On Stratified Sampling for High Coverage Estimations

This paper addresses the problem of estimating the coverage of a fault tolerance mechanism through statistical processing of observations collected in fault-injection experiments. In an earlier paper, several techniques for sampling the fault/activity input space of a fault tolerance mechanism were presented. Various estimators based on simple sampling in the whole space and stratified sampling in a partitioned space were studied; confidence limits were derived based on a normal approximation. In this paper, the validity of this approximation is analyzed, especially for high coverage systems. The theory of confidence regions is then introduced to estimate the coverage without approximation when, for practical reasons, stratification is used. Three statistics are considered for defining confidence regions. It is shown that one of these statistics — a vectorial statistic — is often more conservative than the other two. However, only the vectorial statistic is computationally tractable. The results obtained are compared with those based on approximation by means of three hypothetical example systems.