Statistics and Its Interface

Volume 11 (2018)

Number 2

Nonparametric multivariate Polya tree EWMA control chart for process changepoint detection

Pages: 281 – 293

DOI: http://dx.doi.org/10.4310/SII.2018.v11.n2.a6

Authors

Yuhui Chen (Department of Mathematics, University of Alabama, Tuscaloosa, Al., U.S.A.)

Mingwei Sun (Department of Mathematics, University of Alabama, Tuscaloosa, Al., U.S.A.)

Timothy Hanson (Department of Statistics, University of South Carolina, Columbia, S.C., U.S.A.)

Abstract

In this article, we propose a nonparametric multivariate control scheme for simultaneously monitoring several related characteristics of a process in time. Through the use of a novel weighted multivariate Polya tree, the proposed method can quickly detect small mean and/or variance shifts in various types of longitudinal processes, Gaussian or non-Gaussian. Briefly, we center a weighted multivariate Polya tree at an initial parametric model on the monitored process, such as multivariate Gaussian; then by adding more details via data, departures from the parametric model will be captured and used for adjusting the initial model to obtain robust estimation. By weighting the Polya tree in the test statistic, the proposed chart thus can heighten the sensitivity of detecting one or more out of control characteristics. Examples show that our chart performs good for monitoring a process where the normality assumption is violated. Particularly, the proposed chart is more sensitive to variance shifts compared to the multivariate EWMA and multivariate CUSUM charts.

Keywords

changepoints, control charts, exponentially weighted predictive densities, MCUSUM, MEWMA, multivariate polya trees, nonparametric modelings, statistical process control

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Chen’s research was supported in part by 2015 Research Grants Committee, the University of Alabama.

Received 14 October 2016

Published 7 March 2018