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 X1,X2, …,Xk denote the times between failures. For the customer the main characteristic of interest is T=max(X1,X2,…,Xk). In particular, one would be interested in t for which Pr{T t }=1- for small . 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 . In addition to numerical estimation of t , we perform sensitivity analysis of t with respect to the four models considered.