Safety assessment of offshore platforms is an urgent task. Such assessments are now focusing on the structure, maintenance, and retirement of a platform. Some methods employed have many shortcomings. For example, they cannot make the reliability adequately explicable. Therefore, a mathematical tool, the unascertained measure, was introduced. First, the basic knowledge of the unascertained sets was introduced briefly. Second, the unascertained measure was defined and credible identification was set up. The method has been introduced into the fields for safety assessment of a jacket loadout procedure. Engineering practices showed that it can complete the safety assessment systematically and scientifically without any assumption. The work should have significance in theory and practice for offshore engineering.