Quickest Detection of Failures in Autoregressive Stochastic Systems in Short Periods

The research in this paper is entirely consistent with the following FTC conference topics: primarily “Artificial Intelligence: Decision Making” and secondary, as its applications “Security: Internet Security and Cyber Security”. Namely, this paper is devoted to disruption detection in the operation of stochastic systems described by random autoregressive time series with unknown parameters after change. The main challenge is detecting failures or malfunctions as quickly as possible in an optimal way in short periods. The Bayesian approach based on a bounded number of observations proposed in a research (Pchelintsev, et al., 2024) for the Markov statistical models with known post-change distributions is used to do this. Based on the methods for making optimal stopping decisions, the quickest truncated sequential detection algorithm is proposed that controls the detection error, i.e. one that is optimal in the sense of minimum delay, provided that the error probability is bounded by some fixed known threshold. Moreover, through the numeric Monte Carlo method it is established that in practical calculations the proposed detection procedures are always better than classical Bayesian ones based on the posterior probabilities.