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Reliability Estimation of Modified Weibull Distribution with Type-II Hybrid Censored Data

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Abstract

The study deals with the analysis of Type-II hybrid censored data from the modified Weibull distribution. We provide maximum-likelihood estimates of the parameters, reliability, and hazard rate functions along with their standard errors. The confidence intervals along with their widths have also been obtained. Assuming gamma and Jeffrey’s invariant priors for the unknown parameters, Bayes estimates along with its posterior errors and highest posterior density credible intervals are obtained. The Markov Chain Monte Carlo technique has been used to simulate draws from the complicated posterior densities of the parameters. A simulation study is conducted to compare the performances of classical and Bayesian methods of estimation. Finally, a real data analysis is performed for illustrative purpose.

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References

  • Al-Zahrani B, Gindwan M (2014) Parameter estimation of a two-parameter Lindley distribution under hybrid censoring. Int J Syst Assur Eng Manag. doi:10.1007/s13198-013-0213-2

    Google Scholar 

  • Balakrishnan N, Cohen AC (1991) Order statistics and inference: estimation methods. Academic Press, San Diego

    MATH  Google Scholar 

  • Balakrishnan N, Kundu D (2013) Hybrid censoring: models, inferential results and applications. Comput Stat Data Anal 57(1):166–209

    Article  MathSciNet  MATH  Google Scholar 

  • Banerjee A, Kundu D (2008) Inference based on type-II hybrid censored data from a Weibull distribution. IEEE Trans Reliab 57:369–378

    Article  Google Scholar 

  • Berger J (1985) Statistical decision theory and bayesian analysis. Springer, New York

    Book  MATH  Google Scholar 

  • Chen MH, Shao QM (1999) Monte Carlo estimation of Bayesian credible and HPD intervals. J Comput Graph Stat 8:69–92

    MathSciNet  Google Scholar 

  • Childs A, Chandrasekhar B, Balakrishnan N, Kundu D (2003) Exactlikelihood inference based on type-I and type-II hybrid censored samples from the exponential distribution. Ann Inst Stat Math 338(55):319–330

    MATH  Google Scholar 

  • Dube S, Pradhan B, Kundu D (2011) Parameter estimation for the hybrid censored log-normal distribution. J Stat Comput Simul 81(3):275–282 (343)

    Article  MathSciNet  MATH  Google Scholar 

  • Epstein B (1954) Truncated life tests in the exponential case. Ann Math Stat 25:555–564

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Ganguly et al (2012) Exact inference for the two-parameter exponential distribution under type-II hybrid censoring scheme. J Stat Plan Inference 142(3):613–625

    Article  MATH  Google Scholar 

  • Geman S, Geman A (1984) Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell 6:721–740

    Article  MATH  Google Scholar 

  • Gupta PK, Singh B (2013) Parameter estimation of hybrid censored data with Lindley distribution. Int J Syst Assur Eng Manag 4(4):378–385

    Article  Google Scholar 

  • Harter H, Leon, Balakrishnan N (1996) CRC handbook of tables for the use of order statistics in estimation. CRC Press, Boca Raton

    MATH  Google Scholar 

  • Hastings WK (1970) Monte Carlo sampling methods using Markov Chains and their applications. Biometrika 57:97–109

    Article  MathSciNet  MATH  Google Scholar 

  • Kaplan EL, Meier P (1958) Nonparametric estimation from incomplete observations. J Am Stat Assoc 53:457–481

    Article  MathSciNet  MATH  Google Scholar 

  • Kundu D (2007) On hybrid censoring Weibull distribution. J Stat Plan Inference 137:2127–2142

    Article  MATH  Google Scholar 

  • Kundu D, Pradhan B (2009) Estimating the parameters of the generalized exponential distribution in presence of the hybrid censoring. Commun Stat Theory Methods 38(12):2030–2041

    Article  MathSciNet  MATH  Google Scholar 

  • Lai CD, Xie M, Murthy DN (2003) A modified Weibull distribution. IEEE Trans Reliab 52:33–37

    Article  Google Scholar 

  • Lawless JF (1982) Statistical model and methods for lifetime data. Wiley, NewYork

    MATH  Google Scholar 

  • Lawless JF (2003) Statistical models and methods for lifetime data, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  • Mann NR, Schafer RE, Singpurwala ND (1974) Methods for statistical analysis of reliability and life data. Wiley, New York

    Google Scholar 

  • Metropolis N, Ulam S (1949) The Monte Carlo method. J Am Stat Assoc 44:335–341

    Article  MATH  Google Scholar 

  • Rastogi MK, Tripathi YM (2013) Inference on unknown parameters of Burr distribution under hybrid censoring. Stat Pap 54:619–643

    Article  MathSciNet  MATH  Google Scholar 

  • Robert C (2007) The Bayesian Choice, 2nd edn. Springer, New York

    Google Scholar 

  • Singh B, Gupta PK, Sharma VK (2014) On Type-II hybrid censored Lindley distribution. Stat Res Lett 3(2):58–62

    Google Scholar 

Download references

Acknowledgments

The authors thankfully acknowledge the critical suggestions from the learned referees which greatly helped in the improvement of the paper.

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Authors and Affiliations

  1. Department of Statistics, Ch. Charan Singh University, Meerut, India

    Bhupendra Singh & Reetu Goel

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  1. Bhupendra Singh
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  2. Reetu Goel
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Correspondence to Bhupendra Singh.

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Singh, B., Goel, R. Reliability Estimation of Modified Weibull Distribution with Type-II Hybrid Censored Data. Iran J Sci Technol Trans Sci 42, 1395–1407 (2018). https://doi.org/10.1007/s40995-016-0124-6

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  • DOI: https://doi.org/10.1007/s40995-016-0124-6

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