Statistical Analysis of Time-Varying Characteristics of Testability Index Based on NHPP

The failure detection rate (FDR) is the most common testability index used to evaluate the equipment testability level. According to the testability test theory of FDR, a widespread supposition is that the FDR value of a system is an unknown constant. However, there have been a few attempts to research the sample property of failure detection and the statistical characteristics of FDR to prove this fundamental premise. Considering the real maintenance effects on the failure occurrence process, the value of FDR catches time-varying characteristics, which can be depicted as a special statistical process. A failure occurrence model based on the non-homogeneous Poisson process (NHPP) is proposed to depict failure occurrence samples under the assumption of minimal maintenance policy. The binominal cumulative probability function (CDF) is used to depict the each failure detection action. Combining the NHPP based failure occurrence model and the failure detection model based on a binominal distribution, we can simulate the failure detection samples and statistical characteristics of FDR based on the Monte Carlo method. This paper mainly focuses on the expectation and variance of FDR, which are two key statistical characteristics. To validate the FDR time-varying characteristics, we perform a simulation using two Shop Replaceable Units in a level flight indicator of a helicopter to evaluate the FDR value. Based on theoretic and simulative methods, the FDR expectation of the level flight indicator has an increasing or decreasing tendency in the early stages and tends to be a constant in later stages, while the variation of FDR keeps monotonously decreasing. Under the assumptions made in this paper, the supposition that the FDR value of a system is a certain value is not suitable in all stages of the failure occurrence process.