Vector-Process Models for System Reliability

The theoretical and practical viability of multivariate time-dependent failure rate analysis is considered when the reliability model involves crossings of gauss n-vector processes out of safe-regions. While the mathematical approach is not novel, its potential for engineering application had not been explored significantly before. In this sense, a number of specific results — such as the mean failure rate of systems with piecewise linear failure boundary — are derived, which will ease the application to many cases of engineering interest. Multivariate crossing problems of the type examined here arise in the safety study of structural systems subjected to multivariate time-dependent input or with multimodal failure conditions. Two examples of time-dependent static and dynamic structural safety are studied: an RC column under moment and axial force and the joint safety of three separate stories in a building subjected to random support movement.