Multivariate adaptive approach for monitoring simple linear profiles

Authors:
Galal M. Abdella;Kai Yang;Adel Alaeddini
Affiliations:
Department Industrial and Systems Engineering, Wayne State University, 4815 Fourth St., Detroit, Michigan 48202, USA;Department Industrial and Systems Engineering, Wayne State University, 4815 Fourth St., Detroit, Michigan 48202, USA;Department of Industrial and Operations Engineering, University of Michigan, 1205 Beal Ave., Ann Arbor, MI 48109, USA
Venue:
International Journal of Data Analysis Techniques and Strategies
Year:
2014

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Abstract

Adaptive sample size and sampling intervals schemes have been widely used to improve the statistical efficiency of Hotelling T² control chart in detecting small changes when the quality of a product or a process can be characterised by the multivariate distribution of quality characteristics. In this paper, we design a Hotelling T² scheme varying sample sizes and sampling intervals VSSI-T² for accelerating the speed of detecting off-target conditions in linear profile parameters. We investigate the statistical performance of the adaptive approach versus its fixed sampling counterparts. To find the optimal setting of the VSSI-T², we build an optimisation model solved using genetic algorithm GA. Also, average time to signal ATS is considered as the objective function of the model and estimated using the Markov chain fundamentals. The comparative studies reveal the potentials of the adaptive scheme in improving the performance of the Hotelling T² control chart in monitoring linear profiles.