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# A Fast Product of Conditional Reduction Method for System Failure Probability Sensitivity Evaluation

Jie Yang1,2, Changping Chen1,2,*, Ao Ma1

1 School of Marine and Civil Engineering, Dalian Ocean University, Dalian, 116023, China
2 Liaoning Provincial Key Laboratory of Coastal Engineering, Dalian Ocean University, Dalian, 116023, China

* Corresponding Author: Changping Chen. Email:

(This article belongs to this Special Issue: Novel Methods for Reliability Evaluation and Optimization of Complex Mechanical Structures)

Computer Modeling in Engineering & Sciences 2020, 125(3), 1159-1171. https://doi.org/10.32604/cmes.2020.09640

## Abstract

System reliability sensitivity analysis becomes difficult due to involving the issues of the correlation between failure modes whether using analytic method or numerical simulation methods. A fast conditional reduction method based on conditional probability theory is proposed to solve the sensitivity analysis based on the approximate analytic method. The relevant concepts are introduced to characterize the correlation between failure modes by the reliability index and correlation coefficient, and conditional normal fractile the for the multi-dimensional conditional failure analysis is proposed based on the two-dimensional normal distribution function. Thus the calculation of system failure probability can be represented as a summation of conditional probability terms, which is convenient to be computed by iterative solving sequentially. Further the system sensitivity solution is transformed into the derivation process of the failure probability correlation coefficient of each failure mode. Numerical examples results show that it is feasible to apply the idea of failure mode relevancy to failure probability sensitivity analysis, and it can avoid multi-dimension integral calculation and reduce complexity and difficulty. Compared with the product of conditional marginal method, a wider value range of correlation coefficient for reliability analysis is confirmed and an acceptable accuracy can be obtained with less computational cost.

## Keywords

Yang, J., Chen, C., Ma, A. (2020). A Fast Product of Conditional Reduction Method for System Failure Probability Sensitivity Evaluation. CMES-Computer Modeling in Engineering & Sciences, 125(3), 1159–1171.

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