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Resistively switching electrochemical metallization memory cells are gaining huge interest since they are seen as promising candidates and basic building blocks for future computation-in-memory applications. However, especially filamentary-based memristive devices suffer from inherent variability, originating from their stochastic switching behavior. A variability-aware compact model of electrochemical metallization memory cells is presented in this study and verified by showing a fit to experimental data. It is an extension of the deterministic model. Since 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. In addition, 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.