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Weibull Estimates in Reliability: An Order Statistics Approach

  • V. SujathaEmail author
  • S. Prasanna Devi
  • V. Dharanidharan
  • Krishnamoorthy Venkatesan
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

The Exponential and Weibull distributions are well-known failure time distributions in reliability theory and survival analysis. Order statistics occur naturally in life testing and in survival analysis. The properties of order statistics and the results of order statistics are used to estimate the three-parameter Weibull distributions. This study ranges from order statistics to distribution theory and then to survival analysis. To know the survival distribution function S(t), many distributional forms have been used. Moments of order statistics help us to estimate the one-parameter and two-parameter forms, but to estimate the three-parameter Weibull distribution is a challenging one. Hence we make this study as a twofold study: firstly, to study the order statistics for Weibull distributions and their moments, and secondly, apply the computed moments of order statistics to estimate the location and scale parameters (with the shape parameter being fixed) based on complete as well as type II right-censored samples. To achieve the goal, data have been simulated for the failure time and their moments estimated based on the order statistics, and we explained how the conventional estimators play their role in reliability in order to verify the accuracy of the numerical computations.

Notes

Acknowledgements

I wish to thank my coauthors for their kind help and support in my research work throughout this paper. My heartfelt thanks to my institution for providing me infrastructural facilities and excellent resources to carry out my research in VIT University, Vellore.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • V. Sujatha
    • 1
    Email author
  • S. Prasanna Devi
    • 2
  • V. Dharanidharan
    • 3
  • Krishnamoorthy Venkatesan
    • 4
  1. 1.School of Advanced SciencesVIT UniversityVelloreIndia
  2. 2.Department of Computer ScienceSRM UniversityVadapalani, ChennaiIndia
  3. 3.Department of Computer ScienceApollo Engineering CollegeChennaiIndia
  4. 4.College of Natural SciencesArba Minch UniversityArba MinchEthiopia

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