Abstract In degradation modeling, stochastic processes often do not meet the classical properties necessary for traditional goodness‐of‐fit tests. This paper presents an initial investigation into employing the ACH depth function and its potential in degradation model selection. We commence by presenting various stochastic processes as degradation models and their selection criteria. Subsequently, we delve into the ACH depth function, highlighting its potential in this context. Through simulated data, we assess the application of this functional depth measure for model selection. The methodology's validity is further reinforced by its application to real‐world data, underscoring its effectiveness.