We propose a way to account for inspection errors in a particular framework. We consider a situation where the lifetime of a system depends essentially of a particular part. A deterioration of this part is regarded as an unacceptable state for the safety of the system and a major renewal is deemed necessary. Thus the statistical analysis of the deterioration time distribution of this part is of primary interest for the preventive maintenance of the system. In this context, we faced the following problem. In the early life of the system, unwarranted renewals of the part are decided upon, caused by overly cautious behaviour. Such unnecessary renewals make the statistical analysis of deterioration time data difficult and can induce an underestimation of the mean life of the part. To overcome this difficulty, we propose to regard the problem as an incomplete data model. We present its estimation under the maximum likelihood methodology. Numerical experiments show that this approach eliminates the pessimistic bias in the estimation of the mean life of the part. We also present a Bayesian analysis of the problem which can be useful in a small sample setting.