In this work we propose a new survival model called the Bell-Inverse Gaussian cure rate.
We consider different activation schemes in which the number of factors $M$ has the Bell distribution
and the time of occurrence of an event follows the Inverse Gaussian model. The parameters are
estimated by the classical and Bayesian methods. In a simulation study, we investigate the mean estimates, biases, mean squared errors and coverage probabilities in different activation schemes.
In order to detect possible influential or extreme observations that can cause distortions on the results of the analysis we use the Bayesian method of influence analysis of case deletion based on
$\psi$-divergence. Finally, we show the applicability of the proposed model to a real dataset.