“…where P includes q loading vectors taken into account in PCA model, Λ = diag{λ 1 , λ 2 , ..., λ q }, and λ i are the eigenvalues of the covariance matrix in descending order, and x is an observation vector of dimension p. If at least one statistics exceeds its threshold, it is indicative of a fault detection. The monitoring and fault detection procedure will look as follows: 6 1. To form a sample matrix of the original data X k (k = 0) with N rows (measurements) and p columns (variables) under normal process conditions (in our case, p = 57 real process variables (temperatures, pressures, flow rates, levels, pressure drops, temperature differences) were taken into account; samples of variables were obtained from the SCADA system of the olefin production plant with a period of 5 min).…”