Thomas A. Mazzuchi and Refik Soyer. Adaptive Bayesian replacement strategies. In J.M. Bernardo, J.O. Berger, A.P. Dawid, and A.F.M. Smith, editors, Bayesian Statistics 5, pages 667--674. Oxford: Oxford University Press, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and cannot be expressed in explicit form, we have to resort to approximations. For this purpose, it is customary to define discrete distributions in the same way as they were applied to quantify the uncertainty in the shape parameter of a Weibull distribution in Soland [12] and Mazzuchi Soyer [8, 9]. Using Eq. 7) and Bayes theorem, it follows that p ( h ; i j q Gamma q 0 ) l (q Gamma q 0 j h ; i ) p ( h ) p ( i ) P k h=1 P m i=1 l (q Gamma q 0 j h ; i ) p ( h ) p ( i ) 8) where h = L [ 2h Gamma 1) 2] Delta [ U Gamma L ) k] h = 1; k; i = L [ 2i ....

Thomas A. Mazzuchi and Refik Soyer. Adaptive Bayesian replacement strategies. In J.M. Bernardo, J.O. Berger, A.P. Dawid, and A.F.M. Smith, editors, Bayesian Statistics 5, pages 667--674. Oxford: Oxford University Press, 1996.

....with actual data. To overcome these problems, statistical decision theory offers decision makers the means for encoding a priori beliefs about the deterioration process in a prior distribution and for updating this distribution with new deterioration data using Bayes theorem. As Mazzuchi Soyer [11] note, only a few maintenance optimisation models are Bayesian in nature. Van Noortwijk, Cooke Misiewicz [14] have argued that deterioration can best be characterized by the generalized gamma process. Accordingly, it is possible to define discrete time deterioration processes for which the ....

Thomas A. Mazzuchi and Refik Soyer. Adaptive Bayesian replacement strategies. Technical report, The George Washington University, Washington, D.C., U.S.A., 1994.

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