This research includes the application of non-parametric methods in estimating the conditional survival function represented in a method (Turnbull) and (Generalization Turnbull's) using data for Interval censored of breast cancer and two types of treatment, Chemotherapy and radiation therapy and age is continuous variable, The algorithm of estimators was applied through using (MATLAB) and then the use average Mean Square Error (MSE) as amusement to the estimates and the results showed (generalization of Turnbull's) In estimating the conditional survival function and for both treatments ,The estimated survival of the patients does not show very large differences, but the curves of the patients taking the chemotherapy were more stable and the survival time is longer since the rapid decay or decay, the decrease in the probability value of the patient curve occurs at the time of the ninth and twenty-second periods as well as the period of the twenty-sixth The probability of a survival function is zero at the time of the last Interval.
