Assessing trustworthiness of system operability checking

Abstract

This study proposes a mathematical model for assessing the trustworthiness indicators of the operability checking for a deteriorating system. The set of mutually exclusive events at the time of operability checking are analyzed. Correct and incorrect decisions correspond to events such as true-positive, false-positive, true-negative, and false-negative. General expressions for computing the probabilities of possible decisions when checking the system operability at a discrete time are proposed. The paper introduces the effectiveness indicators of corrective maintenance such as average operating costs, total error probability, and a posteriori probability of failure-free operation. We illustrate the developed approach by calculating the probabilities of correct and incorrect decisions for a specific stochastic deterioration process.

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

“…In 2021, ref. [104] presented a mathematical model designed to assess the trustworthiness indicators associated with operability checks for a system undergoing deterioration. An examination of mutually exclusive events during operability checks is carried out, with correct and incorrect decisions corresponding to events such as false positives, true negatives, false negatives, and true positives.…”

“…• 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].…”

“…We also note that with a symmetric PDF of error in estimating time to failure, the maximum values of the conditional probabilities of a false positive and a false negative for a single inspection are equal to 0.5. It should also be noted that in the maintenance models considered in [27,29,31,32,[34][35][36]56,101,102,104], the conditional probabilities of correct and incorrect decisions during multiple inspections consider both the moments of inspections and the moment of failure. Moreover, these probabilities also depend on the parameters of the degradation process.…”

Probabilistic indicators of imperfect inspections used in modeling condition-based and predictive maintenance

“…Uansky 9,10 considered a corrective maintenance model where the conditional probabilities of correct and incorrect decisions at multiple inspections depend on the system’s failure time and the degradation process parameters. Raza and Ulansky 11 proposed a model for computing the probabilities of possible decisions when inspecting the system’s operability at discrete times. The probabilities of correct and incorrect decisions depend on the failure and inspection time.…”

“…Based on (11), we can convert the previously introduced decision rule to the following form: the system is judged as operable over the time interval (t i , t i + 1 ) if u A,i . t i ; otherwise (i.e.…”