Monitoring medical outcomes is desirable so as to help quickly detect performance changes. Previous applications have mostly focused on binary outcomes, such as 30-day mortality after surgery. However, in many applications, survival time data is routinely collected. Survival analysis examines and models the time that it takes for an event to occur. Proportional hazard regression is the most popular tool for studying the dependency of survival time on predictor variables. By using the maximum partial likelihood method in this regression, the hazard function is approximated. In applications, real data are frequently not precise numbers or vectors but often more or less imprecise. On the other side, the hazard function is the rate of failure at any instant or the rate at which risk accumulated. So when the failure is a fuzzy number, it is better to use fuzzy approaches to estimate the fuzzy hazard function. In this paper, we propose a way to estimate the fuzzy hazard function, and based on that, a CUSUM control chart to monitor risk-adjusted survival times is introduced. By using real data, the chart is compared with the crisp hazard function, which is proposed by Biswas and Kalbfleisch.

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