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Analysing Load-Sharing System Model with Type-I and Type-II Failure Censored Data from Weibull Distribution

Author

Listed:
  • Neha Choudhary

    (Ch. Charan Singh University)

  • Abhishek Tyagi

    (Ch. Charan Singh University)

  • Bhupendra Singh

    (Ch. Charan Singh University)

Abstract

When the load of the failed components within the system shared by the remaining surviving components, the system is called load-sharing system model. The present study deals with the estimation of load-share parameters with Type-I and Type-II failure censored data considering Weibull distribution as the failure time distribution of each component of the system. The maximum likelihood and bootstrap estimates of the parameters, system reliability and hazard rate functions along with estimated errors are obtained. Classical, boot-p and boot-t confidence intervals for the model parameters have been constructed. Assuming informative priors, Bayes estimates and highest posterior density intervals of the reliability parameters are also computed using Markov Chain Monte Carlo methods under symmetric and asymmetric loss functions. For comparing performances of the various point and interval estimates, a simulation study is conducted. Two real datasets analysis is presented to illustrate the applications of the proposed model.

Suggested Citation

  • Neha Choudhary & Abhishek Tyagi & Bhupendra Singh, 2022. "Analysing Load-Sharing System Model with Type-I and Type-II Failure Censored Data from Weibull Distribution," Annals of Data Science, Springer, vol. 9(4), pages 645-674, August.
    • Handle: RePEc:spr:aodasc:v:9:y:2022:i:4:d:10.1007_s40745-020-00242-8
    DOI: 10.1007/s40745-020-00242-8
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    References listed on IDEAS

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    1. Bhupendra Singh & K. Sharma & Anuj Kumar, 2009. "Analyzing the dynamic system model with discrete failure time distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(4), pages 521-542, November.
    2. Paul H. Kvam & Edsel A. Pena, 2005. "Estimating Load-Sharing Properties in a Dynamic Reliability System," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 262-272, March.
    3. Singh, Bhupendra & Gupta, Puneet Kumar, 2012. "Load-sharing system model and its application to the real data set," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(9), pages 1615-1629.
    4. John Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
    5. Chanseok Park, 2010. "Parameter estimation for the reliability of load-sharing systems," IISE Transactions, Taylor & Francis Journals, vol. 42(10), pages 753-765.
    6. Singh, Bhupendra & Sharma, K.K. & Kumar, Anuj, 2008. "A classical and Bayesian estimation of a k-components load-sharing parallel system," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5175-5185, August.
    7. Chanseok Park, 2013. "Parameter estimation from load-sharing system data using the expectation–maximization algorithm," IISE Transactions, Taylor & Francis Journals, vol. 45(2), pages 147-163.
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