Incidents of unexpected ship hull failures have been on the sharp decrease owing to the technological progress in hull structural analysis, prediction of various kinds of loadings and quality of ship production. The emphasis in the hull design from the aspect of strength evaluation has shifted its focus from the early failures to the fracture resulting from deterioration with time. Representative of the latter type fractures is that of fatigue. The structural design that take into account the fatigue fracture, or fatigue design in short, is mandatory not only for LNG carriers but also for critical structural components of other ship types as well. To oil drilling rig structural design, the fatigue design is a matter of primary importance. In the practice of fatigue design, desiding about what factor of safety to use in designing the structural components adequate for avoiding the fatigue crack initiation requires consideration of many factors contributing to the hull structural integrity. The computerized hull damage record data bank allow access to statistical hull failure data amassed and classified according to the size and locations of fatigue cracks. There, however, are only few literatures that address the problem of just what factor of safety to use in designing hull structural members. BS 5400, Part 10, the fatigue rule to be complied with in designing bridges, says “In certain cases, a higher probability of failure could be acceptable, for example, where fatigue cracking would not have serious consequences, or where a crack could be easily located and repaired.” but fall short of being specific as to what percentage of fracture probability to employ for which structural component. The purpose of the author's study is to quantify the structural integrity, which depends for parameters on such ambiguous quantities as the results of inspection, functional evaluation, etc. An approach often taken in such an instance is to resort to the graph-network theory for mutal appreciation of phenomena and to the fuzzy sets based analysis for quantification. The ship hull fatigue failure analysis, on the other hand, depends for parameters on the size of statistical data including those on sea conditions. The reliability engineering is employed in such an instance, and recently the safety index has come into use as factor of safety. This paper assess the importance ratings of individual hull structural members from the fatigue strength standpoint employing the abovementioned techniques.