Detection of Intermittent Faults Based on an Optimally Weighted Moving Average T^2 Control Chart with Stationary Gaussian Observations

The moving average (MA) technique, also known as the smoothing technique, has been well established within the multivariate statistical process monitoring (MSPM) framework since the 1990s. However, it is still limited to handling independent data, and the optimality of its equal weight scheme remains unproven. This paper aims to weaken the independence assumption in the existing MA technique, and then extend it to a broader area of dealing with autocorrelated stationary process, giving birth to a weighted moving average (WMA) technique. The WMA technique is combined with the Hotelling's T^2 statistic to form a WMA T^2 control chart (WMA-TCC), in order to detect a more challenging type of fault, i.e., intermittent fault (IF). Different from the MA technique that puts an equal weight on samples within a time window, WMA-TCC uses correlation (autocorrelation and cross-correlation) information to find an optimal weight vector for the purpose of IF detection (IFD). In order to achieve a best IFD performance, the concept of IF detectability is defined and corresponding detectability conditions are provided, which further serve as selection criteria of the optimal weight. Then, the optimal weight is given in the form of a solution to nonlinear equations, whose existence is proven with the aid of the Brouwer fixed-point theory. Moreover, symmetrical structure of the optimal weight is revealed, and the optimality of an equal weight scheme when data exhibit no autocorrelation is proven. Finally, simulations on a numerical example and the continuous stirred tank reactor process are carried out to give a comprehensive comparison among WMA-TCC and several existing static and dynamic MSPM methods. The results show a superior IFD performance of the developed methods.