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Simultaneous Univariate X_bar Charts to Control Bivariate Processes with Autocorrelated Data
Author(s) -
Leoni Roberto Campos,
Machado Marcela Aparecida Guerreiro,
Costa Antonio Fernando Branco
Publication year - 2015
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.1697
Subject(s) - autocorrelation , bivariate analysis , univariate , statistics , autoregressive model , control chart , mathematics , \bar x and r chart , sample size determination , bar (unit) , covariance matrix , econometrics , multivariate statistics , computer science , physics , control limits , process (computing) , meteorology , operating system
In this article, we consider the simultaneous univariate X_bar charts (SU X_bar charts) for samples of n bivariate observation vectors that are not only cross‐correlated but also autocorrelated. The cross‐covariance matrix of the sample mean vectors was derived with the assumption that the observations are described by a first‐order vector autoregressive model. The combined effect of the cross‐correlation and autocorrelation on the performance of the SU X_bar charts is investigated. Depending on the autocorrelations and the nature of the disturbance, affecting only one or both variables, the SU _bar charts perform better with samples of size one than with samples of size two; in same cases even better than with samples of size four. When the two variables are affected by the assignable cause, the simultaneous charts tend to perform better than the T 2 chart as the autocorrelation and cross‐correlation increase. Copyright © 2014 John Wiley & Sons, Ltd.
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