RESEARCH ON TIME-VARYING CHARACTERISTICS OF TESTABILITY INDEX BASED ON RENEWAL PROCESS

Testability indices are used in the phases of testability design and testability demonstration. This paper focuses on fault detection rate (FDR), which is the most widely used testability index. Leading hypothesis suggests that the value of FDR of a system is usually a certain value. However, few attempts have been made to research the statistical characteristics of FDR. Considering the fault occurrence process and test uncertainty, FDR is time varying and a special statistical process. Under the assumption of perfect repairs, we build a fault occurrence model based on the renewal process theory. Supposing that test uncertainty is mainly induced by test fault, the renewal process is employed to depict the occurrence process of test faults. Simultaneously, we depict the process of test state change and then construct the fault detection logic based on the digraph model. Combining the fault occurrence model and the fault detection logic, we focus on the expectation of FDR, which is one of the key statistical characteristics. By comparison, we introduce the calculation method of expectation of FDR in two cases, including without considering test uncertainty and considering test uncertainty. To validate the conclusions presented in this paper, we carry on a simulation case using an integrated controller. Based on the theoretic and simulating methods, the expectation of FDR tends to be a constant with the increase of time under the assumptions made in this paper. The statistical characteristic of FDR presented in this paper would be the basic theoretical guide to testability engineering.