Resistively switching electrochemical metallization memory (ECM) cells are gaining huge interest, as they are seen as promising candidates and basic building blocks of future computation-in-memory applications. However, especially filamentary-based memristive devices suffer from inherent variability, originating from their stochastic switching behaviour. A variability-aware compact model of Electrochemical Metallization Memory Cells is presented in this work and verified by showing a fit to experimental data. It is an extension of a deterministic model. As this extension consists of several different features allowing for a realistic variability-aware fit, it depicts a unique model comprising physics-based, stochastically and experimentally originating variabilities and reproduces them well. Also, a physics-based model parameter study is executed, which enables a comprehensive view into the device physics and presents guidelines for the compact model fitting procedure.