This research considers a system which has an ultimate terminal event such as death, critical failure, bankruptcy together with a certain indicative events (temporary malfunction, special treatment, kind of defaults) that frequently occurs before the terminal event comes to the system. Some investigation of a model for the corresponding bivariate data of the system have been done with an explanation of the situation in terms of two continuous variables instead of continuous-discrete variables and some other properties. Also an analysis has been carried out to evaluate the effect of intermediate observation of occurrence of indicative event so that the result can be used for a possible suggestion of an intermediate observing schedule.