Using statistics of the extremes for software reliability analysis of safety critical systems

Software reliability models have been successfully applied to many industrial applications, but have the unfortunate drawback of requiring data from which one can formulate a model. The data used for these models frequently comes from pre-release testing and/or field experience, and is of sufficient quantity and quality for most large-scale commercial applications. Software which is developed for safety-critical applications is frequently unable to produce such data, for at least two reasons. First, the software is frequently one-of-a-kind, and second, it rarely fails. Safety-critical software is expected to pass every test, producing precious little failure data. "Statistics of the extremes" is a special branch of statistics developed for analysis of rare events. Where traditional statistical analysis uses the law of large numbers to provide information concerning points which are near the mean of the distribution, statistics of the extremes concentrates on the tails. Analysis of rare event data using statistics of the extremes does not require a-priori assumptions concerning the distributional form of the data, and thus provides an interesting alternative to traditional approaches. In this paper, we develop a software reliability model using statistics of the extremes, which is particularly applicable to safety-critical software systems.