Uncertainty Quantification of Imperfect Diagnostics

Abstract

The operable state of a system is maintained during operation, which requires knowledge of the system’s state. Technical diagnostics, as a process of accurately obtaining information about the system state, becomes a crucial stage in the life cycle of any system. The study deals with the relevant problem of uncertainty quantification of imperfect diagnostics. We considered the most general case when the object of diagnostics, the diagnostic tool, and the human operator can each be in one of the many states. The concept of a diagnostic error is introduced, in which the object of diagnostics is in one of many states but is erroneously identified as being in any other state. We derived the generalized formulas for the probability of a diagnostic error, the probability of correct diagnosis, and the total probability of a diagnostic error. The proposed generalized formulas make it possible to determine the probabilistic indicators of diagnosis uncertainty for any structures of diagnostics systems and any types of failures of the diagnostic tool and human operator. We demonstrated the theoretical material by computing the probabilistic indicators of diagnosis uncertainty for an aircraft VHF communication system and fatigue cracks in the aircraft wings.

A Historical Survey of Corrective and Preventive Maintenance Models with Imperfect Inspections: Cases of Constant and Non-Constant Probabilities of Decision Making

“…In 1987, ref. [94] (also referenced in [27]) proposed a maintenance model featuring a sequential inspection schedule. The inspection policies are considered for both finite and infinite time horizons.…”

“…Considering Equation (120), the equations for conditional probabilities-Equations ( 112)-(115)-are significantly simplified in [94] and [27] (p. 89):…”

“…• These models offer a more realistic representation of maintenance scenarios, considering the impact of scheduled inspections and unscheduled failures on the probability of errors. This class of maintenance models was considered in the studies [27,29,31,32,[34][35][36]56,94,95,[99][100][101][102][103][104].…”

“…. , t j−1 ; t j ξ) are called by the name of the event at the last moment under consideration, i.e., "false positive", "true negative", "true positive", and "false negative", and are determined by the following formulas given by [94], [27] (p. 89), and [29] (p. 17):…”

Classification of Systems and Maintenance Models

“…Studies [53,54] have shown that the probabilities of imperfect inspections at condition-based and predictive maintenance are functions of the degradation model parameters and strongly depend on time. In the study [55], the case of imperfect testing of the crack depth in a fighter wing was considered. The study showed that flight hours have a significant impact on the probabilities of a false positive and a false negative.…”