Abstract
In this paper, we present a new approach for the analysis of lifetime data that are assumed to be described by a two-parameter Weibull distribution. The novel feature of our approach pertains to the incorporation of expert opinion into the analysis. Provision is also made for incorporating our own opinions on the expertise of the experts and also on the lifetimes of items. Our approach involves the use of Laplace’s approximation and this results in formulae which are easy to compute.
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References
Apostolakis, G., and Mosleh, A. (1979). “Expert Opinion and Statistical Evidence: An Application to Reactor Core Melt Frequency,” Nuclear Science Engin eering, No. 70.
Barlow, R. E. and Proschan, F. (1981). Life Distribution Models and Incomplete Data. FSU Statistics Report M-568, The Florida State University, Department of Statistics, Tallahassee, Florida 32306.
De Bruijen, N. G. (1961). Asymptotic Methods in Analysis ,Amsterdam: North-Holland.
Erto, P. (1982). New Practical Bayes Estimators for the 2-Parameter Weibull Distribution. IEEE Transactions on Reliability, Vol. R-31, No. 2 ,pp. 194–197.
Lindley, D. V. (1983). Reconciliation of Probability Distributions. Operations Resear ch, Vol. 31, No. 5 ,pp. 866–880.
Lindley, D. V. and Singpurwalla, N. D. (1986). Reliability (and Fault Tree) Analysis Using Expert Opinion. Journal of the American Statistical Association , Vol. 81, No. 393 ,pp. 87–90.
Martz, H. and Bryson, M. (1984). A Statistical Model for Combining Biased Expert Opinions. IEEE Transactions on Reliability , Vol. R-33, No. 3 ,August 1984.
Martz, H. F., Bryson, C., and Waller, R. A. (1984). Eliciting and Aggregating Subjective Judgments -Some Experimental Results. Proceedings of the 1984 Statistical Symposium on National Energy Issues ,NUREG/CP0063, pp. 63–82.
Mosleh, A., and Apostolakis, G. (1986). “The Assessment of Probability Distributions from Expert Opinions with an Application to Seismic Fragility Curves,” accepted for publication, Risk Analysis ,to appear in 1986.
Okrent, D. (1975). “A Survey of Expert Opinion on Low Probability Earthquakes,” Annals of Nuclear Energy , Vol. 2 ,pp. 601–614.
Singpurwalla, N. D. (1986). An Interactive PC-Based Procedure for Reliability Assessment Incorporating Expert Opinion and Survival Data. The George Washington University Technical Report Serial TR-86/1.
Singpurwalla, N. D. and Song, M. S. (1986). The Analysis of Weibull Lifetime Data Incorporating Expert Opinion. Technical Report GWU/IRRA/Serial TR-86/9, The George Washington University, Washington, DC.
Soland, R. M. (1969). Bayesian Analysis of the Weibull Process with Unknown Scale and Shape Parameters. IEEE Transactions in Reliability , Vol. R-18 ,pp. 181–184.
Tierney, L. and Kadane, J. B. (1986). Accurate Approximations for Posterior Moments and Marginal Densities. Journal of the American Statistical Association, Vol. 81, No. 393 ,pp. 82–86.
Tsokos, C. P. (1972). A Bayesian Approach to Reliability: Theory and Simulation. Proceedings 1972 Annual Reliability and Maintainability Symposium ,San Francisco, pp. 78–87.
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© 1987 Plenum Press, New York
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Singpurwalla, N.D., Song, M.S. (1987). The Analysis of Weibull Lifetime Data Incorporating Expert Opinion. In: Viertl, R. (eds) Probability and Bayesian Statistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1885-9_44
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DOI: https://doi.org/10.1007/978-1-4613-1885-9_44
Publisher Name: Springer, Boston, MA
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