Using statistics of the extremes for software reliability analysis

This paper investigates the use of StEx (statistics of the extremes) [Castillo, Sarabia 1992; Gumbel 1958; Ang, Tang 1984; Castillo 1988; Castillo, Alvarez, Cobo 1993] for analyzing software failure data for highly reliable systems. StEx classifies most distributions into one of three asymptotic families. The asymptotic family to which a set of data belongs is derived graphically on Gumbel-type probability paper. From the resulting empirical Cdf (cumulative distribution function), the asymptotic family to which the data might belong is hypothesized. Once the asymptotic family for a particular data set is determined, the parameters required for an explicit representation of this asymptotic form are derived using known analytic techniques. Using this approach, actual field data from two software case studies [Musa 1979; Kenney 1993] are analyzed using conventional software reliability growth models and using StEx