Software reliability analysis using statistics of the extremes

The existing classes of software reliability models require an a priori distribution for collected data in their analysis. Using these models, analyses can be performed using various assumed distributions. The assumed distributions may not accurately reflect the behavior of the collected data, and as a result, the results predicted by the models can be quite inaccurate. If it is assumed that the occurrence of a failure in highly dependable software is a rare event, then statistics of the extremes can be used. Statistics of the extremes provides for an analysis of rare event data without requiring any a priori knowledge of its distribution. It classifies most distributions into one of three asymptotic families; that is in the limit, most distributions converge to one of three forms. The asymptotic family to which a set of data belongs is derived graphically using a software tool that plots the data on a Gumbel type probability paper. From the resulting empirical cumulative distribution function, the asymptotic family to which the data belongs is determined. Once the asymptotic family for a particular data set is known, then the parameters required for an explicit representation of the asymptotic form are derived using analytical techniques. Using statistics of the extremes, an analysis of actual field data from an IBM case study is performed to estimate the time to failure (TTF) for the software.