Sensitivity Analysis Of System Reliability Research Articles

A novel Bayesian-inference-based method for global sensitivity analysis of system reliability with multiple failure modes

Global reliability sensitivity analysis aims at quantifying the effects of each random source on failure probability or reliability over their whole distribution range and is highly concerned in reliability design and uncertainty control. And in practice, a structure or product usually has more than one component impacting their performance safety, which is essentially a system reliability problem. Therefore, this paper proposes a novel Bayesian-inference-based method for moment-based global sensitivity analysis of system reliability with multiple failure modes. First, the limit-state function of each component involved in the system is linearly approximated based on the reliability index. Then, the global reliability sensitivity is transformed into a problem of multivariable Gaussian probability within a given safe region where the dimension number is double of the failure modes. In this case, the Bayesian-inference-driven expectation propagation technique is introduced to solve this intractable problem in an analytical manner, based on which the closed-form solution to the global reliability sensitivity for system with multiple components is accordingly derived. Finally, a numerical case, a vehicle subjected to impact, a cantilever beam and a practical engineering application to a four-panel spaceborne deployable plane antenna are studied to demonstrate the effectiveness of the proposed method by comparison with Monte Carlo simulation.

Sensitivity analysis of system reliability using the complex-step derivative approximation

Sensitivity analysis of system failure probability is performed to evaluate the dependence of system reliability on design parameters or component events. Sensitivity analysis is integral for the implementation of efficient gradient-based optimization algorithms in system reliability-based design optimization, and for risk-informed decision-making. This paper presents a method for sensitivity analysis of system failure probability using complex-step differentiation. Many derivative approximations use a small step size to minimize subtractive cancellation errors. The complex-step approximation utilizes an imaginary number, such that the subtractive cancellation is not included in the formulation, resulting in calculations without the associated round-off error. The level of accuracy in sensitivity analysis using the finite difference method (FDM) can vary with change in the step size, which is generally selected arbitrarily, as the actual effect of the step size on the result itself is difficult to predict prior to actual calculation. The complex-step approximation, however, is not confined by the step size, as subtraction cancellation is not included. Compared to the FDM, the complex step approximation has only one limit, the numerical precision of evaluating the function. The proposed method integrates complex-step differentiation into a numerical integration scheme, for the assessment of system reliability and sensitivity. System failure probability and sensitivity are obtained by taking the real and imaginary part of the cumulative distribution function, which is numerically evaluated using the proposed method. The computational efficiency for system reliability problems involving high dimensionality is improved with the utilization of a dimension reduction technique. Numerical examples of sensitivity analysis for series, parallel, and general systems are presented to illustrate the performance of the proposed method.

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

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.

Performance analysis of evaporation system in sugar industry using RAMD analysis

The main aim of this study is to analyze the application of reliability, availability, maintainability and dependability in identification of most sensitive subsystem of evaporation system in sugar plant. For this analysis, transition diagram of all subsystems is drawn and respective Chapman–Kolmogorov differential equations are derived using Markov birth–death process. All failure and repair rates of each subsystem are exponentially distributed. Various measures of system effectiveness like mean time between failures, mean time to repair and dependability ratio for all the three subsystems are also computed. Sensitivity analysis of system reliability is also performed. The reliability and maintainability are estimated at various time instants. Analysis of all the subsystems shows that sulphited syrup is highly sensitive from reliability point of view. The derived measures are shared with system designers for their active deliberation.