SPCR-Based Control Chart for Autocorrelated Processes with High Dimensional Exogenous Variables

Year: 2016       Vol.: 65       No.: 2      

Authors: Paul Eric G. Abeto and Joseph Ryan G. Lansangan

Abstract:

Monitoring processes in an industry is one means to ensure the quality of goods produced or services provided. Control charts are constructed by estimating control limits wherein the process could be identified as stable. The estimation is made by analyzing the behavior of the monitored process. However, the assumptions of uncorrelatedness and normality of the measurements, common in most control charts, are sometimes uncharacteristic of the monitored process. Also, data from other variables may be available and may provide meaningful information on the behavior of the monitored process, and thus may be valuable in the estimation of the control limits. In this paper, a methodology of using sparse principal component regression from high dimensional exogenous variables to estimate control limits of autocorrelated processes is proposed. Simulations are made to further study different scenarios that may affect the proposed estimation. The false alarm rate, average run length during stable periods, and first detection rate upon structural change are used as key indicators for characterization and/or comparison. Simulation results suggest that modelling a process using high dimensional exogenous variables through sparse principal components creates better estimation of its corresponding control chart parameters. False alarm rates and average run lengths were comparable with the Exponentially Weighted Moving Average (EWMA) control chart. Also, faster identification of structural change was observed potentially due to the fact that the process is modelled in terms of other information carried by the exogenous variables.

Keywords: Control chart, autocorrelated process, high dimensional data, sparse principal component regression

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