Uncertain Random Optimization Models Based on System Reliability

Abstract

The reliability of a dynamic system is not constant under uncertain random environments due to the interaction of internal and external factors. The existing researches have shown that some complex systems may suffer from dependent failure processes which arising from hard failure and soft failure. In this paper, we will study the reliability of a dynamic system where the hard failure is caused by random shocks which are driven by a compound Poisson process, and soft failure occurs when total degradation processes, including uncertain degradation process and abrupt degradation shifts caused by shocks, reach a predetermined critical value. Two types of uncertain random optimization models are proposed to improve system reliability where belief reliability index is defined by chance distribution. Then the uncertain random optimization models are transformed into their equivalent deterministic forms on the basis of α-path, and the optimal solutions may be obtained with the aid of corresponding nonlinear optimization algorithms. A numerical example about a jet pipe servo valve is put forward to illustrate established models by numerical methods. The results indicate that the optimization models are effective to the reliability of engineering systems. It is our future work to consider an interdependent competing failure model where degradation processes and shocks can accelerate each other.

Keywords

• Optimization model
• Chance theory
• Belief reliability
• Hard failure
• Soft failure
• Jet pipe servo valve