The goal in many data analyses is to produce brief summaries which convey the key conclusions. This will be particularly important in survival analysis in medicine where clinicians could benefit from clear and succint summaries in order to discuss treatment alternatives with the patient. In such situations, the hazard function can be quite useful: it captures risk patterns as a function of time and has the additional advantage of providing conditional probabilities of failure. Here we study a model in which patients are at greatest risk for failing early in the course of the disease. A simple model of this phenomenon is the exponential model with one or two change points. We discuss inference, including hypothesis tests and confidence intervals for one or two change points in the exponential model with censored data.