A Hypothesis Testing Using the Total Time on Test from Censored Data as Test Statistic

  • Shih-Chuan Cheng
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 236)


The total time on test for censored data from an exponentially distributed population has been proved to be a prediction sufficient (or adequate) statistic by Nair and Cheng [10] in light of the works by Cheng and Mordeson [4], and others [1, 9, 12-14]. The test may be repeated for many times. As a result, since the total time on test until the r-th ordered failure time is observed will be recorded for each test, several total time on test (for censored data) for the same system are available for use in analyzing the reliability of the system. The main objective of this proposal is to create a statistical test for the parameter of the exponential distribution on the basis of the total time on test from censored data.


Sufficient statistics Conditional independence Prediction sufficient statistics Factorization criterion Order statistics Censoring data Total time on test 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Basu, D., Cheng, S.-C.: A note on sufficiency in coherent models. Internat. J. Math. & Math. Sci. 4(3), 571–581 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Buckley, J.J.: Fuzzy Statistics. Springer, Heidelberg (2004)CrossRefzbMATHGoogle Scholar
  3. 3.
    Cheng, S.-C.: Crisp Confidence Estimation of the Parameter Involving in the Distribution of the Total Time on Test for Censored Data. In: Proceedings of Academy of Business and Information Technology – 2008 Conference, ABIT 2008 (2008)Google Scholar
  4. 4.
    Cheng, S.-C., Mordeson, J.N.: A Note on the Notion of Adequate Statistics. Chinese Journal of Mathematics, ROC 13(1), 23–41 (1985)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Cheng, S.-C., Mordeson, J.N.: Fuzzy Confidence Estimation of the Parameter Involving in the Distribution of the Total Time on Test for Censored Data. In: Proceedings of 2008 North American Fuzzy Information Processing Society Annual Conference, NAFIPS 2008 (2008)Google Scholar
  6. 6.
    Crowder, M.J., Kimber, A.C., Smith, R.L., Sweeting, T.J.: Statistical Analysis of Reliability Data. Chapman & Hall, London (1994)Google Scholar
  7. 7.
    Fisher, R.A.: On the mathematical foundations of theoretical statistics. Phil. Trans. Roy. Soc. London A 222, 309–368 (1922)CrossRefzbMATHGoogle Scholar
  8. 8.
    Halmos, P.R., Savage, L.J.: Applications of the Radon-Nikodym Theorem to the theory of sufficient statistics. Ann. Statist. 3, 1371–1378 (1949)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Lauritzen, S.L.: Sufficiency and time series analysis. Intst. Math. Statist. 11, 249–269 (1972)Google Scholar
  10. 10.
    Nair, P.S., Cheng, S.-C.: An Adequate Statistic for the Exponentially distributed Censored Data. In: Proceedings of INTERFACE 2001, vol. 33, pp. 458–461 (2001)Google Scholar
  11. 11.
    Skibinsky, M.: Adequate subfields and sufficiency. Ann. Math. Statist. 38, 155–161 (1967)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Sugiura, M., Moriomoto, H.: Factorization theorem for adequate σ-fields (in Japanese). Sūgaku 21, 286–289 (1969)Google Scholar
  13. 13.
    Takeuchi, K., Akahira, M.: Characterizations of prediction sufficiency (adequacy) in terms of risk functions. Ann. Statist. 3, 1018–1024 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Torgenser, E.N.: Prediction sufficiency when the loss function does not depend on the unknown parameter. Ann. Statist. 5, 155–163 (1977)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Shih-Chuan Cheng
    • 1
  1. 1.Department of MathematicsCreighton UniversityOmahaUSA

Personalised recommendations