233 research outputs found

    Affine invariant signed-rank multivariate exponentially weighted moving average control chart for process location monitoring

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    Multivariate statistical process control (SPC) charts for detecting possible shifts in mean vectors assume that data observation vectors follow a multivariate normal distribution. This assumption is ideal and seldom met. Nonparametric SPC charts have increasingly become viable alternatives to parametric counterparts in detecting process shifts when the underlying process output distribution is unknown, specifically when the process measurement is multivariate. This study examined a new nonparametric signed-rank multivariate exponentially weighted moving average type (SRMEWMA) control chart for monitoring location parameters. The control chart was based on adapting a multivariate spatial signed-rank test. The test was affine-invariant and the weighted version of this test was used to formulate the charting statistic by incorporating the exponentially weighted moving average (EWMA) scheme. The test\u27s in-control (IC) run length distribution was examined and the IC control limits were established for different multivariate distributions, both elliptically symmetrical and skewed. The average run length (ARL) performance of the scheme was computed using Monte Carlo simulation for select combinations of smoothing parameter, shift, and number of p-variate quality characteristics. The ARL performance was compared to the performance of the multivariate exponentially weighted moving average (MEWMA) and Hotelling T2. The control charts for observation vectors sampled the multivariate normal, multivariate t, and multivariate gamma distributions. The SRMEWMA control chart was applied to a real dataset example from aluminum smelter manufacturing that showed the SRMEWMA performed well. The newly investigated nonparametric multivariate SPC control chart for monitoring location parameters--the Signed-Rank Multivariate Exponentially Weighted Moving Average (SRMEWMA)--is a viable alternative control chart to the parametric MEWMA control chart and is sensitive to small shifts in the process location parameter. The signed-rank multivariate exponentially weighted moving average performance for data from elliptically symmetrical distributions is similar to that of the MEWMA parametric chart; however, SRMEWMA\u27s performance is superior to the performance of the MEWMA and Hotelling\u27s T2 control charts for data from skewed distributions

    Multivariate Statistical Process Control Charts: An Overview

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    In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.quality control, process control, multivariate statistical process control, Hotelling's T-square, CUSUM, EWMA, PCA, PLS

    Procedure to evaluate multivariate statistical process control using ARIMA-ARCH models

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    Technological development and production processes require statistical process control in the use of alternative techniques to evaluate a productive process. This paper proposes an alternative procedure for monitoring a multivariate productive process using residuals obtained from the principal component scores modeled by the general class of autoregressive integrated moving average (ARIMA) and the generalized autoregressive conditional heteroskedasticity (GARCH) processes. We seek to obtain and investigate non-correlated and independent residuals by means of X-bar and exponentially weighted moving average (EWMA) charts as a way to capture large and small variations in the productive process. The principal component analysis deals with the correlation among the variables and reduces the dimensions. The ARIMA-GARCH model estimates the mean and volatility of the principal components selected, providing independent residuals that are analyzed using control charts. Thus, a multivariate process can be assessed using univariate techniques, taking into account both the mean and the volatility behavior of the process. Therefore, we present an alternative procedure to evaluate a process with multivariate features to determine the level of volatility persistence in the productive process when an external action occurs

    Nonparametric (distribution-free) control charts : an updated overview and some results

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    Control charts that are based on assumption(s) of a specific form for the underlying process distribution are referred to as parametric control charts. There are many applications where there is insufficient information to justify such assumption(s) and, consequently, control charting techniques with a minimal set of distributional assumption requirements are in high demand. To this end, nonparametric or distribution-free control charts have been proposed in recent years. The charts have stable in-control properties, are robust against outliers and can be surprisingly efficient in comparison with their parametric counterparts. Chakraborti and some of his colleagues provided review papers on nonparametric control charts in 2001, 2007 and 2011, respectively. These papers have been received with considerable interest and attention by the community. However, the literature on nonparametric statistical process/quality control/monitoring has grown exponentially and because of this rapid growth, an update is deemed necessary. In this article, we bring these reviews forward to 2017, discussing some of the latest developments in the area. Moreover, unlike the past reviews, which did not include the multivariate charts, here we review both univariate and multivariate nonparametric control charts. We end with some concluding remarks.https://www.tandfonline.com/loi/lqen20hj2020Science, Mathematics and Technology Educatio

    An Explanatory Study on the Non-Parametric Multivariate T2 Control Chart

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    Most control charts require the assumption of normal distribution for observations. When distribution is not normal, one can use non-parametric control charts such as sign control chart. A deficiency of such control charts could be the loss of information due to replacing an observation with its sign or rank. Furthermore, because the chart statistics of T2 are correlated, the T2 chart is not a desire performance. Non-parametric bootstrap algorithm could help to calculate control chart parameters using the original observations while no assumption regarding the distribution is needed. In this paper, first, a bootstrap multivariate control chart is presented based on Hotelling’s T2 statistic then the performance of the bootstrap multivariate control chart is compared to a Hotelling’s T2 parametric multivariate control chart, a multivariate sign control chart, and a multivariate Wilcoxon control chart using a simulation study. Ultimately, the bootstrap multivariate control chart is used in an empirical example to study the process of sugar production

    Some new nonparametric distribution-free control charts based on rank statistics

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    Ph.DDOCTOR OF PHILOSOPH

    Monitoring Animal Well-being

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