This paper provides an overview of proof testing in relation to dangerous random hardware failures of safety-rated systems and provides a basic introduction to the concept of proof testing and its importance in seeking compliance with IEC 61508 (or other standards in the series, e.g. IEC 61511, IEC 62061). In particular, it examines the concepts of perfect and imperfect proof testing. Experience indicates that the full implications during the operational phase of the safety-rated system, of what constitutes an effective proof test, are often not fully appreciated. If the design assumptions relating to proof tests are not effectively carried out in the operational phase then the tolerable risk target for the plant or equipment may not be achieved. Also, if during the operational phase the proof test is based on perfect proof testing assumptions, and these are not achieved in practice, then the design target failure measure may not be met. The paper provides practical proposals for addressing situations where perfect proof testing cannot readily be achieved and an imperfect proof test approach is adopted. The objective is to ensure that the target failure measure, for the safety function under consideration, does not exceed its design maximum; if it did, the tolerable risk target for the plant or equipment might not be met.