Assessment of Health Monitoring Trustworthiness of Avionics Systems

Abstract

The article provides a methodology for assessing the trustworthiness of health monitoring the dismounted avionics systems with automated test equipment (ATE). The indicators include the probabilities of false-positive, false-negative, true-positive, and true-negative. For the first time, we introduced into consideration the instability of the source of stimulus signal (SSS), the random and systematic component of the measuring channel error, and the reliability characteristics of the systems themselves. We consider a specific case of an exponential distribution of permanent failures and intermittent faults and derive formulas for calculating the trustworthiness indicators. Numerical calculations illustrate how the probabilities of correct and incorrect decisions depend on accuracy parameters. We show that the probabilities of false-positive and false-negative increase much faster than the probabilities of true-positive and true-negative decrease when the standard deviation of stimulus signal increases. For a Very High-Frequency Omni-Directional Range (VOR) receiver, we demonstrate that even with a zero random error generated by the source of the stimulus signal, the probabilities of false-positive and false-negative are different from zero.

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

“…63, 100; also referenced in [30] (pp. 57, 58), [31,32]) considered a mathematical model of corrective maintenance in the interval (0, ∞) with multiple imperfect inspections for a system that can be in one of the following states:…”

“…[27] (pp. 92, 97; also referenced in [34]) determined MS 1 ,..., MS 5 for the finite-horizon maintenance policy with the system states in (13) and the exponential distribution of time to failure as follows:…”

“…MTBUR, an operational metric, is calculated by dividing the total flight hours of a fleet by the number of unscheduled onboard component removals. Within the considered maintenance model, MTBUR is determined as follows [34]:…”

“…Aerospace 2024, 11, x FOR PEER REVIEW 14 of 58 component removals. Within the considered maintenance model, MTBUR is determined as follows [34]:…”

“…, if, at time t, the system is used for its intended purpose and is in the operable state S 2 , if, at time t, the system is used for its intended purpose and is in an inoperable state (unrevealed failure) S 3 , if, the system is not used for its intended purpose at the time t because of inspection S 4 , if, at timet, a false positive occurs and a repair of falsely rejected system is performed S 5 , if, at time t, a true positive occurs and a repair is performed S 6 , if, at time t, an unscheduled repair is carried out due to revealed failure (32) In the case of the exponential distribution of time to both unrevealed and revealed failure, F(t) = 1 − exp(−λt) and Φ(t) = 1 − exp(−λ 0 t), the mean times of the system staying in states S 1 , S 2 , S 3 , S 4 , S 5 , and S 6 in the interval (0, ∞), are as follows [27,35]:…”