and discussion.