Of crucial importance for the application of high temperature superconducting coated conductors (CCs) is the delamination strength due to thermal stress and Lorentz force during their operation. This paper reports the mechanical delamination strengths of YBCO CCs at room temperature and 77 K, as well as the electro-mechanical delamination strength form a modified anvil tensile method. Compared to previous measurement setups, our anvil device only has one degree of freedom of transverse tension. Moreover, we use a vertical soldering technique to ensure the data reliability. Since we eliminate the influence of the measurement method on the experimental results, a naturally discrete property of the delamination strength is obtained. To describe these experimental data, a three-parameter Weibull distribution function has been suggested and a new criterion for determining delamination strength is proposed from the reliability function, which can be conveniently referred to for engineering design.