A variance-reduction technique via fault-expansion for fault-coverage estimation

The estimation of fault coverage (FC) for ultra dependable systems is a daunting task. Typically, system FC is estimated via experimental techniques such as fault injection, and the gathered data are analyzed using statistical models. Specifically, faults are randomly selected, then injected into the system, and the response of the system is recorded. If the injected fault is detected, then the result is recorded as a 1; otherwise it is a 0. A point estimate and s-confidence interval are then derived from the experimental data. The difficulty with this approach is that ultra-dependable systems have FC, C⩾1-10^-5 . To estimate C accurately requires: more than 10ⁱ data points, i≡-log₁₀(1-C). A technique for enumerating equivalent fault classes can be used to reduce the number of required experiments. The enumeration process is fault expansion, which determines the set of equivalent faults via an analysis of the system structure. This paper presents a fault expansion (FE), variance reduction technique (VRT) that uses the expanded fault data to calculate a point estimate and confidence interval for the fault detection coverage. This FE-VRT can reduce appreciably the number of fault injection experiments required to estimate C for an ultra-dependable system. Typically, performing fault injection experiments is costly, in terms of both process time and computer resources. Fault injection results and the equivalent expanded fault-set for each fault are included in this paper to demonstrate the power of FE-VRT. FE-VRT is a viable method for increasing the accuracy of a FC estimate