Abstract
The construction of a reliability function from the results of accelerated failure time (AFT) models is considered. The constructed AFT models are verified by analyzing a sample of residuals. The fit of the residual sample to the baseline probability distribution is tested using modified nonparametric goodness-of-fit tests. In the absence of censoring in tests, it is proposed to use previously constructed models of distribution of statistics for testing composite hypotheses. In the case of censoring of type I or II, distributions of the goodness-of-fit test statistics are found by statistical modeling.
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References
J. P. Klein and M. L. Moeschberger, Survival Analysis: Techniques for Censored and Truncated Data (Springer, New York, 2003).
J. F. Lawless, Statistical Models and Methods for Lifetime Data (John Wiley and Sons, Hoboken, 2002).
J. D. Kalbeisch and R. L. Prentice, The Statistical Analysis of Failure Time Data (John Wiley and Sons, New York, 2002).
C. Huber, N. Limnios, and M. Nikulin, Mathematical Methods in Survival Analysis, Reliability and Quality of Life (Wiley-ISTE, New Jersey, 2008).
V. Bagdonavicius and M. Nikulin, Accelerated Life Models. Modeling and Statistical Analysis (Chapman and Hall/CRC, New York, 2002).
M. Nikulin, Accelerated life models, Encyclopedia of Statistics in Quality and Reliability (John Wiley and Sons, New York, 2007), pp. 503–506.
M. Nikulin, “Step Stress Accelerated Life Testing: Classical Methods,” Ibid, pp. 57–62.
A. V. Antonov and M. C. Nikulin, Statistical Models in Reliability Theory: Textbook (Abris, Moscow, 2012).
E. T. Lee and J. W. Wang, Statistical Methods for Survival Data Analysis (John Wiley and Sons, Hoboken, 2003).
D. R. Cox and D. Oakes, Analysis of Survival Data (Finansy i Statistika, Moscow, 1988; Chapman and Hall/CRC, 1984).
B. Yu. Lemeshko, S. Y. Gil’debrant, and S. N. Postovalov, “On the Estimation of Reliability Parameters from Censored Samples,” Zavodskaya Laboratoriya. Diagnostika Materialov 67(1), 52–64 (2001).
B. Yu. Lemeshko, “On the Estimation of the Distribution Parameters and Testing of Hypotheses from Censored Samples,” Metody Menedzmenta Kachestva, No. 4, 32–38 (2001).
B. Yu. Lemeshko and S. N. Postovalov, “On the Distribution of Nonparametric Goodness-of-Fit Tests as Estimated by the Sample Parameters of Experimentally Observed Laws,” Zavodskaya Laboratoriya. Diagnostika Materialov 64(3), 61–72 (1998).
B. Yu. Lemeshko and S. N. Postovalov, “Application of the Nonparametric Goodness-of-Fit Tests for Testing Composite Hypotheses,” Avtometriya, 37(2), 88–102 (2001).
R 50.1.037 — 2002. Recommendations for standardization. Applied Statistics. Rules of Testing the Goodness of Fit of Experimental and Theoretical Distributions. Part II. Nonparametric Tests (Izd. Standartov, Moscow, 2002) [in Russian].
B. Yu. Lemeshko and A. A. Maklakov, “Nonparametric Tests for Testing Composite Hypotheses on Goodnessof-Fit to Exponential Family Distributions,” Avtometriya 40(3), 3–20 (2004).
B. Yu. Lemeshko, S. B. Lemeshko, and S. N. Postovalov, “Statistic Distribution Models for Some Nonparametric Goodness-of-Fit Tests in Testing Composite Hypotheses,” Commun. Statist. Theory and Methods 39(3), 460–471 (2010).
B. Yu. Lemeshko and C. B. Lemeshko, “Models of Distributions of Nonparametric Goodness-of-Fit Test Statistics in Verifying Composite Hypotheses Using Maximum-Likelihood Estimators, Part. I,” Izmeritel’naya Tekhnka, No. 6, 3–11 (2009).
B. Yu. Lemeshko and S. B. Lemeshko, “Models of Distributions of Nonparametric Goodness-of-Fit Test Statistics in Verifying Composite Hypotheses Using Maximum-Likelihood Estimators. Part II”, Izmeritel’naya Tekhnka, No. 8, 17–26 (2009).
K. A. Akushkina, S. B. Lemeshko, and B. Yu. Lemeshko, “Models for Statistical Distributions in Nonparametric Goodness-of-Fit Tests in Testing Composite Hypotheses of the Generalized Weibull Distribution,” in Proc. of the 3rd Intern. Conf. on Accelerated Life Testing, Reliability-Based Analysis and Design, 19–21 May, 2010, Clermont-Ferrand, France, pp. 125–132.
B. Yu. Lemeshko, C. B. Lemeshko, M. C. Nikulin, and H. Saaidia, “Modeling Distributions of Nonparametric Goodness-of Fit Test Statistics in Testing Composite Hypotheses with Respect to the Inverse Gaussian Law,” AIT, No. 7, 83–102 (2010).
B. Yu. Lemeshko and S. B. Lemeshko, “Models of Statistic Distributions of Nonparametric Goodness-of-Fit Tests in Composite Hypotheses Testing for Double Exponential Law Cases,” Commun. Statist. Theory and Methods 40(16), 2879–2892 (2011).
B. Yu. Lemeshko and S. B. Lemeshko, “Construction of Statistic Distribution Models for Nonparametric Goodness-of-Fit Tests in Testing Composite Hypotheses: The Computer Approach,” Quality Technology and Quantitative Management, 8(4), 359–373 (2011).
B. Yu. Lemeshko, C. B. Lemeshko, C. N. Postovalov, and E. V. Chimitova, Statistical Analysis, Modeling, and Investigation of Probabilistic Regularities: Computer Approach (Izd. NGTU, Novosibirsk, 2011).
B. Yu. Lemeshko, E. V. Chimitova, and T. A. Pleshkova, “Testing Simple and Composite Goodness-of-Fit Hypotheses from Censored Samples,” Nauch. Vestn. NGTU, No. 4, 13–28 (2010).
E. L Kaplan and P. Meier, “Nonparametric Estimation from Incomplete Observations,” J. Amer. Statist. Association 5(282), 457–481 (1958).
A. H. Bol’shev and H. V. Smirnov, Tables of Mathematical Statistics (Nauka, Moscow, 1983) [in Russian].
LiTiS — The Software System for Statistical Analysis of Lifetime Data. http://amsa.conf.nstu.ru/amsa2011/Litis.msi.
D. E. Crawford, “Analysis of Incomplete Life Test Data on Motorettes,” Insulation/Circuits 16(10), 43–48 (1970).
R. L. Prentice, “Exponential Survivals with Censoring and Explanatory Variables,” Biometrika 60(2), 279–288 (1973).
B. Yu. Lemeshko and C. N. Postovalov, Computer Technologies of Data Analysis and Investigation of Statistical Regularities: Textbook (Izd. NGTU, Novosibirsk, 2004).
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Original Russian Text © N.S. Galanova, B.Yu. Lemeshko, E.V. Chimitova, 2012, published in Avtometriya, 2012, Vol. 48, No. 6, pp. 53–68.
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Galanova, N.S., Lemeshko, B.Y. & Chimitova, E.V. Using nonparametric goodness-of-fit tests to validate accelerated failure time models. Optoelectron.Instrument.Proc. 48, 580–592 (2012). https://doi.org/10.3103/S8756699012060064
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DOI: https://doi.org/10.3103/S8756699012060064