Many life testing procedures which have been developed involve continuous monitoring of the items under test. In storage deterioration problems, as an example, the failure of items can only be ascertained by means of inspection. Continuous observation, in these cases, is either not possible or not feasible. This paper is concerned with design problems related to the choice of the number and timing of inspections. A general class of survival functions is investigated and optimal procedures, for estimating parameters, derived. The efficiency is compared with continuous monitoring.