Some Estimation Techniques in Reliability and Survival Analysis Based on Record-Breaking Data
In this paper we review some of the classical and Bayesian results on statistical inference from records that can be used in reliability and survival analysis. We focus on some important lifetime models, giving special attention to heavy-tailed distributions in order to consider applications of record-breaking data to the study of extreme events. Results on the estimation of the number of observations needed to attain a given number of records are also studied in depth. Numerical illustrations and results on the estimation of cost functions are included as well. This chapter can serve as a guide for people interested in making inferences in the fields of reliability and survival analysis when only record values are available.
KeywordsRecord values Heavy tailed distributions Classical inference Bayesian inference Sample-size estimation
The authors thank the referees for their constructive suggestions, which helped to improve the presentation of the paper. Barranco-Chamorro’s research was supported by grant UJA2013/08/01.
- 2.Ahsanullah, M.: Record Values. Theory and Applications. University Press of America, Lanham (2004)Google Scholar
- 11.Gulati, S., Padget, W.J.: Parametric and Nonparametric Inference from Record-Breaking Data. Lecture Notes in Statistics, vol. 172. Springer, Berlin (2003)Google Scholar
- 12.Gulati, S., Shapiro, S.S.: Goodness of fit tests for the Pareto distribution. In: Vonta, F., Nikulin, M., Limnios, N., Huber, C. (eds.) Statistical Models and Methods for Biomedical and Technical Systems, pp. 263–277. Birkhauser, Boston (2008)Google Scholar
- 19.Nelson, W.B.: Accelerated Testing-Statistical Models, Test Plans, and Data Analysis. Wiley, New York (2004)Google Scholar
- 20.Nevzorov, V.B., Balakrishnan, N.: A record of records. In: Handbook of Statistics-16: Order Statistics: Theory and Methods, pp. 515–570. North-Holland, Amsterdam (1998)Google Scholar
- 24.Soh Fotsing, B.D., Anago, G.F., Fogue, M.: Statistical techniques of sample size estimating in fatigue tests. Int. J. Eng. Technol. 2(6), 477–481 (2010)Google Scholar