Safety-Critical Software - Quantification of Test Results

Safety-critical software systems have traditionally been found in few domains, e.g., aerospace, nuclear and medical. As technology advances and software capability increases, such systems can be found in more and more applications, e.g., selfdriving cars, autonomous trains. This development will dramatically increase the operational exposure of such systems. All safety-critical applications need to meet exceptionally stringent criteria in terms of dependability. Proving compliance is a challenge for the industry and there is a lack of accepted methods to determine the status of safety-critical software. The regulatory bodies often require a certain amount of testing to be performed but do not, for software systems, require evidence of a given failure rate. This paper addresses quantification of test results. It examines both theoretical and practical aspects. The contribution of this paper is an equation that estimates the remaining undetected faults in the software system after testing. The equation considers partial test coverage. The theoretical results are validated with results from a large industry study (commercial military software). Additionally, the industry results are used to analyze the concept of entropy also known as Shannon information, which is shown to describe the knowledge gained from a test effort.