Reliability estimation method based on nonlinear Tweedie exponential dispersion process and evidential reasoning rule

It is critical to accurately evaluate component reliability to avoid economic losses and safety hazards. Stochastic process models capture dynamic degradation characteristics and incorporate multiple uncertainties and randomness; thus, they have been widely applied in reliability modeling. However, classical stochastic process models do not consider model uncertainty and epistemic uncertainties, such as data conflict, data deviation, and data quality. Among of these, data conflict may result in opposite conclusions and inaccurate reliability evaluation results. Therefore, it is necessary to consider model uncertainty and data conflict in reliability evaluations. In this paper, we propose a novel data-driven reliability evaluation method based on nonlinear Tweedie exponential dispersion process (TEDP) and evidential reasoning rule to address the above problems. The nonlinear TEDP, a general stochastic process model, is proposed to model component degradation. The parameter estimation method is proposed based on evidential reasoning rule considering degradation data conflict. In specific, the likelihood function of nonlinear TEDP is utilized to determine the reliability of evidence. The evidence-integrated importance measure (EIIM) is proposed to assess the weight of evidence by considering evidence conflict and correlation. Two methods for determining the unknown parameters then are proposed based on the evidence joint belief degree matrix (JBDM). Furthermore, optimization model of the discernment frame and the number of hypotheses is constructed to optimize the unknown parameters. Finally, a simulation study is used to demonstrate the effectiveness of the proposed algorithm for statistical inference. Besides, two real case studies are used to demonstrate the model's validity.