Safety and reliability are essential engineering concerns for energy-harvesting installations. In the case of the piezoelectric galloping energy harvester, there is a risk that excessive wake galloping may lead to instability, overload, and thus damage. With this in mind, this paper studies bivariate statistics of the extreme, experimental galloping energy harvester dynamic response under realistic environmental conditions. The bivariate statistics were extracted from experimental wind tunnel results, specifically for the voltage-force data set. Authors advocate a novel general-purpose reliability approach that may be applied to a wide range of dynamic systems, including micro-machines. Both experimental and numerically simulated dynamic responses can be used as input for the suggested structural reliability analysis. The statistical analysis proposed in this study may be used at the design stage, supplying proper characteristic values and safeguarding the dynamic system from overload, thus extending the machine’s lifetime. This work introduces a novel bivariate technique for reliability analysis instead of the more general univariate design approaches.