Bayesian reliability demonstration with multiple independent tasks

We consider optimal testing of a system in order to demonstrate 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 explicitly assume that testing reveals zero failures. The optimal numbers of tasks to be tested are derived by optimisation of a cost criterion, taking into account the costs of testing and the costs of failures in the process after testing, assuming that such failures are not catastrophic to the system. Cost and time constraints on testing are also included in the analysis. We focus on study of the optimal numbers of tests for different types of tasks, depending on the arrival rate of tasks in the process and the costs involved. We briefly compare the results of this study with optimal test numbers in a similar setting, but with an alternative optimality criterion which is more suitable in case of catastrophic failures, as presented elsewhere. For these two different optimality criteria, the optimal numbers to be tested depend similarly on the costs of testing per type and on the arrival rates of tasks in the process after testing.