[en] New results in reliability theory pertinent to fault tree analysis are given. Concepts of probabilistic importance are described within the framework of fault tree analysis and applied to the areas of system design, diagnosis and simulation. The IMPORTANCE computer code ranks basic events and cut sets according to various measures of importance. A general simulation model of system failure in terms of fault tree logic is described. The model is intended for efficient diagnosis of the causes of system failure in the event of a system breakdown. It can also be used to assist an operator in making decisions under a time constraint regarding the future course of operations. The model is well suited for computer implementation. New results incorporated in the simulation model include (1) an algorithm to generate repair checklists on the basis of fault tree logic and (2) a one-step-ahead optimization procedure that minimizes the expected time to diagnose system failure. The methods developed are applied to aerospace, chemical and nuclear systems