Reliability modelling considering multi-dimensional cognitive uncertainties based on uncertainty theory

Aiming at the multi-dimensional cognitive uncertainties in performance degradation modelling for small samples, a reliability assessment method is proposed based on uncertainty theory. First, a degradation model is established based on the uncertain process, which considers cognitive uncertainties from the time fluctuation, the measurement error, and the individual differences in initial value and degradation rate, and the reliability function is derived. Then, a two-step parameter estimation method for the degradation model is proposed based on the α-path and the least square, which is verified by numerical simulation. Finally, the effectiveness and superiority of the proposed method are verified by the cases of GaAs lasers and magneto-optic data storage disks, and parameter sensitivity analysis is conducted. The results indicate that uncertainty affects product reliability greatly. For small samples, the degradation models considering multi-dimensional uncertainties based on the Liu process has smaller fitting errors than that based on the Wiener process.