Bayesian zero-failure reliability demonstration

We study required numbers of tasks to be tested for a technical system, including systems with built-in redundancy, in order to demonstrate its reliability with regard to its use in a process after testing, where the system has to function for different types of tasks, which we assume to be independent. We consider optimal numbers of tests as required for Bayesian reliability demonstration in terms of failure-free periods, which is suitable in case of catastrophic failures, and in terms of the expected number of failures in a process after testing. We explicitly assume that testing reveals zero failures. For the process after testing, we consider both deterministic and random numbers of tasks. We also consider optimal numbers of tasks to be tested when aiming at minimal total expected costs, including costs of testing and of failures in the process after testing. Cost and time constraints on testing are also included in the analysis. We consider such reliability demonstration for a single type of task, as well as for multiple types of tasks to be performed by one system. We also consider optimal Bayesian reliability demonstration testing in combination with flexibility in the system redundancy, where more components can be installed to reduce test effort. For systems with redundancy, we restrict attention to systems with exchangeable components, with testing only at the component level. We use the Bayesian approach with the Binomial model and Beta prior distributions for the failure probabilities. We discuss the influence of choice of prior distribution on the required zero-failure test numbers, where these inferences are very sensitive to the choice of prior distribution, which requires careful attention to the interpretation of non-informativeness of priors