System Testability threshold design effectiveness via signal detection theory

Complex dynamic engineering systems i.e. Radar, gimbal, missile, infrared sensors, land vehicles, aircraft, ships, power plants become challenges for classical fault diagnostic system. They are modular consisting of modules or line replaceable units (LRU). Each module has its own BIT circuit that is linked with the system level BIT through the BIT architecture. The performance characteristic of the diagnostic system i.e. sensitivity and specificity is usually poor. Fault diagnostic for these systems are plagued with conditions known as False Alarm (FA), Missed Detection, Cannot Duplicate (CND) and Retest OK (RTOK) that have adverse impacts in Performance, Reliability, Maintainability, Availability, Safety and Affordability. These costly elusive problems may be due to many reasons; some of them are: absence or lack of fault modeling during the threshold design, absence or lack of test verticality, unobservable and uncontrollable modes of state variables in the system state space model. Where do Signal Detection Theory Techniques (SDTT) fit in the general scheme of classical fault diagnostic i.e. BIT threshold design? Signal detection theory models lend themselves readily to numerical computations suitable for solution on a computer that is applicable to classical BIT Testability threshold design. Nevertheless, several mathematical strategies must be used before one can apply SDTT into BIT detection. Since SDTT has been very reliable in many fields, in radar detection application, in medicine diagnostic tests, in biometrics, it can as well be a valuable tool in BIT threshold design with a few mathematical manipulations. This paper presents the foundations of SDTT in radar target detection theory in a coherent manner easy to follow and in a way to advance the BIT diagnostic threshold design while at the same time emphasizes the underlying physics. These techniques make use of Gaussian distribution and Bayesian statistics. Some of the most important performance measure- are sensitivity, specificity, prevalence. This paper addresses as well the test verticality issue and will introduce the unobservable and uncontrollable state variable issues. However, state observability and state controllability are beyond the scope of this paper and should be fully addressed in a control engineering model-based fault diagnostic research task.