Reliability Evaluation of an Imprecise Multistate System With Mixed Uncertainty

Reliability evaluation of complex systems like bridge systems or network model is of great interest but challenging as such reliability models cannot be recursively decomposed into combinations of series and parallel systems. The task becomes even more challenging if imprecise parameters are involved. To address such challenges, this article proposes a survival signature-based reliability framework for an imprecise multistate system (IMSS). For probability estimation, the survival signature of IMSS is first defined according to the combination of states of composing elements, and corresponding multistate survival functions are obtained. A simulation method is then developed to calculate the p-box when imprecision is involved. To further address the uncertainty, an approximate Bayesian computation method with a novel Jensen-Shannon divergence-based kernel is developed to perform a stochastic model updating. This method allows a better reliability evaluation result with less uncertainty by calibrating imprecise parameters in the presence of mixed uncertainty. A typical bridge system, which cannot be decomposed as simpler ones, is first cited as a numerical case, followed by a real application example for validation and benefit illustration.

Automated summary

This article proposes a survival signature-based reliability framework for an imprecise multistate system (IMSS) to address the challenges of reliability evaluation for complex systems with imprecise parameters. The framework defines the survival signature and calculates the multistate survival functions based on the combination of states of composing elements. A simulation method is developed for probability estimation when imprecision is involved. An approximate Bayesian computation method with a Jensen-Shannon divergence-based kernel is developed to perform stochastic model updating and calibrate imprecise parameters. The proposed framework is validated with a numerical case of a typical bridge system and a real application example.