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The life-cycle reliability of high-power DC electromagnetic devices due to multi-source heterogeneous uncertainties in the design, manufacturing, loads, degradation and cumulative damages has become increasingly prominent, life-cycle reliability optimization has attracted extensive attention. The design optimization strategy based on reliability, which combines the static/time-independent hypothesis and random theory, is inapplicable to life-cycle design optimization. Therefore, a time-dependent uncertainty analysis and life-cycle quality reliability optimization method are proposed in this study. Based on the information entropy transformation method, the fuzzy uncertainty is transformed into a probability density function of equivalent random variables, and intervals for the random variables are determined in the standard normal space. In this way, the heterogeneous uncertainty is unified as an interval type. Moreover, the time-dependent characteristics of the uncertainty parameters are transformed into a time-dependent of the characteristics through ellipsoidal model process. A life-cycle expression method based on an orthonormal basis is proposed to form a life-cycle time-dependent non-probabilistic convex model process. Therefore, the analytical expression of out-crossing rate in which there are many non-probabilistic convex model process parameters are derived and the corresponding upper and lower bounds of out-crossing rate can be obtained. Then, a life-cycle reliability design optimization model is constructed and the optimal solution is determined from intelligence algorithm. The effectiveness of proposed method was verified by a high-power DC electromagnetic relay in renewable energy systems. [ABSTRACT FROM AUTHOR]