Reliability Test based on a Binomial Experiment for Probabilistic Worst-Case Execution Times

Measurement-Based Probabilistic Timing Analysis (MBPTA) produces Probabilistic Worst-Case Execution Times (pWCETs), i.e., WCET estimates associated with known low exceedance probabilities. Despite applicability and goodness-of-fit tests being used within MBPTA, any method based on the sampling of a population is subject to a degree of uncertainty. The acceptance of MBPTA in industrial engineering processes depends on obtaining enough evidence that the produced pWCETs are indeed reliable. In this paper we propose a statistical hypothesis test to check the reliability of pWCET estimates, done at a specified significance level. We assume as null hypothesis that the pWCET estimate is reliable, and as alternative hypothesis that it is optimistic. Both Type I and Type II errors are considered. The reliability test is based on a binomial experiment and it is complementary to applicability and goodness-of-fit tests. We evaluated the test using multiple synthetic and real-hardware execution time samples, and applied it on 20 pWCET estimates generated for each of them. The combined use of the proposed reliability test with applicability and goodness-of-fit tests could detect most of the knowingly unreliable estimates on synthetic samples. Similar behaviour was observed for real-hardware samples, evidencing the test's usefulness for selecting pWCET estimates with increased confidence.