Reliability assessment under incomplete information: an evaluative study

Abstract

Traditionally, in reliability design, the random variables acting on a system are assumed independent. This assumption is usually poor because in most real life problems the variables are correlated. The available information, most of the time, is limited to the first and second moments. Very few methods can handle correlation between the variables when the joint probability density function is unknown. There are no reports that provide information of the accuracy of these methods.

This work presents an evaluative study of reliability under incomplete information, comparing three existing methods for calculating the probability of failure: The method presented by Ang and Tang which assumes the correlation between the variables to be invariant; Kiureghian and Liu/s method which accounts for the change in correlation and; Rackwitz's method under the assumption of independence. We have also developed a new algorithm to generate random samples of correlated random variables when the marginal distributions and correlation coefficients of these variables are specified. These samples can be used in Monte Carlo simulation which is a tool for comparison of the three methods described above. This Monte Carlo simulation approach is based on the assumption of normal joint probability density function as considered by Kiureghian and Liu. To examine if this approach is biased towards Kiureghian and Liu, a second Monte Carlo simulation approach with no assumption about the joint probability density function is developed and compared with the first one.

Both methods that account for correlation show a clear advantage over the traditional approach of assuming that the variables are independent. Moreover, Kiureghian and Liu's approach proved to be more accurate in most cases than Ang and Tang's method.

In this study, it is also shown that there is an error in calculating the safety index for correlated variables when either one of the methods in study is implemented, because the joint probability density function of the random variables is neglected.