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Abstrakty
During the last two decades, statistical methods using lower and upper probabilities have become increasingly popular. One such method is Nonparametric Predictive Inference (NPI), which makes relatively few modelling assumptions. Due to the specic nature of many reliability and risk scenarios, NPI provides attractive new solutions to many problems in these elds. This paper provides an introductory overview to this area, including examples on competing risks, system reliability and prediction of unobserved or even unknown failure modes.
Rocznik
Tom
Strony
39--50
Opis fizyczny
Bibliogr. 48 poz., tab.
Twórcy
autor
- Durham University, Durham, UK
Bibliografia
- [1] Aboalkhair, A.M., Coolen, F.P.A., MacPhee, I.M. (2011). Nonparametric predictive inference for system reliability with subsystems consisting of multiple component types. Proceedings 19th Advances in Reliability and Risk Technology Symposium, Stratford-upon-Avon (UK), April 2011, to appear.
- [2] Al-Nefaiee, A., Coolen, F.P.A. (2011). Nonparametric predictive inference for failure times of systems consisting of exchangeable components. Proceedings 19th Advances in Reliability and Risk Technology Symposium, Stratford-upon-Avon (UK), April 2011, to appear.
- [3] Augustin, T., Coolen, F.P.A. (2004). Nonparametric predictive inference and interval probability. Journal of Statistical Planning and Inference 124, 251-272.
- [4] Augustin, T, Coolen, F.P.A., de Cooman, G., Troffaes, M.C.M. (2011). An Introduction to Imprecise Probabilities. Wiley, to appear (expected early 2012).
- [5] Berger, J.O. (1990). Robust Bayesian analysis: sensitivity to the prior. Journal of Statistical Planning and Inference 25, 303-328.
- [6] Cai, K.Y. (1996). Introduction to Fuzzy Reliability. Kluwer Academic Publishers.
- [7] Coolen, F.P.A. (1993). Imprecise conjugate prior densities for the one-parameter exponential family of distributions. Statistics & Probability Letters 16, 337-342
- [8] Coolen, F.P.A. (1997). An imprecise Dirichlet model for Bayesian analysis of failure data including right-censored observations. Reliability Engineering and System Safety 56, 61-68.
- [9] Coolen, F.P.A. (1998). Low structure imprecise predictive inference for Bayes’ problem. Statistics & Probability Letters 36, 349-357.
- [10] Coolen, F.P.A. (2004). On the use of imprecise probabilities in reliability. Quality and Reliability Engineering International 20, 193-202.
- [11] Coolen, F.P.A. (2006). On nonparametric predictive inference and objective Bayesianism. Journal of Logic, Language and Information 15, 21-47.
- [12] Coolen, F.P.A. (2006). On probabilistic safety assessment in case of zero failures. Journal of Risk and Reliability 220, 105-114.
- [13] Coolen, F.P.A. (2007). Nonparametric prediction of unobserved failure modes. Journal of Risk and Reliability 221, 207-216.
- [14] Coolen, F.P.A. (2011). Nonparametric predictive inference. In: International Encyclopedia of Statistical Science, M. Lovric (Ed.). Springer, pp. 968-970.
- [15] Coolen, F.P.A., Augustin, T. (2005). Learning from multinomial data: a nonparametric predictive alternative to the Imprecise Dirichlet Model. In: Proceedings ISIPTA’05 (www.sipta.org/isipta05), pp. 125-134.
- [16] Coolen, F.P.A., Augustin, T. (2009). A nonparametric predictive alternative to the Imprecise Dirichlet Model: the case of a known number of categories. International Journal of Approximate Reasoning 50, 217-230.
- [17] Coolen, F.P.A., Coolen-Schrijner, P. (2005). Nonparametric predictive reliability demonstration for failure-free periods. IMA Journal of Management Mathematics 16, 1-11.
- [18] Coolen, F.P.A., Coolen-Schrijner, P. (2007). Nonparametric predictive comparison of proportions. Journal of Statistical Planning and Inference 137, 23-33.
- [19] Coolen, F.P.A., Coolen-Schrijner, P., Yan, K.J. (2002). Nonparametric predictive inference in reliability. Reliability Engineering and System Safety 78, 185-193.
- [20] Coolen, F.P.A., Maturi T. (2010). Nonparametric predictive inference for order statistics of future observations. In: Combining Soft Computing and Statistical Methods in Data Analysis, C. Borgelt, et al (Eds.). Springer, pp. 97-104.
- [21] Coolen, F.P.A., Newby, M.J. (1994). Bayesian reliability analysis with imprecise prior probabilities. Reliability Engineering and System Safety 43, 75-85.
- [22] Coolen, F.P.A., Troffaes, M.C., Augustin, T. (2011). Imprecise probability. In: International Encyclopedia of Statistical Science, M. Lovric (Ed.). Springer, 645-648.
- [23] Coolen, F.P.A., Utkin, L.V. (2011). Imprecise reliability. In: International Encyclopedia of Statistical Science, M. Lovric (Ed.). Springer, 649-650.
