Some of the advances made during the past 25 years in the statistical treatment of reliability problems are reviewed. The impact of statistical methods on reliability is discussed, and some areas where work is needed are suggested.

Statistical Methods in Reliability

When branches of a fault tree are pruned, their probabilities are not fully transferred to the "all other" branch. We test 3 explanations for this underestimation of the "all other" probability: availability, ambiguity, and credibility. In an experiment, we varied the credibility of a cover story and separately observed the generation of a fault's causes to isolate availability, and the categorization of causes to assess ambiguity. The results identify biased availability as a broad threat to the validity of likelihood estimates. Ambiguity adds to the problem whenever tree designers are unable to eliminate it from causes or categories. Finally, though subjects had clear expectations for what constitutes a credible fault tree, none of the "all other" underestimation could be traced to credibility factors. The discussion covers both underlying mechanisms and corrective techniques. A fault tree is a schematic, hierarchical representation of the possible causes of some undesired event. It represents accumulated, often collective, expert knowledge in an accessible format. Fault trees are used both retrospectively to diagnose the cause of a particular occurrence of the fault and prospectively to devise plans for preventing it. These models of the many parallel and sequential causes of a fault were developed in the aerospace industry of the 1960s (Barlow & Lambert, 1975; Vesely, Goldberg, Roberts, & Haash, 1981). They remain best suited to the physical systems that typically concern engineers and are most commonly constructed when failure entails high cost. Examples of systems to which fault trees have been applied are chemical (explosion, fire, or release of toxic material), electrical (failure of a motor to start or switch to close), mechanical (rupture of a pressure tank or no spray from an automatic sprinkler system), and nuclear (fire in the reactor building or excessive leakage from a reactor containment system). However, fault trees can also be used to explain more mundane events, such as why a car might not start or why a restaurant might fail. An example of a fault tree, for causes of death in the United States, is displayed in Figure 1. Fischhoff, Slovic, and Lichtenstein (1978) demonstrated a serious problem with fault trees that are incomplete. Using a fault tree for a car's failure to start, they compared a full tree, consisting of six labeled branches and a seventh catchall branch ("All Other Problems") to a pruned version of the same tree. The pruned tree omitted three of the six labeled branches, leaving three labeled branches and the catch-all category. Subjects estimated the probabilities of each branch, either the seven branches of the full tree or the four branches of a pruned tree. The only legitimate difference between the branch probabilities of the full and pruned trees is that the

Where is the fault in fault trees

Reliability of k-out-of-n systems with phased-mission requirements and imperfect fault coverage

In this chapter, a state-of-the-art review of various analytical modeling techniques for reliability analysis of phased-mission systems (PMS) is presented. The analysis approaches can be broadly classified into three categories: combinatorial, state-space oriented, and modular. The combinatorial approaches are computationally efficient for analyzing static PMS. A combinatorial binary decision diagram based method is discussed in detail. Methods to consider imperfect fault coverage and common-cause failures in the reliability analysis of PMS will also be presented.

Reliability of Phased-mission Systems

Bridge engineers and bridge inspectors recognize that deterioration of one element influences the deterioration of another. The effect of this phenomenon may be crititcal if it increases the deterioration rate of the affected elements. The phenomenon is known as element interaction. The consequences of element interaction can help to explain why elements of the same type have varying deterioration rates. No practical model exists for modeling element interaction. This paper presents the use of a fault tree for qualitative and quantitative evaluation of element interaction phenomena. The fault-tree results can be used to better assess the deterioration rate and improve deterioration prediction of an element. An example of the fault-tree model for accelerated deterioration of concrete bridge decks is presented. The fault-tree model is not a deterioration model, but can be used to focus on mitigating accelerated element deterioration by certain maintenance or repair actions. Systematic implementation of the fault-tree approach presented herein must be preceded by field verification.

Jerry B. Fussell

Papers

Reliability and fault tree analysis : theoretical and applied aspects of system reliability and safety assessment : papers