An Efficient Discrete-Time Method for Time-Variant Reliability of Monotonic and Antimonotonic Series and Parallel Systems  
Author Gordon J. Savage


Co-Author(s) Young Kap Son


Abstract Most engineering time-variant reliability problems with component degradation and stochastic loads produce limit-state surfaces with an unpredictable temporal trajectory that may exhibit a combination of increasing and decreasing failure probabilities. In many cases the trajectory is monotonic so that the failure increases predictably. In this paper we present the discrete-time set theory derivation for an important case that can be labelled anti-monotonic motion wherein the limit-state surfaces recede in a predictable manner to provide, what only appears to be, ever decreasing failure probability. Many systems with multiple failure modes exhibit this anti-monotonic motion along with the common monotonic motion. The presence of both monotonic and anti-monotonic motion can be easily detected by a parametric polar plot of the most-likely failure points on the limitstate surfaces. The impact of the work is that the cumulative distribution function (cdf) can be provided with a minimum of fail and safe regions. This in turn gives rise to several solution options such as the multi-normal integral method or a Monte-Carlo simulation that obviates the usual tedious marching-out routine. A series system and a parallel system show the efficacy of the theory.


Keywords Time-variant reliability, Parametric polar plot, Set theory, Monotonic and anti-monotonic motion
    Article #:  RQD28-61

Proceedings of 28th ISSAT International Conference on Reliability & Quality in Design
August 3-5, 2023