In this paper, modifiable risk factors (hypertension and diabetes) of Coronary Artery Bypass Graft Surgery (CA BG) patients are considered. The objective is to analyse survivor's proportions of CABG patients in the considered risk factors, in co mplete and inco mplete Populations, using suitable survival models. A new approach of comp lete population fro m its inco mplete population of CA BG patients of 12 years observations is used for the survival analysis. In the co mplete population,

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... d patients are proportionally included into the known survived and died patients respectively. The availability of a co mplete population may represent better behaviour of lifetimes / survival proportions for medical research. Survival p roportions of the CABG patients of complete and inco mplete populations, with respect to the risk factors (hypertension and diabetes) are obtained fro m suitable, lifet ime representing models (Weibull and Exponential). Maximu m likelihood method, in -conjunction with Davidon-Fletcher-Po well (DFP) optimization method and Cubic Interpolation method is used in estimation of survivor's proportions fro m the parametric models. coronary artery disease are noted in the advanced stage of the disease. Initially, most of the individuals with CA D show no evidence of disease, whereas the disease progresses before the first onset of symptoms and often there is a sudden heart attack. The CA D is the most common cause of sudden death of men and wo men over 20 years of age [30] . The medical scientists; William, Ellis, Josef, Ralph and Robert [36], Hey mann[15], Go ldstein, Adams, Alberts, Appel, Brass, Bushnell, Culebras, DeGraba, Gorelick & Guyton[11] and Jennifer[17] are of the opinion that CA BG is an effective treatment option for CAD patients. The med ical research organizations like Heart and Stroke Foundation Canada[14] and American Heart Association[2] have classified risk factors of CABG patients as modifiable and non-modifiable. Modifiable risk factors are those factors, which may be controlled by changing life style or taking med ications to reduce cardiovascular risk. These risk factors include high blood pressure (hypertension), diabetes, smoking, high cholesterol, sedentary lifestyle and obesity. Non-modifiab le risk factors are those factors, which may not be changed. These factors include age, gender and family h istory (Genetic predisposition). William, Ellis, Josef, Ralph and Robert[35] in 1995 carried out the survival study on incomp lete population (progressive censoring of type 1) of 121 American Journal of M athematics and Statistics 2012, 2(5): 120-128