Modelling and estimation of system reliability under dynamic operating environments and lifetime ordering constraints

This paper proposes a stress-strength time-varying correlation interference model for structural reliability analysis using Copulas. First, the stochastic stress is developed by incorporating the interaction between basic variables and time variable into the quadratic response surface method, and the stochastic strength is characterized by the linear or exponential degradation model. Second, the Copula selection method is given, and we propose time-varying stable (unstable) model for Kendall's tau to describe the time-varying correlation characteristic. Third, the structural reliability estimation method is developed, especially the method for the nondifferentiable Copulas can be used to calculate the probability in any area for any type of Copula when the marginal distribution is continuous. Finally, the lower confidence limit of structural reliability is given based on the survival coefficient. The comparison results of the high-temperature structural reliability estimation from different situations are illustrated in the simulation example to demonstrate the availability of the proposed model.

A Stress-Strength Time-Varying Correlation Interference Model for Structural Reliability Analysis Using Copulas

This paper develops an improved dynamic reliability model for compressor rotor system, defined as a “unconventional active system” here. First, regarding to the variety of system-component connections, system specific reliability modeling technique is presented, in which the stress and strength are both nonnegative stochastic processes. The new model fully considers the load characteristics of rotor blades, and inherently embodied the effect of the statistical dependence between the failures of the rotor blades. Then, calculated by the new model, the relationship between reliability and time, and that between the hazard rate and time, for a compressor rotor system are discussed, respectively. Comparing to the traditional series system reliability model, the new system reliability model developed in this paper has higher accuracy for compressor rotor system, since the traditional models neglect the difference between compressor rotor system and traditional active system. Moreover, in order to master the cruise characteristics of the aero-plane during reliability analysis of its compressor rotor blade set, a flight cruise is separated into several stages based on the value of Mach number and its change rate, and a subsection solution method is innovatively proposed accordingly. At the end of the paper, a certain cruise of fighter plane is analyzed to verify the accuracy of the new method. The results show that, as to a flight cruise with different stages, the new method is basically reasonable to most of the load histories, especially for the situation with impact loads existing.

Reliability Analysis of Aero-Engine Compressor Rotor System Considering Cruise Characteristics

Components in a system work under the same dynamic operating conditions, and their lifetimes are generally positively correlated. Ignorance of the correlation may lead to a significant bias in the evaluation of system reliability. Using the cumulative exposure principle, we model the equivalent operating time of the components, resulting from the cumulative effects of the dynamic environments, as a monotone increasing stochastic time scale. Commonly-used models, such as the compound Poisson, gamma, and the inverse Gaussian processes, are adopted for the stochastic time scale. Based on the above settings, reliability models for multicomponent systems are developed. We investigate how the stochastic time scale influences the system reliability and the correlations between component lifetimes. Under the stochastic time scale, the component lifetimes are shown to be positively quadrant dependent. Overlook of the correlation would overestimate the reliability of a parallel system but underestimate the reliability of a series system. When the stochastic time scale degenerates to a deterministic function of the calendar time, on the other hand, the system reliability becomes the reliability of the system where components work independently. The proposed models are successfully applied to lifetime data of brake pads in the automobile braking system.

System Reliability Evaluation Under Dynamic Operating Conditions

The dynamic reliability model of components is developed using order statistics, and probability differential equations. The relationship between reliability and time, and that between the hazard rate and time, are discussed in this paper. First, according to the statistical meaning of random load application, the cumulative distribution function, and probability density function of equivalent load, when random load is applied at multiple times, are derived. Further, the reliability model of components under repeated random load, is developed. Then, the loading process described under a Poisson process, the dynamic reliability model of components without strength degeneration, and that with strength degeneration are developed respectively. Finally, the reliability, and the hazard rate of components are discussed. The result shows that, when strength doesn't degenerate, the reliability of components decreases over time, and the hazard rate of components decreases over time, too. When strength degenerates, the reliability of components decreases over time more obviously, and the hazard rate curve is bathtub-shaped.

Wang Zheng

Papers

Dynamic Reliability Model of Components Under Random Load