Detection of intermittent faults based on an optimally weighted moving average <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e256" altimg="si3.svg"><mml:msup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> control chart with stationary observations

The moving average (MA)-type scheme, also known as the smoothing method, has been well established within multivariate statistical process monitoring (MSPM) framework since 1990s. However, its theoretical basis is still limited to independent data, and optimality of equally or exponentially weighted scheme remains unproven. This paper aims weaken independence assumption in existing MA then extend it a broader area dealing with autocorrelated weakly stationary processes. With discovery non-optimality schemes used for fault detection when data have autocorrelation, essence that they do not effectively utilize correlation information samples revealed, giving birth an optimally (OWMA) theory. OWMA method combined Hotelling's $T^2$ statistic form control chart (OWMA-TCC), order detect more challenging type fault, i.e., intermittent (IF). Different from puts equal weight on time window, OWMA-TCC uses (autocorrelation cross-correlation) find optimal vector (OWV) purpose IF (IFD). In achieve best IFD performance, concept detectability defined corresponding conditions are provided, which further serve selection criteria OWV. Then, OWV given solution nonlinear equations, whose existence proven aid Brouwer fixed-point Moreover, symmetrical structure any directions exhibit no autocorrelation proven.