Dependability analysis for ultra-dependable systems using statistics of the extremes
L.M. Kaufman · 1998
The occurrence of an uncovered fault or failure in an ultra-dependable piece of hardware or software is a rare event. Such rare events can be modeled using statistics of the extremes to predict their probability of occurrence. Existing hardware and software models use a priori assumptions pertaining to the distributions of the collected data for their respective dependability models. As a result, such models can be in error if the actual distribution for the data differs from its assumed distribution. The use of statistics of the extremes precludes the need for such assumptions. In this dissertation, a fault coverage model is developed using statistics of the extremes for when testing reveals no failures. From this model, the probability that the coverage level is at or above a specific level can be ascertained, as well as the minimum number of fault injection experiments that are required to demonstrate a given coverage level. Also, the time to failure for ultra-dependable software is modeled using a similar approach. From this software reliability model, the probability that a given piece of software is at or above a specified level is presented. This new modeling methodology is compared against an existing model using actual data. In this comparison, the robustness of the statistics of the extremes model is demonstrated, as well as the limitations of the existing model.