×

A Bayesian failure model based on isotropic deterioration. (English) Zbl 0905.90092

Summary: We focus on determining a new failure model for hydraulic structures. The failure model is based on the only information which is commonly available: the amount of deterioration averaged over a finite or an infinite time-horizon. By introducing a prior density for the average deterioration per unit time, we account for uncertainty in a decision problem. Advantages of our Bayesian approach are that we base our probabilistic models on a physical observable quantity, the deterioration, and that the probabilities of preventive repair and failure can be expressed explicitly conditional on the average deterioration. One illustration from the field of hydraulic engineering is studied.

MSC:

90B25 Reliability, availability, maintenance, inspection in operations research
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ang Alfredo, H.-S.; Tang Wilson, H., (Probability Concepts in Engineering Planning and Design; Volume II: Decision, Risk and Reliability (1984), Wiley: Wiley New York, NY)
[2] Barlow Richard, E.; Mendel Max, B., De Finetti-type representations for life distributions, Journal of the American Statistical Associations, 87, 420, 1116-1122 (December 1992)
[3] Cooke, R.; Misiewicz, J.; Mendel, M., Applications of \(l_p\) symmetric measures to bayesian inference, (Kasprzak, W.; Weron, A., Stochastic Methods in Experimental Sciences (1990), World Scientific: World Scientific Singapore), 96-113 · Zbl 0817.62020
[4] de Finetti, Bruno, La prévision: ses lois logiques, ses sources subjectives, Annales de l’Institute Henri Poincaré, 7, 1-68 (1937) · Zbl 0017.07602
[5] DeGroot Morris, H., Optimal Statistical Decisions (1970), McGraw-Hill: McGraw-Hill New York · Zbl 0225.62006
[6] Dekker, Rommert, Applications of maintenance optimisation models: A review and analysis, (Technical Report 9228/A (May 1992), Erasmus University Rotterdam: Erasmus University Rotterdam The Netherlands) · Zbl 0905.90086
[7] Diaconis, Persi; Ylvisaker, Donald, Quantifying prior opinion, (Bernardo, J. M.; DeGroot, M. H.; Lindley, D. V.; Smith, A. F.M., Bayesian Statistics 2 (1985), North-Holland: North-Holland Amsterdam), 133-156 · Zbl 0673.62004
[8] Gijsbers, F. B.J., Optimalisatie van onderhoud, Technical Report B-86-549, IBBC-TNO (April 1987), Delft, The Netherlands
[9] Kok, M., Onderhoud; methoden voor rationeel onderhoud van civiele constructies, (Technical Report Q606 (September 1990), Delft Hydraulics: Delft Hydraulics Delft, The Netherlands)
[10] Mendel, Max B., Bayesian parametric models for lifetimes, (Bernardo, J. M.; Berger, J. O.; Dawid, A. P.; Smith, A. F.M., Bayesian Statistics 4 (1992), Oxford University Press), 697-705
[11] Mendel, Max Bernhard, Development of Bayesian parametric theory with applications to control, (PhD thesis (June 1989), Massachusetts Institute of Technology: Massachusetts Institute of Technology Cambridge, MA)
[12] Raiffa, Howard; Schlaifer, Robert, Applied Statistical Decision Theory, (Studies in Managerial Economics (1961), Harvard University: Harvard University Boston, MA) · Zbl 0952.62008
[13] van Noortwijk, Jan M., Inspection and repair decisions for hydraulic structures under symmetric deterioration, (Technical Report ESRC 92-17 (June 1992), University of California at Berkeley)
[14] van Noortwijk, Jan M.; Cooke, Roger M.; Misiewicz, Jolanta K., A characterization of generalized gamma processes in terms of isotropy, (Technical Report 94-65 (1994), Delft University of Technology: Delft University of Technology Delft, The Netherlands)
[15] Watson, Ian; Finkl, Charles W., Simplified technical summary of the complete Delta Works, including the Eastern Scheldt, Journal of Coastal Research, 10, 1-56 (1992)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.