- [24] Coolen, F.P.A., Yan, K.J. (2003). Nonparametric predictive inference for grouped lifetime data3. Reliability Engineering and System Safety 80, 243-252.
- [25] Coolen, F.P.A., Yan, K.J. (2004). Nonparametric predictive inference with rightcensored data. Journal of Statistical Planning and Inference 126, 25-54.
- [26] Coolen-Maturi, T., Coolen, F.P.A. (2011). Unobserved, re-defined, unknown or removed failure modes in competing risks. Journal of Risk and Reliability, to appear.
- [27] Coolen-Schrijner, P., Coolen, F.P.A. (2004). Adaptive age replacement based on nonparametric predictive inference. Journal of the Operational Research Society 55, 1281-1297.
- [28] Coolen-Schrijner, P., Coolen, F.P.A. (2007). Nonparametric predictive comparison of success-failure data in reliability. Journal of Risk and Reliability 221, 319-327.
- [29] Coolen-Schrijner, P., Coolen, F.P.A. (2007). Nonparametric adaptive age replacement with a one-cycle criterion. Reliability Engineering and System Safety 92, 74-84.
- [30] Coolen-Schrijner, P., Coolen, F.P.A., Shaw, S.C. (2006). Nonparametric adaptive opportunity-based age replacement strategies. Journal of the Operational Research Society 57, 63-81.
- [31] Coolen-Schrijner, P., Coolen, F.P.A., MacPhee, I.M. (2008). Nonparametric predictive inference for systems reliability with redundancy allocation. Journal of Risk and Reliability 222, 463-476.
- [32] Coolen-Schrijner P., Maturi, T.A., Coolen, F.P.A. (2009). Nonparametric predictive precedence testing for two groups. Journal of Statistical Theory and Practice 3, 273-287.
- [33] Fetz, T., Tonon, F. (2008). Probability bounds for series systems with variables constrained by sets of probability measures. International Journal of Reliability and Safety 2, 309-339.
- [34] Hill, B.M. (1968). Posterior distribution of percentiles: Bayes’ theorem for sampling from a population. Journal of the American Statistical Association 63, 677-691.
- [35] Hill, B.M. (1988). De Finetti’s theorem, induction, and A(n) or Bayesian nonparametric predictive inference (with discussion). In: Bayesian Statistics 3, J.M. Bernardo, et al. (Eds.). Oxford University Press, pp. 211-241.
- [36] Lawless, J.F. (2003). Statistical Models and Methods for Lifetime Data (2nd ed.). Wiley.
- [37] Lawless, J.F., Fredette, M. (2005). Frequentist prediction intervals and predictive distributions. Biometrika 92, 529-542.
- [38] MacPhee, I.M., Coolen, F.P.A., Aboalkhair, A.M. (2009). Nonparametric predictive system reliability with redundancy allocation following component testing. Journal of Risk and Reliability 223, 181-188.
- [39] Maturi, T.A., Coolen-Schrijner, P., Coolen, F.P.A. (2010). Nonparametric predictive inference for competing risks. Journal of Risk and Reliability 224, 11-26.
- [40] Oberguggenberger, M., King, J., Schmelzer, B. (2009). Classical and imprecise probability methods for sensitivity analysis in engineering: a case study. International Journal of Approximate Reasoning 50, 680-693.
- [41] Samaniego, F. (2007). System Signatures and their Applications in Engineering Reliability. Springer.
- [42] Troffaes, M.C.M., Coolen, F.P.A. (2009). Applying the Imprecise Dirichlet Model in cases with partial observations and dependencies in failure data. International Journal of Approximate Reasoning 50, 257-268.
- [43] Utkin, L.V., Coolen, F.P.A. (2007). Imprecise reliability: an introductory overview. In: Computational Intelligence in Reliability Engineering, Volume 2: New Metaheuristics, Neural and Fuzzy Techniques in Reliability, G. Levitin (Ed.). Springer, pp. 261-306.
- [44] Utkin, L.V., Zatenko, S.I., Coolen, F.P.A. (2009). Combining imprecise Bayesian and maximum likelihood estimation for reliability growth models. In: Proceedings ISIPTA’09 (www.sipta.org/isipta09), pp. 421-430.
- [45] Walley, P. (1991). Statistical Reasoning with Imprecise Probabilities. Chapman and Hall.
- [46] Walley, P. (1996). Inferences from multinomial data: learning about a bag of marbles (with discussion). Journal of the Royal Statistical Society B 58, 3-57.
- [47] Weichselberger, K. (2000). The theory of interval-probability as a unifying concept for uncertainty. International Journal of Approximate Reasoning 24, 149-170.
- [48] Weichselberger, K. (2001). Elementare Grundbegriffe einer Allgemeineren Wahrscheinlichkeitsrechnung I. Intervallwahrscheinlichkeit als Umfassendes Konzept. Physika.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-538d1fea-5eb5-4aaf-8de5-cb778d281c3e