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Estimation of the number of failures in the Weibull model using the ordinary differential equation

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  • Hirose, Hideo

Abstract

In estimating the number of failures using right truncated grouped data, we often encounter cases that the estimate is smaller than the true one when we use the likelihood principle to conditional probability. In infectious disease spread predictions, the SIR model described by simultaneous ordinary differential equations is commonly used, and it can predict reasonably well the number of infected patients even when the size of observed data is small. We have investigated whether the ordinary differential equation model can estimate the number of failures more accurately than does the likelihood principle under the condition of right truncated grouped data. The positive results are obtained in the Weibull model, similarly to the cases of the SARS, A(H1N1), and FMD.

Suggested Citation

  • Hirose, Hideo, 2012. "Estimation of the number of failures in the Weibull model using the ordinary differential equation," European Journal of Operational Research, Elsevier, vol. 223(3), pages 722-731.
    • Handle: RePEc:eee:ejores:v:223:y:2012:i:3:p:722-731
    DOI: 10.1016/j.ejor.2012.07.011
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    1. P. K. Kapur & H. Pham & A. Gupta & P. C. Jha, 2011. "Software Reliability Growth Models," Springer Series in Reliability Engineering, in: Software Reliability Assessment with OR Applications, chapter 0, pages 49-95, Springer.
    2. Pham, Hoang & Zhang, Xuemei, 2003. "NHPP software reliability and cost models with testing coverage," European Journal of Operational Research, Elsevier, vol. 145(2), pages 443-454, March.
    3. D. S. Bai & Y. I. Kwon, 1994. "An economic sequential screening procedure for limited failure populations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(4), pages 523-535, June.
    4. Jeremy Ginsberg & Matthew H. Mohebbi & Rajan S. Patel & Lynnette Brammer & Mark S. Smolinski & Larry Brilliant, 2009. "Detecting influenza epidemics using search engine query data," Nature, Nature, vol. 457(7232), pages 1012-1014, February.
    5. Ghitany, M. E. & Maller, R. A. & Zhou, S., 1994. "Exponential Mixture Models with Long-Term Survivors and Covariates," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 218-241, May.
    6. Hirose, Hideo, 2007. "The mixed trunsored model with applications to SARS," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(6), pages 443-453.
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