A non-homogeneous Markov chain framework predicts the load-deflection curve in relation to different loads and deflections for the beams being tested. The load–deflection response was modeled using six discrete load levels and seven deflection states, where the deflection at midspan (discrete-state) can occur in a defined range or “delta c” (minimum to maximum). The transition matrices are derived from characteristics of the specimen beams (using ACI and AISC) and from the experimental measurement of the epochal test results of load and deflections, along with the associated time sequences through the “Markov” model. Incremental deflection was modeled using a normal distribution as a simplifying probabilistic assumption to estimate transition probabilities between discrete deflection states. Furthermore, the distribution has been evaluated by analyzing the mean-square-error (MSE). Two specimen beams were included in the evaluation (C1 and C2), and the performance was assessed using root mean square error (RMSE), normalized root mean square error (NRMSE), mean absolute percentage error (MAPE), accuracy acceptance (AA), coefficient of determination (R²), and Pearson correlation coefficient (Pearson R). Beam C1 RMSE was 3.03 mm, AA = 97.62%, and R2 = 0.9920. Beam C2 RMSE was 6.64 mm, AA = 93.03%, and R2 = 0.9783. Within the proposed Markov framework, failure probability is defined as the probability that the beam reaches the terminal deflection state associated with a predefined limit state.
