基于不确定理论的退化数据分析方法

As a traditional mathematical tool in reliability field, the probability theory is not applicable to solve the problem that modern reliability engineering encounters with. Taking the application of the uncertainty theory in degraded data analysis as the entry point, the fundamental axioms, operational rules and statistical methods of the uncertainty theory are expounded, and the reliability modeling guideline based on the brief reliability theory is provided. The methods of degraded data analysis and reliability modeling considering uncertain failure threshold is proposed. The degradation equation is established by adopting the time-varying uncertain normal distribution, and the uncertainty distribution of the failure threshold is constructed according to the expert's knowledge, so as to obtain the margin equation of the product. Finally, the reliability model is deduced based on the measurement equation. The problems of parameter estimation and model verification are solved by using the maximum likelihood estimation method and hypothesis test method of uncertain statistics, respectively. The case study shows that the reliability assessment results will obviously deviate if the uncertainty of failure threshold is not considered. The research indicates that the uncertainty theory is suitable to deal with the uncertainty problems in degradation data analysis and has a broad application prospect.