Skip to main content
SpringerLink
Log in

Point Estimation in Progressive Type-I Censoring

  • Chapter
  • First Online:
The Art of Progressive Censoring

Part of the book series: Statistics for Industry and Technology ((SIT))

  • 1693 Accesses

Abstract

Results on likelihood inference in progressive Type-I censoring are reviewed for a plenty of distributions including one- and two-parameter exponential, extreme value, Weibull, normal, and Burr distributions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Balakrishnan N, Aggarwala R (2000) Progressive censoring: theory, methods, and applications. Birkhäuser, Boston

    Book  Google Scholar 

  2. Balakrishnan N, Cohen AC (1991) Order statistics and inference: estimation methods. Academic, Boston

    MATH  Google Scholar 

  3. Balakrishnan N, Kateri M (2008) On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data. Stat Probab Lett 78:2971–2975

    Article  MATH  MathSciNet  Google Scholar 

  4. Balakrishnan N, Han D, Iliopoulos G. (2011c) Exact inference for progressively Type-I censored exponential failure data. Metrika 73:335–358

    Article  MATH  MathSciNet  Google Scholar 

  5. Cohen AC (1963) Progressively censored samples in life testing. Technometrics 5:327–329

    Article  MATH  MathSciNet  Google Scholar 

  6. Cohen AC (1965) Maximum likelihood estimation in the Weibull distribution based on complete and on censored samples. Technometrics 7:579–588

    Article  MathSciNet  Google Scholar 

  7. Cohen AC (1966) Life testing and early failure. Technometrics 17:347–351

    Article  Google Scholar 

  8. Cohen AC (1975) Multi-censored sampling in the three parameter Weibull distribution. Technometrics 17:347–351

    Article  MATH  MathSciNet  Google Scholar 

  9. Cohen AC (1976) Progressively censored sampling in the three parameter log-normal distribution. Technometrics 18:99–103

    Article  MATH  MathSciNet  Google Scholar 

  10. Cohen AC (1991) Truncated and censored samples. theory and applications. Marcel Dekker, New York

    Google Scholar 

  11. Cohen AC (1995) MLEs under censoring and truncation and inference. In: Balakrishnan N, Basu AP (eds) The exponential distribution: theory, methods, and applications. Gordon and Breach, Newark, pp 33–51

    Google Scholar 

  12. Cohen AC, Norgaard NJ (1977) Progressively censored sampling in the three-parameter gamma distribution. Technometrics 19:333–340

    Article  MATH  MathSciNet  Google Scholar 

  13. Cohen AC, Whitten BJ (1988) Parameter estimation in reliability and life span models. Marcel Dekker, New York

    MATH  Google Scholar 

  14. Cramer E, Tamm M (2013) On a correction of the scale MLE for a two-parameter exponential distribution under progressive Type-I censoring. Comm Stat Theory Meth (to appear)

    Google Scholar 

  15. Epstein B (1960) Estimation from life test data. Technometrics 2:447–454

    Article  MATH  MathSciNet  Google Scholar 

  16. Gajjar A, Khatri C (1969) Progressively censored samples from log-normal and logistic distributions. Technometrics 11:793–803

    Article  MATH  Google Scholar 

  17. Gibbons DI, Vance LC (1983) Estimators for the 2-parameter Weibull distribution with progressively censored samples. IEEE Trans Reliab 32:95–99

    Article  MATH  Google Scholar 

  18. Gupta PL, Gupta RC, Lvin SJ (1996) Analysis of failure time data by Burr distribution. Comm Stat Theory Meth 25:2013–2024

    Article  MATH  MathSciNet  Google Scholar 

  19. Jalali A, Watkins AJ (2009) On maximum likelihood estimation for the two parameter Burr XII distribution. Comm Stat Theory Meth 38:1916–1926

    Article  MATH  MathSciNet  Google Scholar 

  20. Johnson LG (1964) The statistical treatment of fatigue experiments. Elsevier, Amsterdam

    Google Scholar 

  21. Lemon GH (1975) Maximum likelihood estimation for the three parameter Weibull distribution based on censored samples. Technometrics 17:247–254

    Article  MATH  MathSciNet  Google Scholar 

  22. Montanari GC, Cacciari M (1988) Progressively-censored aging tests on XPLE-insulated cable models. IEEE Trans Electr Insul 23:365–372

    Article  Google Scholar 

  23. Nelson W (1982) Applied life data analysis. Wiley, New York

    Book  MATH  Google Scholar 

  24. Ringer LJ, Sprinkle EE (1972) Estimation of the parameters of the Weibull distribution from multicensored samples. IEEE Trans Reliab 21:46–51

    Article  Google Scholar 

  25. Tadikamalla PR (1980) A look at the Burr and related distributions. Int Stat Rev 48:337–344

    Article  MATH  MathSciNet  Google Scholar 

  26. Wang FK, Cheng YF (2010) EM algorithm for estimating the Burr XII parameters with multiple censored data. Qual Reliab Eng Int 26:615–630

    Article  Google Scholar 

  27. Wingo DR (1973) Solution of the three-parameter Weibull equations by constrained modified quasilinearization (progressively censored samples). IEEE Trans Reliab R-22: 96–102

    Article  Google Scholar 

  28. Wingo DR (1983) Maximum likelihood methods for fitting the Burr type XII distribution to life test data. Biom J 25:77–84

    MATH  MathSciNet  Google Scholar 

  29. Wingo DR (1993b) Maximum likelihood methods for fitting the Burr type XII distribution to multiply progressively censored life test data. Metrika 40:203–210

    Article  MATH  MathSciNet  Google Scholar 

  30. Wong JY (1993) Simultaneously estimating the three Weibull parameters from progressively censored samples. Microelectron Reliab 3:2217–2224

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada

    N. Balakrishnan

  2. Institute of Statistics, RWTH Aachen University, Aachen, Germany

    Erhard Cramer

Authors
  1. N. Balakrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erhard Cramer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this chapter

Cite this chapter

Balakrishnan, N., Cramer, E. (2014). Point Estimation in Progressive Type-I Censoring. In: The Art of Progressive Censoring. Statistics for Industry and Technology. Birkhäuser, New York, NY. https://doi.org/10.1007/978-0-8176-4807-7_13

Download citation

Publish with us

Policies and ethics

Search

Navigation