519.248 Cox model validity checking for several progressively censored samples

Timonin V. I. (Bauman Moscow State Technical University), Tyannikova N. D. (Bauman Moscow State Technical University)

NONPARAMETRIC STATISTICS, KIEFER — GIHMAN TYPE CRITERION, KAPLAN — MEYER ESTIMATES, PROGRESSIVE CENSORING, COX MODEL


doi: 10.18698/2309-3684-2017-1-102117


The article proposes a nonparametric criterion of the Kiefer — Gihman type to test the Cox model validity for several progressively censored samples. As estimates of the reliability function for each sample we are using the Kaplan — Meyer ones. The paper proves that if the hypothesis is valid, the Kiefer — Gihman distribution can be used as an approximation of the asymptotic distribution of the criterionstatistics. Based on the particle random walk model over a multidimensional cells array, the paper has developed the method for calculating the exact statistics distributions. The article presents obtained probability values tables of the proposed statistics exact distributions for a wide range of samples possible values. Statistical modeling methods show Cox parameters estimating method consistency, based on the statistics minimization. We present the obtained estimates histograms for the developments exponential distribution to failure. The research results are used when analyzing the redundant technical systems of different multiplicity tests results operating in different operating conditions.
Analyzed systems find applications in all industries — from machine building to radio electronic.


[1] Gnedenko B.V., Belyaev Yu.K., Solovev A.D. Matematicheskie metody v teorii nadezhnosti. Osnovnye kharakteristiki nadezhnosti i ikh statisticheskiy analiz [Mathematical methods in reliability theory. The main characteristics of reliability and their statistical analysis]. Moscow, Librokom Publ., 2013, 584 p.
[2] Sadykhov G.S., Krapotkin V.G., Kazakova O.I. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2014, no. 1 (1), pp. 82–98.
[3] Zarubin V.S., Kuvyrkin G.N. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2014, no. 1 (1), pp. 5–17.
[4] Kiefer J. The Annals of Mathematical statistics, 1959, vol. 30, no. 2, pp. 420–447.
[5] Gihman I.I. Teoriya veroyatnostey i ee primeneniya — Theory of Probability and its Applications, 1957, no. 2, pp. 380–384.
[6] Timonin V.I., Ermolaeva M.A. Elektromagnitnye volny i elektronnye sistemy — Electromagnetic Waves and Electronic Systems, 2011, no. 11, pp. 6–11.
[7] Timonin V.I., Tyannikova N.D. Fizicheskie osnovy priborostroeniya — Physical Bases of Instrumentation, 2016, vol. 5, no. 2 (19), pp. 80–87.
[8] Balakrishnan N., Cramer E. The art of progressive censoring. Applications to reliability and quality. New York, Springer, 2014, 645 p.
[9] Bagdonavicius V., Kruopis J., Nikulin M.S. Nonparametric tests for censored data. London, Wiley, 2011, 233 p.
[10] Ng N., Balakrishnan N. Journal of Statistical Planning and Inference, 2010, vol. 140, no. 8, pp. 2295–2311.
[11] Timonin V.I., Tyannikova N.D. Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki — Herald of Bauman Moscow State Technical University. Series Natural Sciences, 2015, no. 6, pp. 68–84.
[12] Bordes L. Journal of Statistical Planning and Inference, 2004, no. 119, pp. 171–189.
[13] Bolshev L.N., Smirnov N.V. Tablitsy matematicheskoy statistiki [Tables of mathematical statistics]. Moscow, Nauka Publ., 1983, 416 p.
[14] Tyannikova N.D., Timonin V.I. Nauka i obrazovanie — Science and Education, 2014, no. 11. Available at: http://technomag.bmstu.ru/doc/740251.html (accessed May 23, 2017).
[15] Timonin V.I., Tyannikova N.D. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2015, no. 3 (7), pp. 89–100.


Timonin V., Tyannikova N. Cox model validity checking for several progressively censored samples. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 102-117



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