An adaptive step-down procedure for fault variable identification

In a process with a large number of process variables (high-dimensional process), identifying which variables cause an out-of-control signal is a challenging issue for quality engineers. In this paper, we propose an adaptive step-down procedure using conditional T -super-2 statistic for fault variable identification. While existing procedures focus on selecting variables that have strong evidence of a change, the proposed step-down procedure selects a variable having the weakest evidence of a change at each step based on the variables that are selected in previous steps. The information of selected unchanged variables is effectively utilised in obtaining a powerful conditional T -super-2 test statistic for identifying the changed elements of the mean vector. The proposed procedure is designed to utilise the correlation information between fault and non-fault variables for the efficient fault variables identification. Further, the simulation results show that the proposed procedure has the better diagnostic performance compared with existing methods in terms of fault variable identification and computational complexity, especially when the number of the variables is high and the number of fault variables is small.