Since the physical structure and mathematical models are more complex, reliability analysis in practical engineering can be expensive and difficult. A two-level multifidelity metamodel method for reliability analysis is introduced. Following the surrogate model in most of the relevant works, low-fidelity data and high-fidelity data are integrated by co-Kriging model. Besides, the co-Kriging model also provide an approximation for initial performance function. Bayesian method is adopted in model solution and a hybrid Markov chain Monte Carlo (MCMC) sampling algorithm is proposed. High-fidelity response of reliability performance function is estimated by the conditional distribution derivation based on Bayesian theory. Failure domain is identified by indicator function in sampling space that consists of samples derived from MCMC. Accordingly, failure probability estimations are obtained using Monte Carlo simulation (MCS). It is demonstrated through an illustrative example that the proposed method is valid and accurate.

Reliability analysis based on data from various source is common today. Bayes theory is proved effectively in integrating prior information and field information. However, the complicated calculation and limited applicability have a negative effect on solution. And the fusion is imbalanced in some case. This paper investigates a novel approach to integrate degradation data and lifetime data for reliability analysis. Firstly, inverse Gaussian process model is adopted to model the degradation and the crude estimation can be solved by degradation data. After that, a constrained maximum-entropy Bayesian integration model is proposed for exploring more information from reliability life test. For simplifying the calculation, a pivot variable, failure probability, is defined and updated in this model. This allows us to derive the model parameters by fitting the failure probability curve rather than the calculation on Bayes posterior distribution. Accordingly, the reliability assessment can be conducted based on the inverse Gaussian process model. A case study illustrates the validity and improvement of the proposed method.

The high-fidelity data (HF) referring to the test data from real experiments can more accurately reflect the real performance indicators of the workpieces for reliability analysis in engineering. Due to the limited cost, enough HF data is difficult to be collected to meet the requirement of reliability analysis. Alternatively, a large amount of low-fidelity (LF) experimental data from simulation experiments can be integrated with HF data to achieve reliability estimates with high precision. Existing literatures have studied this problem and made some progress, but the model is rather complicated and the solving efficiency is limited. Therefore, a new data fusion prediction model on reliability evaluation is introduced by Gaussian process (GP) and Bayesian theory. The key idea is to describe the LF and HF response models, respectively, with the same regression parameter and GP correlation parameter. Furthermore, the joint parameters sampling is adopted to estimate the unknown parameters and predict the reliability based on the hybrid Markov chain Monte Carlo algorithm. It is demonstrated through an illustrative example on the Nonlinear oscillation workpiece that the proposed model and sampling methods are flexible and efficient.