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Rejoinder: Concert unlikely, “Jugalbandi” perhaps. (English) Zbl 1442.62222

Summary: This rejoinder to the discussants of “Filtering and tracking survival propensity” [ibid. 31, No. 4, 521–540 (2016; Zbl 1442.62221)] begins with a brief history of the statistical aspects of reliability and its impact on survival analysis and responds to the several issues raised by the discussants [Zbl 1442.62221; Zbl 1442.62218; Zbl 1442.62217; Zbl 1442.62219; Zbl 1442.62220], some of which are conceptual and some pragmatic.

MSC:

62N05 Reliability and life testing
62A01 Foundations and philosophical topics in statistics
62M20 Inference from stochastic processes and prediction
62P30 Applications of statistics in engineering and industry; control charts
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References:

[1] Arjas, E. (1981). The failure and hazard processes in multivariate reliability systems. Math. Oper. Res.6 551-562. · Zbl 0501.60091
[2] Barlow, R. E. and Proschan, F. (1965). Mathematical Theory of Reliability. Wiley, New York. · Zbl 0132.39302
[3] Barlow, R. E. and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York. · Zbl 0379.62080
[4] Bienvenu, L., Shafer, G. and Shen, A. (2009). On the history of martingales in the study of randomness. J. Électron. Hist. Probab. Stat.5 1-40. · Zbl 0071.00414
[5] Cox, D. R. (1972). Regression models and life-tables. J. R. Stat. Soc. Ser. B. Stat. Methodol.34 187-220. · Zbl 0243.62041
[6] Davis, D. J. (1952). An analysis of some failure data. J. Amer. Statist. Assoc.47 113-150.
[7] Dawid, A. P. (2004). Probability, causality and the empirical world: A Bayes-de Finetti-Popper-Borel synthesis. Statist. Sci.19 44-57. · Zbl 1077.60003
[8] Epstein, B. and Sobel, M. (1953). Life testing. J. Amer. Statist. Assoc.48 486-502. · Zbl 0051.36502
[9] Epstein, B. and Sobel, M. (1954). Some theorems relevant to life testing from an exponential distribution. Ann. Math. Stat.25 373-381. · Zbl 0056.38203
[10] Gnedenko, B. V., Belyaev, Y. K. and Soloview, A. D. (1965) Mathematical Methods in Reliability Theory. Nauka, Moscow.
[11] He, W., Williard, N., Osterman, M. and Pecht, M. (2011). Pronostics of lithium-ion batteries on Dempster-Shafer theory and the Bayesian Monte Carlo method. J. Power Sources196 10314-10321.
[12] Kao, J. H. K. (1956). A new life quality measure for electron tubes. IRE Trans. Reliab. Qual. Control7 1-11.
[13] Kao, J. H. K. (1959). A graphical estimation of mixed Weibull parameters in life testing of electronic tubes. Technometrics1 389-407.
[14] Kaplan, E. L. and Meier, P. (1958). Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc.53 457-481. · Zbl 0089.14801
[15] Shafer, G. (1990). The unity and diversity of probability. Statist. Sci.5 435-462. With comments and a rejoinder by the author. · Zbl 0955.01562
[16] Ville, J. (1939). Étude Critique de la Notion de Collectif. Gauthier-Villars, Paris. · Zbl 0021.14601
[17] Weibull, W. (1951). A statistical distribution functions of wide applicabiity. · Zbl 0042.37903
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