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A Laplacian spectral method in phase I analysis of profiles

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  • Francisco Moura Neto
  • Maysa S. De Magalhães

Abstract

The statistical process control of certain complex production processes or products rely on the monitoring of profiles. In this work, we consider a spectral‐based method to distinguish between outlier and nonoutlier observations to establish profile parameters. The proposed method is based on the spectral theory of the Laplacian of a graph, more specifically, a Laplacian eigenmap. The graph is constructed by considering each profile as a node, and by adjusting edge weights on the graph to reflect the resemblance between profiles. Laplacian eigenmaps have been used to represent data, to reduce data dimension, and for clustering. The proposed method can be used for complex profiles because it does not require the function between the dependent and independent variables. We apply the proposed method to an artificially generated data set from a nonlinear profile and to a wood board production problem. The results are compared with existing methods in the literature and show that the proposed method performs satisfactorily. Copyright © 2012 John Wiley & Sons, Ltd.

Suggested Citation

  • Francisco Moura Neto & Maysa S. De Magalhães, 2012. "A Laplacian spectral method in phase I analysis of profiles," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 28(3), pages 251-263, May.
    • Handle: RePEc:wly:apsmbi:v:28:y:2012:i:3:p:251-263
    DOI: 10.1002/asmb.1916
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    1. Moura Neto, F. & Souza, P. & de Magalhães, M.S., 2019. "Determining baseline profile by diffusion maps," European Journal of Operational Research, Elsevier, vol. 279(1), pages 107-123.

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