We propose a methodology design for quantitatively analyzing service delivery systems of service organizations. The methodology design is developed by applying Kaplan-Meier estimator of survival analysis. We carry out sensitivity analysis through statistical significance test for survival function and hazard function considering different groups. We also consider the characteristics of viability in censored data. In order to test the validity of proposed methodology design of service delivery systems we apply it to Korean Hospital of Oriental Medicine focused on a diet. Case analysis of Korean Hospital is done considering fundamental categorization and content categorization. Fundamental categorization is classified into patient type (new patients and returning patients) and age group (20s, 30s, and 40s) and content categorization is classified into intention to recommend others and revisit Intention. We find as a result that there is a significant difference in the survival function and hazard function for new patients and returning patients. We also show the significant difference among age groups. Survival function of returning patients is lower than that of new patients. Hazard function of returning patients increases rapidly compared to that of new patients as patients move to the end of stages of service delivery systems. Result shows that the survival function of new patients decreases significantly at SE9 (schedule for revisit) and survival function for returning patients decreases significantly at SE8 (medical bill). For Hazard function, returning patients show the greatest increase at SE10 (oriental medicine delivery) and new patients show the greatest increase at SE9 (schedule for revisit). The greatest change in survival function is found in 40s and then the second greatest change is in 20s. The greatest decrease in survival function is shown at SE3 (medical waiting time) for 40s and at SE9 (Medical bill) for 20s. For Hazard function, the greatest increase is seen at SE9 (schedule for revisit) for 40s and at SE10 (oriental medicine delivery) for 20s. For revisit intention of content categorization, survival function graph shows a substantial decrease at SE3 (medical waiting time), SE9 (schedule for revisit), and SE8 (medical bill). For intention to recommend others, there is immense decrease at SE5 (medical treatment) and SE8 (medical bill) for survival rate. We, in this research, focus on process approach not on multi-dimensional service attributes in analyzing service delivery systems. We present a methodology design for quantitative analysis of service delivery systems. Our results allow service organization to evaluate its service level at each service stage and propose strategic guideline for its improvement.