A General Approach to Assessing the Trustworthiness of System Condition Prognostication

This paper proposes a mathematical model for assessing the trustworthiness of the system condition prognosis. The set of mutually exclusive events at the time of predictive 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 predicting the system condition at discrete times are proposed. The paper introduces the effectiveness indicators of predictive maintenance in the form of average operating costs, total error probability, and a posteriori probability of failure-free operation in the upcoming interval. We illustrate the developed approach by calculating the probabilities of correct and incorrect decisions for a specific stochastic deterioration process.