Simplified Exhaustive Search Approach for Estimating the Nonhomogeneous Transition Probabilities for Infrastructure Asset Management

A simplified exhaustive search approach is proposed to estimate the nonhomogeneous transition probabilities for a particular infrastructure element. The yearly nonhomogeneous transition probabilities associated with discrete-time Markovian chains can be estimated for a given analysis period mainly using observed performance ratings. The proposed approach is applicable to Markov chains comprised of only two state transitions, namely remaining in the same current state or transiting to the next worse one. The exhaustive search aims at finding two optimal deterioration exponents that would yield the optimal initial and terminal transition probabilities subject to a minimal difference between the predicted and observed performance ratings for each transition. Therefore, the exhaustive optimization is mainly carried out with respect to two parameters only. A limited number of annual infrastructure performance ratings spanned over an analysis period is required to estimate the corresponding initial and terminal transition probabilities. In contrast, the intermediate transition probabilities for each transition can be estimated using either linear or quadratic approximation. The sample results presented for both hypothetical and actual performance data indicated the simplicity and efficiency of the proposed approach in yielding reliable optimal solutions. In particular, the results indicated that there is more than one compatible solution, and that a Markov chain with a smaller size is required when the deterioration rates are higher considering only two state transitions.