Skip to main content
SpringerLink
Log in

Reliability evaluation for Weibull distribution under multiply type-І censoring

  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

The multiply type-І censoring represented that all units in life test were terminated at different times. For estimations of Weibull parameters, it was easy to compute the maximum likelihood estimation (MLE) and least-squares estimation (LSE) while it was hard to build confidence intervals (CI). The concept of generalized confidence interval (GCI) was introduced to build CIs of parameters under multiply type-I censoring. Further, GCI based on LSE and GCI based on MLE were proposed. It is mathematically proved that the former is exact and the latter is approximate. Besides, a Monte Carlo simulation study and an illustrative example also turn out that the GCI method based on LSE yields rather satisfactory results by comparison with the ones based on MLE. It should be clear that the GCI method is a sensible choice to evaluate reliability under multiply type-I censoring.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. XU Zhi-jun, ZHENG Jun-jie, BIAN Xiao-ya, LIU Yong. A modified method to calculate reliability index using maximum entropy principle [J]. Journal of Central South University, 2013, 20(3): 1058–1063.

    Article  Google Scholar 

  2. LIU Ji, LI Yun. An improved adaptive response surface method for structural reliability analysis [J]. Journal of Central South University, 2012, 19(3): 1148–1154.

    Article  Google Scholar 

  3. XIE Gui-hua, ZHANG Jia-sheng, LIU Rong-gui. Application of matrix-based system reliability method in complex slopes [J]. Journal of Central South University, 2013, 20(2): 812–820.

    Article  Google Scholar 

  4. ZHANG Chun-yi, BAI Guang-chen. Extremum response surface method of reliability analysis on two-link flexible robot manipulator [J]. Journal of Central South University, 2012, 19(1): 101–107.

    Article  Google Scholar 

  5. WANG Xiao-lin, JIANG Ping, GUO Bo, CHENG Zhi-jun. Real-time reliability evaluation based on damaged measurement degradation data [J]. Journal of Central South University, 2012, 19(1): 3162–3169.

    Article  Google Scholar 

  6. WANG Fu-sheng, ZHANG Jun-ran, WANG Pei-yan, HUO Shi-hui, YUE Zhu-feng. Reliability analysis of laminated composite under compression and shear loads [J]. Journal of Central South University, 2012, 19(7): 2712–2717.

    Article  Google Scholar 

  7. CASTET J F, SALEH J H. Satellite and satellite subsystems reliability: Statistical data analysis and modeling [J]. Reliability Engineering & System Safety, 2009, 94(11): 1718–1728.

    Article  Google Scholar 

  8. OLTEANU D, FREEMAN L. The evaluation of median-rank regression and maximum likelihood estimation techniques for a two-parameter Weibull distribution [J]. Quality Engineering, 2010, 22(4): 256–272.

    Article  Google Scholar 

  9. THOMAN D R, BAIN L J, ANTLE C E. Maximum likelihood estimation, exact confidence intervals for reliability, and tolerance limits in the weibull distribution [J]. Technometrics, 1970, 12(2): 363–371.

    Article  MATH  Google Scholar 

  10. BALAKRISHNAN N, KATERI M. On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data [J]. Statistics & Probability Letters, 2008, 78(17): 2971–2975.

    Article  MATH  MathSciNet  Google Scholar 

  11. JOARDER A, KRISHNA H, KUNDU D. Inferences on Weibull parameters with conventional type-I censoring [J]. Computational Statistics & Data Analysis, 2011, 55(1): 1–11.

    Article  MATH  MathSciNet  Google Scholar 

  12. SKINNER K R, KEATS J B, ZIMMER W J. A comparison of three estimators of the Weibull parameters [J]. Quality and Reliability Engineering International, 2001, 17(4): 249–256.

    Article  Google Scholar 

  13. FOTHERGILL J. Estimating the cumulative probability of failure data points to be plotted on Weibull and other probability paper [J]. IEEE Transactions on Electrical Insulation, 1990, 25(3): 489–492.

    Article  Google Scholar 

  14. ZHANG L F, XIE M, TANG L C. A study of two estimation approaches for parameters of Weibull distribution based on WPP [J]. Reliability Engineering & System Safety, 2007, 92(3): 360–368.

    Article  Google Scholar 

  15. GENSCHEL U, MEEKER W Q. A comparison of maximum likelihood and median-rank regression for Weibull estimation [J]. Quality Engineering, 2010, 22(4): 236–255.

    Article  Google Scholar 

  16. YANG Z, XIE M, WONG A C M. A unified confidence interval for reliability-related quantities of two-parameter Weibull distribution [J]. Journal of Statistical Computation and Simulation, 2007, 77(5): 365–378.

    Article  MATH  MathSciNet  Google Scholar 

  17. TAN Zhi-bin. A new approach to MLE of Weibull distribution with interval data [J]. Reliability Engineering and System Safety, 2009, 94: 394–403.

    Article  Google Scholar 

  18. KRISHNAMOORTHY K, LIN Y, XIA Y. Confidence limits and prediction limits for a Weibull distribution based on the generalized variable approach [J]. Journal of Statistical Planning and Inference, 2009, 139(8): 2675–2684.

    Article  MATH  MathSciNet  Google Scholar 

  19. WEERAHANDI S. Generalized confidence intervals [J]. J Am Statist Assoc, 1993, 88: 899–905.

    Article  MATH  MathSciNet  Google Scholar 

  20. ROY A, MATHEW T. A generalized confidence limit for the reliability function of a two-parameter exponential distribution [J]. Journal of Statistical Planning and Inference, 2005, 128(2): 509–517.

    Article  MATH  MathSciNet  Google Scholar 

  21. MITRA P K, SINHA B K. A generalized p-value approach to inference on common mean [J]. Journal of Statistical Planning and Inference, 2007, 137(11): 3634–3642.

    Article  MATH  MathSciNet  Google Scholar 

  22. KRISHNAMOORTHY K, MATHEW T. Inferences on the means of lognormal distributions using generalized p-values and generalized confidence intervals [J]. Journal of Statistical Planning and Inference, 2003, 115(1): 103–121.

    Article  MATH  MathSciNet  Google Scholar 

  23. FERN NDEZ A J. On calculating generalized confidence intervals for the two-parameter exponential reliability function [J]. Statistics, 2007, 41(2): 129–135.

    Article  MathSciNet  Google Scholar 

  24. WU Wei-Hwa, HSIEH Hsin-Neng. Generalized confidence interval estimation for the mean of delta-lognormal distribution: An application to new zealand trawl survey data [J]. Journal of Applied Statistics, 2014, 41(7): 1471–1485.

    Article  MathSciNet  Google Scholar 

  25. THOMAN D R, BAIN L J, ANTLE C E. Inferences on the parameters of the Weibull distribution [J]. Technometrics, 1969, 11(3): 445–460.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Information Systems and Management, National University of Defense Technology, Changsha, 410073, China

    Xiang Jia  (贾祥), Ping Jiang  (蒋平) & Bo Guo  (郭波)

Authors
  1. Xiang Jia  (贾祥)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ping Jiang  (蒋平)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bo Guo  (郭波)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiang Jia  (贾祥).

Additional information

Foundation item: Project(71371182) supported by the National Natural Science Foundation of China

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jia, X., Jiang, P. & Guo, B. Reliability evaluation for Weibull distribution under multiply type-І censoring. J. Cent. South Univ. 22, 3506–3511 (2015). https://doi.org/10.1007/s11771-015-2890-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-015-2890-2

Keywords

Search

Navigation