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International Society of Science and Applied Technologies |
| An Efficient Discrete-Time Method for Time-Variant Reliability of Monotonic and Antimonotonic Series and Parallel Systems | ||||
| Author | Gordon J. Savage
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| Co-Author(s) | Young Kap Son
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| 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.
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| 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 |