Uncertain random accelerated degradation modelling and statistical analysis with aleatory and epistemic uncertainties from multiple dimensions

Accelerated degradation testing (ADT) is commonly employed for degradation analysis and reliability evaluations. Due to limitations in practical ADTs, aleatory and epistemic uncertainties are simultaneously embodied in time, unit, and stress dimensions but they are not considered comprehensively and integrated scientifically currently. To address such problems, we focus on the most common situation in ADTs that test time is relatively long (reflecting aleatory uncertainties in time dimension) while the numbers of test units and stress levels are quite small (reflecting epistemic uncertainties in unit and stress dimensions), and establish an uncertain random accelerated degradation model (URADM). In the URADM, aleatory and epistemic uncertainties are quantified using probability theory and uncertainty theory, respectively, and they are integrated using chance theory. Then, first passage time and reliability evaluations are derived. Next, a three-step uncertain random statistical method is presented for parameter estimations, where aleatory and epistemic uncertainties are divided carefully and quantified separately. A simulation study and a practical case are conducted to show the effectiveness of the URADM. Results reveal that the URADM can not only predict deterministic degradation trends with high accuracy as existing methods do, but contribute degradation boundaries well covering ADT data with narrower boundaries and higher stability.