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Load-sharing system model and its application to the real data set

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  • Singh, Bhupendra
  • Gupta, Puneet Kumar

Abstract

This study deals with the classical and Bayesian estimation of the parameters of a k-components load-sharing parallel system model in which each component's lifetime follows Lindley distribution. Initially, the failure rate of each of the k components in the system is h(t,θ1) until the first component failure. However, upon the first failure within the system, the failure rates of the remaining (k−1) surviving components change to h(t,θ2) and remain the same until next failure. After second failure, the failure rates of (k−2) surviving components change to h(t,θ3) and finally when the (k−1)th component fails, the failure rate of the last surviving component becomes h(t,θk). In classical set up, the maximum likelihood estimates of the load share parameters, system reliability and hazard rate functions along with their standard errors are computed. 100×(1−γ)% confidence intervals and two bootstrap confidence intervals for the parameters have also been constructed. Further, by assuming Jeffrey's invariant and gamma priors of the unknown parameters, Bayes estimates along with their posterior standard errors and highest posterior density credible intervals of the parameters are obtained. Markov Chain Monte Carlo technique such as Metropolis–Hastings algorithm has been utilized to generate draws from the posterior densities of the parameters.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:matcom:v:82:y:2012:i:9:p:1615-1629
    DOI: 10.1016/j.matcom.2012.02.010
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    References listed on IDEAS

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    1. M. E. Ghitany & D. K. Al-Mutairi, 2008. "Size-biased Poisson-Lindley distribution and its application," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-311.
    2. 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.
    3. 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.
    4. Krishna, Hare & Kumar, Kapil, 2011. "Reliability estimation in Lindley distribution with progressively type II right censored sample," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 281-294.
    5. 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.
    6. Ghitany, M.E. & Al-Mutairi, D.K. & Nadarajah, S., 2008. "Zero-truncated Poisson–Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 279-287.
    7. Ghitany, M.E. & Atieh, B. & Nadarajah, S., 2008. "Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 493-506.
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    Cited by:

    1. repec:spr:ijsaem:v:8:y:2017:i:2:d:10.1007_s13198-016-0528-x is not listed on IDEAS
    2. repec:eee:reensy:v:156:y:2016:i:c:p:97-108 is not listed on IDEAS
    3. repec:eee:reensy:v:170:y:2018:i:c:p:127-136 is not listed on IDEAS
    4. repec:eee:reensy:v:167:y:2017:i:c:p:67-74 is not listed on IDEAS
    5. Iman Makhdoom & Parviz Nasiri & Abbas Pak, 2016. "Bayesian approach for the reliability parameter of power Lindley distribution," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 7(3), pages 341-355, September.

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