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An evaluation of the multivariate dispersion charts with estimated parameters under non‐normality

An evaluation of the multivariate dispersion charts with estimated parameters under non‐normality Various charts such as |S|, W, and G are used for monitoring process dispersion. Most of these charts are based on the normality assumption, while exact distribution of the control statistic is unknown, and thus limiting distribution of control statistic is employed which is applicable for large sample sizes. In practice, the normality assumption of distribution might be violated, while it is not always possible to collect large sample size. Furthermore, to use control charts in practice, the in‐control state usually has to be estimated. Such estimation has a negative effect on the performance of control chart. Non‐parametric bootstrap control charts can be considered as an alternative when the distribution is unknown or a collection of large sample size is not possible or the process parameters are estimated from a Phase I data set. In this paper, non‐parametric bootstrap multivariate control charts |S|, W, and G are introduced, and their performances are compared against Shewhart‐type control charts. The proposed method is based on bootstrapping the data used for estimating the in‐control state. Simulation results show satisfactory performance for the bootstrap control charts. Ultimately, the proposed control charts are applied to a real case study. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Stochastic Models in Business and Industry Wiley

An evaluation of the multivariate dispersion charts with estimated parameters under non‐normality

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References (43)

Publisher
Wiley
Copyright
Copyright © 2017 John Wiley & Sons, Ltd.
ISSN
1524-1904
eISSN
1526-4025
DOI
10.1002/asmb.2272
Publisher site
See Article on Publisher Site

Abstract

Various charts such as |S|, W, and G are used for monitoring process dispersion. Most of these charts are based on the normality assumption, while exact distribution of the control statistic is unknown, and thus limiting distribution of control statistic is employed which is applicable for large sample sizes. In practice, the normality assumption of distribution might be violated, while it is not always possible to collect large sample size. Furthermore, to use control charts in practice, the in‐control state usually has to be estimated. Such estimation has a negative effect on the performance of control chart. Non‐parametric bootstrap control charts can be considered as an alternative when the distribution is unknown or a collection of large sample size is not possible or the process parameters are estimated from a Phase I data set. In this paper, non‐parametric bootstrap multivariate control charts |S|, W, and G are introduced, and their performances are compared against Shewhart‐type control charts. The proposed method is based on bootstrapping the data used for estimating the in‐control state. Simulation results show satisfactory performance for the bootstrap control charts. Ultimately, the proposed control charts are applied to a real case study.

Journal

Applied Stochastic Models in Business and IndustryWiley

Published: Jan 1, 2017

Keywords: ; ; ; ; ; ;

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