Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Point and interval estimation for a simple step-stress model with Type-I censored data from geometric distribution

  • Arefi, Ahmad (Department of Statistics, Ferdowsi University of Mashhad) ;
  • Razmkhah, Mostafa (Department of Statistics, Ferdowsi University of Mashhad)
  • Received : 2016.07.18
  • Accepted : 2016.12.02
  • Published : 2017.01.31
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Abstract

The estimation problem of expected time to failure of units is studied in a discrete set up. A simple step-stress accelerated life testing is considered with a Type-I censored sample from geometric distribution that is a commonly used distribution to model the lifetime of a device in discrete case. Maximum likelihood estimators as well as the associated distributions are derived. Exact, approximate and bootstrap approaches construct confidence intervals that are compared via a simulation study. Optimal confidence intervals are suggested in view of the expected width and coverage probability criteria. An illustrative example is also presented to explain the results of the paper. Finally, some conclusions are stated.

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References

  1. Arefi A and Razmkhah M (2013). Optimal simple step-stress plan for Type-I censored data from geometric distribution, Journal of the Iranian Statistical Society (JIRSS), 12, 193-210.
  2. Arefi A, Razmkhah M, and Mohtashami Borzadaran GR (2011). Bayes estimation for a simple stepstress model with Type-I censored data from the geometric distribution, Journal of Statistical Research of Iran, 8, 149-169.
  3. Bagdonavicius V and Nikulin M (2002). Accelerated Life Models: Modeling and Statistical Analysis, Chapman & Hall/CRC Press, Boca Raton, FL.
  4. Balakrishnan N, Cramer E, and Dembinska A (2011). Characterizations of geometric distribution through progressively Type-II right-censored order statistics, Statistics, 45, 559-573. https://doi.org/10.1080/02331880903573146
  5. Balakrishnan N and Han D (2008). Exact inference for a simple step-stress model with competing risks for failure from exponential distribution under Type-II censoring, Journal of Statistical Planning and Inference, 138, 4172-4186. https://doi.org/10.1016/j.jspi.2008.03.036
  6. Balakrishnan N and Iliopoulos G (2010). Stochastic monotonicity of the MLEs of parameters in exponential simple step-stress models under Type-I and Type-II censoring, Metrika, 72, 89-109. https://doi.org/10.1007/s00184-009-0243-6
  7. Balakrishnan N and Xie Q (2007a). Exact inference for a simple step-stress model with Type-I hybrid censored data from the exponential distribution, Journal of Statistical Planning and Inference, 137, 3268-3290. https://doi.org/10.1016/j.jspi.2007.03.011
  8. Balakrishnan N and Xie Q (2007b). Exact inference for a simple step-stress model with Type-II hybrid censored data from the exponential distribution, Journal of Statistical Planning and Inference, 137, 2543-2563. https://doi.org/10.1016/j.jspi.2006.04.017
  9. Balakrishnan N, Xie Q, and Kundu D (2009). Exact inference for a simple step-stress model from the exponential distribution under time constraint, Annals of the Institute of Statistical Mathematics, 61, 251-274. https://doi.org/10.1007/s10463-007-0135-3
  10. Casella G and Berger R (1990). Statistical Inference, Brooks/Cole Publishing, Pacific Grove, CA.
  11. Chen SM and Bhattacharyya GK (1988). Exact confidence bound for an exponential parameter under hybrid censoring, Communication in Statistics-Theory and Methods, 17, 1858-1870.
  12. Childs A, Chandrasekar B, Balakrishnan N, and Kundu D (2003). Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution, Annals of the Institute of Statistical Mathematics, 55, 319-330.
  13. Davarzani N and Parsian A (2011). Statistical inference for discrete middle-censored data, Journal of Planning and Inference, 141, 1455-1462. https://doi.org/10.1016/j.jspi.2010.10.012
  14. Efron B and Tibshirani RJ (1993). An Introduction to the Bootstrap, Chapman & Hall, New York.
  15. Gupta RD and Kundu D (1998). Hybrid censoring with exponential failure distributions, Communication in Statistics-Theory and Methods, 27, 3065-3083. https://doi.org/10.1080/03610929808832273
  16. Han D and Balakrishnan N (2010). Inference for a simple step-stress model with competing risks for failure from the exponential distribution under time constraint, Computational Statistics & Data Analysis, 54, 2066-2081. https://doi.org/10.1016/j.csda.2010.03.015
  17. Kundu D and Basu S (2000). Analysis of incomplete data in presence of competing risks, Journal of Statistical Planning and Inference, 87, 221-239. https://doi.org/10.1016/S0378-3758(99)00193-7
  18. Nelson W (1990). Accelerated Testing: Statistical Models, Test, Plans and Data Analyses, Wiley, New York.
  19. Rezaei AH and Arghami NR (2002). Right censoring in a discrete life model, Metrika, 55, 151-160. https://doi.org/10.1007/s001840100135
  20. Wang R, Xu X, Pan R, and Sha N (2012). On parameter inference for step-stress accelerated life test with geometric distribution, Communication in Statistics-Theory and Methods, 41, 1796-1812. https://doi.org/10.1080/03610926.2010.551455