Extensions Of Multivariate Coefficient Of Variation Control Charts
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Date
2021-02
Authors
Ayyoub, Heba Nasr Awwad
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Publisher
Universiti Sains Malaysia
Abstract
Control charts for monitoring multivariate coefficient of variation (MCV) are applied when the interest is in monitoring the relative multivariate variability to the mean vector of a multivariate process. This thesis proposes an upper-sided variable sampling interval (VSI) exponentially weighted moving average (EWMA) chart to detect upward shifts in the MCV squared (𝛾2), that is, the upper-sided VSI EWMA-𝛾2 chart. Formulae to compute the control limits and performance measures (using the Markov chain approach) of the upper-sided VSI EWMA-𝛾2 chart are given. The findings show that a large sample size (𝑛), a small number of variables monitored simultaneously (𝑝) and a small value of in-control MCV (𝛾0) result in a faster detection of process shifts. Comparative studies show that the upper-sided VSI EWMA-𝛾2 chart outperforms the existing upper-sided MCV charts in detecting upward shifts in the process MCV. In addition, the effects of measurement errors on the performances of the Shewhart-MCV chart are studied. Consequently, this thesis also proposes two one-sided Shewhart-MCV charts in the presence of measurement errors for detecting downward and upward MCV shifts separately. The distributional properties of the population and sample MCVs with a linearly covariate error model are derived. The formulae to compute the control limits and average run lengths (ARLs) of these measurement errors based Shewhart-MCV charts are derived. A step-by-step procedure explaining the effects of a false assumption of no measurement error on the Shewhart-MCV charts is detailed. The findings show that for the lower-sided Shewhart-MCV chart, the ARL value becomes larger than expected as the value of the diagonal elements of 𝜽 increases. On the contrary, for the upper-sided Shewhart-MCV chart, the ARL value becomes smaller than expected as the value of the diagonal elements of 𝜽 increases. Thus, the lower-sided and upper-sided Shewhart-MCV charts are no longer reliable when the control limits adopted are computed by ignoring the presence of measurement errors when in actuality measurement errors exist. Furthermore, in this thesis, the upper-sided Shewhart-MCV and EWMA-𝛾2 charts in the presence of measurement errors are developed. A different approach in the formulae derivation of the population and sample MCVs with a linearly covariate error model is used in developing the two one-sided Shewhart-MCV charts and the upper-sided Shewhart-MCV chart. The formulae for computing the control limits and performance measures of the upper-sided Shewhart-MCV and EWMA-𝛾2 charts in the presence of measurement errors are derived. The effect of the presence of measurement errors on these two latter charts is studied. The findings show that the smaller the value of the measurement error ratio (𝜃2), the faster are the Shewhart-MCV and EWMA-𝛾2 charts in detecting an out-of-control situation, indicating the negative effect of measurement errors on the performances on both charts. In addition, by increasing the number of times an item is measured (𝑚) and the value of the diagonal elements of matrix 𝑩, the effect of the presence of measurement errors is reduced. The MATLAB software is used to conduct all the numerical analyses, while simulation using the SAS software is employed to verify the accuracy of the numerical computations obtained using MATLAB. Finally, illustrative examples using real life data are presented for all the proposed charts.
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Mathematics