An important part of optimization is the consideration of convex and non-convex functions. Furthermore, there is no denying the connection between the ideas of convexity and stochastic processes. Stochastic processes, often known as random processes, are groups of variables created at random and supported by mathematical indicators. Our study introduces a novel stochastic process for center-radius (cr) order based on harmonic h-Godunova-Levin ( $\mathcal{G}\mathcal{L}$) in the setting of interval-valued functions ( $\mathcal{I}\mathcal{V}\mathcal{F}\mathcal{S}$). With some interesting examples, we establish some variants of Hermite-Hadamard ( $\mathcal{H}\mathcal{.}\mathcal{H}$) types inequalities for generalized interval-valued harmonic cr-h-Godunova-Levin stochastic processes.