Statistical variations in input parameters that affect structural reliability have historically been incorporated approximately in engineering designs by application of safety factors. Increased concerns over the injury potential and costs of licensing, insurance, field repairs or recalls, and product liability claims now demand more quantitative evaluation of possible flaws or unusual usage conditions that might result from statistical variations or uncertainties. This paper describes the basic concepts of probabilistic fracture mechanics that are used to assess and control risk. Recent developments in combined analysis methods are presented that utilize field experience data with probabilistic analysis to improve the accuracy of the structural integrity predictions. Several specific examples are described that illustrate how these probabilistic methods are used to assess risk and to provide a quantitative basis for establishing design, operation or maintenance allowables. These procedures, which realistically model the actual statistical variations that exist, can eliminate unnecessarily conservative approximations and often achieve improved reliability at reduced cost.