Abstract
The length of the gap is the key factor affecting its reliability. Based on the mechanism of the gap null gate, this paper regards the two endpoint thresholds of the gap length as bivariate random variables and establishes successful response models. Score test statistic is presented to test the correlation coefficient. The DIC criterion is also provided to compare the models. With the experimental data of the gap null gate, we build Probit model and Logit model as the successful response models, and prove that the correlation coefficients in the both models can be regarded as 0. By comparing the DIC value, we find that the Probit model is more suitable to describe the distribution of the endpoint thresholds of the reliability window. Finally, both the point estimation and interval estimation results of the reliability window are given to illustrate the feasibility of the method shown in the paper.