Asymmetric monitoring of multivariate data with nonlinear dynamics

We consider asymmetric change detection by generalizing the one-sided MEWMA control chart. In particular, we revise and extend the one-sided MEWMA algorithm to cope with mixed alternatives where some coordinates are allowed to increase and others may change in any direction. The motivating application is related to massive brake-disk production for the automotive industry. We consider monitoring of seven geometrical and dimensional parameters and show how the proposed method discriminates between geometrical deformation and dimensional shifts. As often happens in complex industrial processes, these data are nonlinear serially correlated. Therefore, we compute the thresholds of the one-sided MEWMA control charts using the semi-parametric stationary block bootstrap.     

A “maximum node clustering” problem

In this note we introduce a graph problem, called Maximum Node Clustering (MNC). We prove that the problem (which is easily shown to be strongly NP-complete) can be approximated in polynomial time within a ratio arbitrarily close to 2. For the special case where the graph is a tree, the problem is NP-complete in the ordinary sense; for this case we present a pseudopolynomial algorithm based on dynamic programming, and a related Fully Polynomial Time Approximation Scheme (FPTAS). Also, the tree case is shown to be exactly solvable in time, where n is the number of nodes.