This paper provides a general theoretical framework of time space modelling for Lebesgue sampling-based fault diagnosis and prognosis, with the detailed theoretical analysis and experimental simulation for its mathematical modelling and uncertainty quantification. The developed framework introduces the concept of sequential estimation and prediction of "Mean Reach Time" for fault degrading to predefined Lebesgue states. The proposed formulation comprehensively shows the robustness and generalization of the Time Space Model. It also demonstrates its effectiveness in reducing model complexity and elaborates its easy integration with commonly used techniques. Two applications are presented regarding batteries capacity degradation and bearings degradation. The results demonstrate the compatibility, effectiveness, and modelling simplicity of the proposed formulation.