




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














European Journal of Operational
Research , Vol.223,
No.3, pp. 722731 (2012.12.16) Available online
2012.8.3 http://dx.doi.org/10.1016/j.ejor.2012.07.011 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.





Reliability; right truncated grouped data;
likelihood principle; differential equation; Weibull distribution;
SARS A(H1N1) FMD.









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