Estimating Worst Case Failure Dependency with Partial Knowledge of the Difficulty Function

For systems using software diversity, well-established theories show that the expected probability of failure on demand (pfd) for two diverse program versions failing together will generally differ from what it would be if they failed independently. This is explained in terms of a “difficulty function” that varies between demands on the system. This theory gives insight, but no specific prediction unless we have some means to quantify the difficulty function. This paper presents a theory leading to a worst case measure of “average failure dependency” between diverse software, given only partial knowledge of the difficulty function. It also discusses the possibility of estimating the model parameters, with one approach based on an empirical analysis of previous systems implemented as logic networks, to support pre-development estimates of expected gain from diversity. The approach is illustrated using a realistic safety system example.