Using a model of visual search that predicts fixation probabilities for hard-to-see targets in naturalistic images, it is possible to stochastically generate fixation sequences and time to detection for targets in these images. The purpose of the current work is to calibrate some of the parameters of a time to detection model. In particular, this work is an attempt to elucidate the parameters of the proposed fixation memory model, the strength and decay parameters. The methods used to perform this calibration consist chiefly of comparison of the stochastic model with both experimental data and a theoretical analysis of a simplified scenario. The experimental data have been collected from ten observers performing a visual search experiment. During the experiment, eye fixations were tracked with an ISCAN infrared camera system. The visual search stimuli required fixation on target for detection (i.e. hard-to-detect stimuli). The experiment studied re-fixations of previously fixated targets ,where the fixation memory failed. The theoretical analysis is based on a simplified scenario that parallels the experimental setup, with a fixed number, N, of equally probable objects. It is possible to derive analytical expressions for the re- fixation probability in this case. The results of the analysis can be used in three different ways: (1) to verify the implementation of the stochastic model, (2) to estimate the stochastic parameters of the model (i.e., number of fixations sequences to generate), and (3) to calibrate the fixation memory parameters by fitting the experimental data.