The motivation for the problem considered in this paper comes from a survival analysis problem in quality-assurance systems that are becoming more popular. For example, when an automobile failures occur within the automotive warranty period, a manufacturer can develop a record of mileage to failure from owners' request for repair. When no failure occur during the warranty period the owner naturally will not report the mileages, and it may be inferred that no record of failures. By using a follow-up survey data can be acquired to include a partial record of nonfailures. A method of estimating life time parameters is proposed for analyzing this kind of data under various scenarios assuming an Exponential lifetime distribution.