Abstract: To solve the problem of updated comprehensive reliability prediction involving correlated multiple failure modes for the long-life products. The statistical analysis of performance degradation data is studied for the high-reliability and long-life products. Deterministic time series combined models are used to extract the characteristic information of the distribution of degradation variables, and according to the differential equation method, the suited methods are given to estimate the dynamic characteristic parameters of the distribution of degradation variables, also the scalar parameter of correlation among in multiple degradation variables. Based on the positive correlation among in degradation characteristic variables, it builds the suitable copulas reliability model to calculate the comprehensive reliability of products which have dependent multiple failure modes, and promote it to the general model involving correlative interference between random failure threshold and degradation characteristic variables. The Copula theoretical models show that the reliability value of products both rely on the time series characteristics of their strength, but also change in a special interval dynamically with the scalar parameter of correlation among in multiple degradation variables. Finally, an example is given to demonstrate the feasibility and effectiveness of the model.

Key words: Copula, Correlation, Multiple failure modes, Reliability, Time series