Extreme Value Models for Software Reliability

When a new software is produced it is usually tested for failure several times in succession (whenever a failure is detected the software is rectified and tested again for failure). Suppose X ₁,X ₂,…,X _k denote the times between failures. For the customer the main characteristic of interest is T=max(X ₁,X ₂,…,X _k ). In particular, one would be interested in t _α for which Pr{T≤t _α }=1?α for small α. In this paper we consider four models for T based on the class of extreme value distributions (Gumbel, Fre´chet, Weibull and Pareto) and provide methods for estimating t _α . In addition to numerical estimation of t _α , we perform sensitivity analysis of t _α with respect to the four models considered.