×

zbMATH — the first resource for mathematics

Confidence regions in step-stress experiments with multiple samples under repeated type-II censoring. (English) Zbl 1412.62128
Summary: In a multi-sample general step-stress model with pre-specified numbers of observations under all stress levels, confidence regions for associated parameters are provided with minimum volume, minimum coverage probabilities of false parameters, or based on divergence measures.

MSC:
62N01 Censored data models
62G30 Order statistics; empirical distribution functions
62L12 Sequential estimation
62G15 Nonparametric tolerance and confidence regions
Software:
SPLIDA
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bagdonavińćius, V.; Nikulin, M., Accelerated Life Models: Modeling and Statistical Analysis, (2001), Chapman & Hall/CRC: Chapman & Hall/CRC Boca Raton · Zbl 1100.62544
[2] Balakrishnan, N., A synthesis of exact inferential results for exponential step-stress models and associated optimal accelerated life-tests, Metrika, 69, 2, 351-396, (2009) · Zbl 1433.62287
[3] Balakrishnan, N.; Kamps, U.; Kateri, M., A sequential order statistics approach to step-stress testing, Ann. Inst. Statist. Math., 64, 2, 303-318, (2012) · Zbl 1237.62100
[4] Bedbur, S., UMPU tests based on sequential order statistics, J. Statist. Plann. Inference, 140, 9, 2520-2530, (2010) · Zbl 1188.62264
[5] Bedbur, S.; Beutner, E.; Kamps, U., Generalized order statistics: an exponential family in model parameters, Statistics, 46, 2, 159-166, (2012) · Zbl 1241.62074
[6] Bedbur, S.; Beutner, E.; Kamps, U., Multivariate testing and model-checking for generalized order statistics with applications, Statistics, 48, 6, 1297-1310, (2014) · Zbl 1304.62040
[7] Bedbur, S.; Kamps, U.; Kateri, M., Meta-analysis of general step-stress experiments under repeated type-II censoring, Appl. Math. Model., 39, 8, 2261-2275, (2015)
[8] Bedbur, S.; Lennartz, J. M.; Kamps, U., Confidence regions in models of ordered data, J. Stat. Theory Pract., 7, 1, 59-72, (2013)
[9] Billingsley, P., Convergence of Probability Measures, (2008), Wiley: Wiley New York · Zbl 0172.21201
[10] Cramer, E.; Kamps, U., Sequential \(k\)-out-of-\(n\) systems, (Balakrishnan, N.; Rao, C. R., Advances in Reliability, Handbook of Statistics, vol. 20, (2001), Elsevier: Elsevier Amsterdam), 301-372 · Zbl 0988.62027
[11] Deshpande, J. V.; Dewan, I.; Naik-Nimbalkar, U. V., A family of distributions to model load sharing systems, J. Statist. Plann. Inference, 140, 6, 1441-1451, (2010) · Zbl 1185.62174
[12] Dharmadhikari, S.; Joag-Dev, K., Unimodality, Convexity, and Applications, (1988), Elsevier: Elsevier Boston · Zbl 0646.62008
[13] Han, D.; Ng, H. K.T., Comparison between constant-stress and step-stress accelerated life tests under time constraint, Nav. Res. Logist., 60, 7, 541-556, (2013)
[14] Jeyaratnam, S., Minimum volume confidence regions, Statist. Probab. Lett., 3, 6, 307-308, (1985) · Zbl 0586.62040
[15] Kamps, U., A concept of generalized order statistics, J. Statist. Plann. Inference, 48, 1, 1-23, (1995) · Zbl 0838.62038
[16] Kamps, U., Generalized order statistics, (Balakrishnan, N.; Brandimarte, P.; Everitt, B.; Molenberghs, G.; Piegorsch, W.; Ruggeri, F., Wiley StatsRef: Statistics Reference Online, (2016), Wiley: Wiley Chichester), 1-12
[17] Kateri, M.; Kamps, U., Hazard rate modeling of step-stress experiments, Annu. Rev. Stat. Appl., 4, 1, 147-168, (2017)
[18] Kateri, M.; Kamps, U.; Balakrishnan, N., A meta-analysis approach for step-stress experiments, J. Statist. Plann. Inference, 139, 9, 2907-2919, (2009) · Zbl 1168.62092
[19] Kateri, M.; Kamps, U.; Balakrishnan, N., Step-stress testing with multiple samples: the exponential case, (Balakrishnan, N., Methods and Applications of Statistics in Engineering, Quality Control and the Physical Sciences, (2011), Wiley: Wiley Hoboken), 644-665
[20] Meeker, W. Q.; Escobar, L. A., Statistical Methods for Reliability Data, (1998), Wiley: Wiley Hoboken · Zbl 0949.62086
[21] Nelson, W. B., Accelerated Testing: Statistical Models, Test Plans and Data Analysis, (2004), Wiley: Wiley Hoboken
[22] Pardo, L., Statistical Inference Based on Divergence Measures, (2006), Chapman & Hall/CRC: Chapman & Hall/CRC Boca Raton · Zbl 1118.62008
[23] Shao, J., Mathematical Statistics, (2003), Springer: Springer New York · Zbl 1018.62001
[24] Vuong, Q. N.; Bedbur, S.; Kamps, U., Distances between models of generalized order statistics, J. Multivariate Anal., 118, 24-36, (2013) · Zbl 1277.62133
[25] Wang, R.; Fei, H., Conditions for the coincidence of the TFR, TRV and CE models, Statist. Papers, 45, 3, 393-412, (2004) · Zbl 1048.62097
[26] Xu, H.; Tang, Y., Commentary: the Khamis/Higgins model, IEEE Trans. Reliab., 52, 1, 4-6, (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.