  So far, problems of intermittent fault (IF) detection and detectability have
not been fully investigated in the multivariate statistics framework. The
characteristics of IFs are small magnitudes and short durations, and
consequently traditional multivariate statistical methods using only a single
observation are no longer effective. Thus in this paper, moving average T^2
control charts (MA-TCCs) with multiple window lengths, which simultaneously
employ a bank of MA-TCCs with different window lengths, are proposed to address
the IF detection problem. Methods to reduce false/missing alarms and infer the
IFs' appearing and disappearing time instances are presented. In order to
analyze the detection capability for IFs, definitions of guaranteed
detectability are introduced, which is an extension and generalization of the
original fault detectability concept focused on permanent faults (PFs). Then,
necessary and sufficient conditions are derived for the detectability of IFs,
which may appear and disappear several times with different magnitudes and
durations. Based on these conditions, some optimal properties of two important
window lengths are further discussed. In this way, a theoretical framework for
the analysis of IFs' detectability is established as well as extended
discussions on how the theoretical results can be adapted to real-world
applications. Finally, simulation studies on a numerical example and the
continuous stirred tank reactor (CSTR) process are carried out to show the
effectiveness of the developed methods.
