How Fast Do Bridge Decks Deteriorate? A Markov Chain From 35,528 Re-inspections in Ohio, Pennsylvania and New York, and a Chapman–Kolmogorov Test That Rejects It

I estimate bridge-deck deterioration from consecutive National Bridge Inventory submissions (2024 and 2025) for Ohio, Pennsylvania and New York. Of 58,003 matched bridges with numeric deck ratings, 35,528 were re-inspected between the two files; 9.2% of re-inspected decks dropped at least one rating and 2.8% improved. From 15,109 inspections 10 to 14 months apart I estimate an annual transition matrix; one-year stay probabilities are 0.92 to 0.96 for ratings 9 to 4. The fundamental matrix gives an expected 67.7 years (bootstrap interval 63.2 to 73.2) for a new deck rated 9 to reach a poor rating of 4 or less, 43.8 years from rating 7 and 16.6 years from rating 5. I prove that for a chain without improvements the expected time is at most the sum of the reciprocal exit rates (73.6 years from rating 9), with equality only if no ratings are skipped. A Chapman–Kolmogorov test compares the squared annual matrix with transitions observed over 22 to 26 months. Within Ohio, two-year stay probabilities exceed the squared one-year values at ratings 9, 8 and 7 (z from 6.2 to 12.2). I prove that such an excess is exactly what a mixture of slow and fast decks produces, and show that Ohio bridges coded for 12-month inspections decline at 7.2% a year against 4.0% for those coded for 24 months. The single homogeneous Markov chain used in many bridge management systems therefore overstates short-run and understates long-run persistence.