<![CDATA[It is the general character of most engineering systems that failure statistical correlation of elements exists in the fatigue happened process due to the twin loads．Based on randomized Basquin equation，the constitutive relations are established between element life and random variable including twin loads，initial strength,fatigue strength exponent．Product-moment correlation coefficients are derived and used to quantify the dependence of logarithm life of elements．Aim at fatigue life correlation of elements in structural systems, the computation model of the system reliability is preliminarily established by means of using copula function. The new model can express the dependence of elements fatigue life in structural systems, can be used probability prediction of structural systems under common stochastic cyclic load, which gives a new path for reliability-based design and probability assesment in equipment systems with multi-mode damage coupling．]]>
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