{"references": ["A.S. Ahmad, Bridge preservation guide, maintaining a state of good repair using cost effective investment strategies. Publication FHWA \u2013HIF-11042. FHWA, U.S. Department of Transportation, 2011.", "AASHTO. Manual for Bridge Element Inspection. ISBN: 978-156051-622-4. Pub Code: MBEI-1-I1. American Association of State Highway and Transportation Officials. First Edition. 2013.", "NDOT. Nevada Bridge Inspection Program. Structures Manual, Chapter 28. Nevada Department of transportation, September, 2008.", "A. A. Islam, F. Li, H. Hamid and A. Jaroo, Bridge Condition Assessment and Load Rating using Dynamic Response. The Ohio Department of Transportation. Office of Statewide Planning & Research. State Job Number 134695. July, 2014.", "L.S. Lijun, and G. Ning, \"Deterioration Prediction of Urban Bridges on Network Level Using Markov-Chain Model,\" Hindawi Publishing Corporation, Mathematical problems in Engineering, vol. 2014, Article ID 728107, 2014. doi: 10.1155/2014/728107.", "Y. Jiang, M. Saito, and K.C. Shina, \"Bridge performance prediction model using the Markov chain,\" In Transportation Research Record: Journal of the Transportation Research Board, No. 1180, Transportation Research Board of the National Academies, Washington, D.C., 1988, pp. 25-32.", "Y. Jiang. The development of performance prediction and optimization models for bridge management systems. Dissertation Thesis, Purdue University. Ann-Arbor: ProQuest/UMI, 1990. (Publication No. AAI 9116409.)", "K. Kobayashi, M. Do, and D. Han, \"Estimation of Markovian Transition Probabilities for Pavement Deterioration Forecasting,\" KSCE Journal of Civil Engineering, vol. 14, No. 3, 2009, pp. 343-351. doi: 10.1007/s12205-010-0343-x.", "D. Tolliver, and P. Lu, \"Analysis of Bridge Deterioration Rates: A Case Study of the Northern Plains Region,\" Journal of the Transportation Research Forum, vol. 50, No. 2, Summer 2011, pp. 87-100. \n[10]\tR. M. Gutkowski, and N. D. Arenella, Investigation of Pontis a Bridge Management Software. MPC Report No. 98-95. Colorado State University, 1998\n[11]\tM. A. Shirole, \"Bridge Management to the year 2020 and Beyond,\" In Transportation research record: Journal of the Transportation Research Board, No. 2202, Transportation Research Board of the National Academies, Washington, D.C., 2010, pp. 159\u2013164. \n[12]\tG. Morcous, \"Performance prediction of bridge deck systems using Markov Chains,\" Journal of Performance of Constructed Facilities, American Society of Civil Engineers, vol. 20, No. 2, May 1, 2006. doi: 10.1061/ASCE 0887-3828200620:2146.\n[13]\tS. Ranjith, S. Sentunge, R. Gravina, and S. Venkatesan, \"Deterioration Prediction of timber Bridge Elements using the Markov Chain,\" Journal of Performance of Constructed Facilities, American Society of Civil Engineers, vol. 27, No. 3, 2013, pp. 319-325. Doi: 10.1061/(ASCE)CF.1943-5509.0000311.\n[14]\tD. Tolliver, and P. Lu. Analysis of Bridge Deterioration Rates: A Case Study of the Northern Plains Region.\n[15]\tS. Setunge, and M. S. Hasan. Concrete Bridge Deterioration Prediction using Markov Chain Approach, 2011, Digital Library, University of Moratuwa, Sri Lanka. http://dl.lib.mrt.ac.lk/handle/123/9508. Accessed: December 25th of 2015. \n[16]\tG. Morcous, Developing Deterioration Models for Nebraska Bridges. M302 Final Combined, Mid- America Transportation Center. University of Nebraska-Lincoln, 2011. \n[17]\tD. Veshosky, C. R. Beidleman, G. W. Buetow, and M. Demir, \"Comparative Analysis of Bridge Superstucture Deterioration,\" Journal of Structural Engineering, vol. 120, No 7, 1994. ASCE, ISSN 0733-9445/9/0007-2123\n[18]\tM. A. Cesare, C. Santamarina, C. Turkstra, and H. E. Vanmarcke, \"Modeling bridge deterioration with Markov chains,\" Journal of Transportation Engineering, American Society of Civil Engineers, vol. 118, No. 6, 1992, pp. 1129-1145.\n[19]\tH. Elbehairy, Bridge management system with integrated life cycle cost optimization. University of Waterloo. Thesis requirement for the degree of Doctor of Philosophy in Civil Engineering. Waterloo, Ontario, Canada, 2007."]}

The primary approach for estimating bridge deterioration uses Markov-chain models and regression analysis. Traditional Markov models have problems in estimating the required transition probabilities when a small sample size is used. Often, reliable bridge data have not been taken over large periods, thus large data sets may not be available. This study presents an important change to the traditional approach by using the Small Data Method to estimate transition probabilities. The results illustrate that the Small Data Method and traditional approach both provide similar estimates; however, the former method provides results that are more conservative. That is, Small Data Method provided slightly lower than expected bridge condition ratings compared with the traditional approach. Considering that bridges are critical infrastructures, the Small Data Method, which uses more information and provides more conservative estimates, may be more appropriate when the available sample size is small. In addition, regression analysis was used to calculate bridge deterioration. Condition ratings were determined for bridge groups, and the best regression model was selected for each group. The results obtained were very similar to those obtained when using Markov chains; however, it is desirable to use more data for better results.