Importance Sampling of Test Cases in Markovian Software Usage Models

Recently, some authors have suggested usage models of Markov type as a technique of specifying the estimated operational use distribution of a given program. A main purpose of such models is the derivation of random test cases allowing unbiased estimates on the (un)reliability of the program in its intended environment. In this article, we show that by a shift of the transition probabilities of the Markov chain corresponding to such a model, prior information on the error{ proneness of single program operations can be taken into account. An unbiased unreliability estimator with reduced variance is obtained. Furthermore, it is shown that minimization of the variance leads to a special stochastic optimization problem which can be demonstrated to be convex, such that eecient solution techniques apply. Some related questions are also treated in a more general, non{Markovian framework.