Coverage Estimation Methods for Stratified Fault Injection

ÐThis paper addresses the problem of estimating fault tolerance coverage through statistical processing of observations collected in fault-injection experiments. In an earlier paper, various estimators based on simple sampling in the complete fault/activity input space and stratified sampling in a partitioned space were studied; frequentist confidence limits were derived based on a normal approximation. In this paper, the validity of this approximation is analyzed. The theory of confidence regions is introduced to estimate coverage without approximation when stratification is used. Three statistics are considered for defining confidence regions. It is shown that oneÐa vectorial statisticÐis often more conservative than the other two. However, only the vectorial statistic is computationally tractable. We then consider Bayesian estimation methods for stratified sampling. Two methods are presented to obtain an approximation of the posterior distribution of the coverage by calculating its moments. The moments are then used to identify the type of the distribution in the Pearson distribution system, to estimate its parameters, and to obtain the coverage confidence limit. Three hypothetical example systems are used to compare the validity and the conservatism of the frequentist and Bayesian estimations. Index TermsÐFault tolerance coverage, coverage estimation, fault-injection, stratified sampling, confidence regions, confidence limits, frequentist estimation, Bayesian estimation.