Bayesian approach to shipping reliability and safety

• Autorzy: Smolarek L.
• Języki publikacji: EN

Abstrakty

EN

In a Bayesian approach, there are two main sources of information about parameters of interest such as prior beliefs or the prior distribution of the parameter and the likelihood of observing the data given our expectations about the parameter. The prior distribution may be based on previous studies, literature reviews or expert opinions and indicates how we believe the parameter would behave if we had no data upon which to base our judgments. In case where we have less data, the prior has greater influence. The maximum likelihood estimate predominates only when we have a lot of data. The posterior distribution is the result of combining the prior distribution and the likelihood. In the paper the examples of using Bayes approach to shipping operational reliability and safety is presented.

Słowa kluczowe

EN

reliability; safety; shipping; hierarchical Bayes model; prior model

• Wydawca: Polskie Towarzystwo Bezpieczeństwa i Niezawodności
• Czasopismo: Journal of Polish Safety and Reliability Association
• Rocznik: 2012
• Tom: Vol. 3, No. 2
• Strony: 227--236
• Opis fizyczny: Bibliogr. 34 poz.

Twórcy

autor

Smolarek L.

• Maritime University, Gdynia, Poland

Bibliografia

• [1] Alagumalai, S., Curtis, D.D. & Hungi, N. (2005). Applied Rasch Measurement: A Book ofExemplars. Dordrecht, The Netherlands: Springer.
• [2] Banerjee, S., Carlin, B.P., & Gelfand, A.E. (Eds.). (2004). Hierarchical modeling and analysis for spatial data. Boca Raton, Fla.: Chapman & Hall/CRC.
• [3] Barlow, R. E. & Proschan, F. (1975). Statistical Theory of Reliability and Life Testing. Probability Models. Holt Rinehart and Winston, Inc., New York, 1975.
• [4] Bernardo J.M. & Smith A.F.M. (1994). Bayesian Theory. London: Wiley.
• [5] Chien-Min Su1, Ki-Yin Chang, Chih-Yung Cheng. (2012). Fuzzy Decision On Optimal Collision Avoidance Measures For Ships In Vessel Traffic Service. Journal of Marine Science and Technology, Vol. 20, No. 1, 38-48,
• [6] da Silva S.A. & Melo L.M. (2004). Spatial analysis of incidence rates: a Bayesian approach. Retrieved 22 December, 2006, from http://www.leg.ufpr.br/~ehlers/mypapers/ehl04.ht m
• [7] Dey, K.A. (1983). Practical Statistical Analysis for the Reliability Engineer. IIT Research Institute, Rome Air Development Center, Griffiss AFB, NY 13441, USA.
• [8] Devine, O.J., Louis, T.A., & Halloran, M.E. (1994). Empirical Bayes methods for stabilizing incidence rates before mapping. Epidemiology, 5(6), 622-630.
• [9] Everitt, B.S. & Hand D.J. (1981). Finite Mixture Distributions. London: Chapman and Hall.
• [10] Feller, W. (1957). An introduction to Probability Theory and its Applications. New York: Wiley.
• [11] Gelman, A., Carlin, J.B., Stern, H.S. & Rubin, D.B. (2003). Bayesian Data Analysis. Second Edition . Chapman & Hall.
• [12] Gelfand, A. & Smith, A. (1990). Sampling based approaches to calculating marginal densities. J American Statist Assoc, 85, 398-409.
• [13] Greenland, S. (2006). Bayesian perspectives for epidemiological research: I. Foundations and basic methods. Int J Epidemiol, 35(3), 765-775.
• [14] Gucma, L. (1998). Kryterium bezpieczeństwa manewru na torze wodnym. Materiały na Konferencję Explo-Ship, WSM, Szczecin.
• [15] Guze, S. & Smolarek, L. (2011). An approach to modelling the random map of hazards to assess the navigational safety. Zeszyty Naukowe Akademi Morskiej w Szczecinie, 25(97), 59-62.
• [16] Guze, S. Smolarek, L. (2010) Markov model of the ship’s navigational safety model on the open water area. Logistyka, Warszawa.
• [17] Hannaman, G.W., Lukic Y.D., & Spurgin A.J. (1985). Consideration of cognitive processing in human reliability analysis for PRAs, Trans. Am. Nucl. Soc. Annual meeting of the American Nuclear Society, vol. 49.
• [18] Helpern, S. (2001). Podejmowanie decyzji w warunkach ryzyka i niepewności. Wydawnictwo Akademii Ekonomicznej im. Oskara Langego, 2001.
• [19] Kaplan, S. & Garrick, B.J., (1979). On The Use of a Bayesian Reasoning in Safety and reliability Decisions Three Examples. Nuclear Technology, Vol.44, 231-245.
• [20] Koroliuk, V.S. & Limnios, N. (2005). Stochastic Systems in Merging Phase Space. World Scientific Publishing Company Co. Pte. Ltd,Singapore.
• [21] Kopacz, Z., Morgaś, W. & Urbański, J. (2001). The maritime Safety system. Its components and elements. The Journal of Navigation, No 2.
• [22] Padgett, W.J. & Tsokos, C.P. (1979). Bayes Estimation of Reliability Using an Estimated Prior Distribution. Operations Research Vol. 27, No. 6, 1142-1157.
• [23] Purcz (1998). Ship collision aspect unique to inland waterways. Ship Collision Analysis. Gluver H. And Olsen D. (edts.), Balkema, Rotterdam.
• [24] Pietrzykowski, Z. (2007). Assessment of the navigational safety level in ship encounter situations in an open area. Proceedings of the 12th International Scientific and Technical Conference on Marine Traffic Engineering – MTE 2007, Szczecin, 299-206.
• [25] Rost, J. (1990). Rasch models in latent classes: An integration of two approaches to item analysis. Applied Psychological Measurement, 14, 271-282.
• [26] Ripley, B. (1987). Stochastic Simulation. New York: Wiley.
• [27] Ruoxue Zhang, Sankaran Mahadevan, ( 2003). Bayesian methodology for reliability model acceptance. Reliability Engineering and System Safety 80, 95–103.
• [28] Smalko, Z. & Smolarek, L. (2010). Modelling a ship safety according to collision threat for ship routes crossing. Scientific Journals, Maritime University of Szczecin, 20(92), 120-127.
• [29] Smolarek, L. (2008). Niezawodność człowieka w aspekcie bezpieczeństwa statku. Journal of KONBiN, Vol. 2, No 2 (5), 200-207.
• [30] Schum, D.A., (2001). The Evidential Foundations of Probabilistic Reasoning. Northwestern University Press.
• [31] Sinha, S.K. (1986). Bayesian Estimation of the Reliability Function of the Inverse-Gaussian Distribution. Statistics and Probability Letters, 4, 319-323.North-holland.
• [32] Tsionas, G.E. (2001). Bayesian inference in Birnbaum-Saunders Regression. Communication in Statistics-Theory and Methods, 30, 179-193.
• [33] Zhao, J., Wilson, P.A. & Price, W.G. (1994). A study of the ship domain with collision making simulation models. In, 3rd Conference on Marine Craft Manoeuvering and Control (MCMC'94), Southampton, UK, 07 - 09 Sep 1994. Southampton, UK, Computational Mechanics Publications,10pp, 251-260.
• [34] http://www.itl.nist.gov/div898/handbook/