Reliability analysis for complex systems subject to competing failure processes in an uncertain environment

Reliability analysis of complex systems subject to competing failure processes based on probability theory has received increasing attention. However, in many situations, the observed data is too limited to estimate the parameters and probability distributions of the system by statistic methods. To address this problem, an uncertain degradation models is proposed in this paper under the framework of uncertainty theory. Based on this model, a complex system which is subject to both continuous internal degradation and external shocks is introduced. The continuous internal degradation of the system is controlled by some uncertain factors, and the external shocks are deemed to an uncertain renewal reward process. Reliability for the complex systems is obtained by employing the uncertainty theory. Finally, a case study is presented to demonstrate the effectiveness of the results obtained in the paper.

Condition Maintenance Decision of Wind Turbine Gearbox Based on Stochastic Differential Equation

Maintenance decision analysis is necessary to ensure the safe and stable operation of wind turbine equipment. To address gearboxes with a high failure rate in wind turbines, this paper establishes a new stochastic differential equation model of gearbox state transition to maximize the utilization of gearboxes. This model divides the state of the gearbox into two parts: internal degradation and external random interference. Weibull distribution and polynomial approximation were used to construct the internal degradation model of the gearbox. The external random interference is simulated by Brownian motion. On the basis of the analysis of monitoring data, the parameters of the gearbox state model were solved using the Newton–Raphson iterative method and entropy method. The state change of the gearbox was simulated in MATLAB, and the residual value between the predicted state and the real state was calculated. Compared with the state transformation model constructed by the traditional ordinary differential equation and the gamma distribution, the Weibull polynomial approximation stochastic model can better reflect the state of the device. With reliability set as the decision goal, the maintenance time of the gearbox is predicted, and the validity of the model is verified through case analysis.

Reliability assessment for systems suffering competing degradation and random shocks under fuzzy environment

Reliability assessment of multi-component systems under competing degradation and random shocks has been intensively investigated in recent years. In most cases, the parameters associated with competing degradation and random shocks are represented by crisp values. However, due to insufficient data and vague judgments from experts, it may produce epistemic uncertainty with those parameters and they are befitting to be described as fuzzy numbers. In this article, the internal degradation is treated as a continuous monotonically increasing random process with respect to operating time, whereas the amount of cumulative damage produced by each external random shock is modeled by a geometric process. As components in a system suffer the same environmental condition, an external random shock will produce different amounts of cumulative damage to each component simultaneously. Each component fails when either the internal degradation or cumulative damage from the random shocks, whichever comes first, exceeds its corresponding random thresholds. Moreover, the parameters associated with the internal degradation and the random shocks are represented by triangular fuzzy numbers. The fuzzy reliability functions of components and the entire system are evaluated by a set of optimization models. A multi-component system, together with some comparative results, is presented to illustrate the implementation of the proposed method.