Multivariate Coefficient Of Variation Research Articles

A multivariate coefficient of variation for functional data

A multivariate coefficient of variation for functional data

New adaptive control charts for monitoring the multivariate coefficient of variation

Abstract An adaptive control chart is one of the most effective techniques in Statistical Process Control (SPC). The coefficient of variation (CV) is common in many real life applications, especially in manufacturing and materials engineering, finance, medical and biological sciences. This paper proposes three adaptive charts to monitor the multivariate coefficient of variation (MCV), in order to improve the sensitivity of the standard MCV chart, in detecting small and moderate MCV shifts. The proposed charts are designed using the Markov chain approach and they are compared with the existing standard MCV chart using the average time to signal (ATS), standard deviation of the time to signal (SDTS) and expected average time to signal (EATS) criteria. The performance comparison shows that the proposed adaptive MCV charts, particularly the variable sample size and sampling interval (VSSI) MCV chart, outperform the existing MCV charts, in terms of the ATS and EATS criteria. By allowing the sample size and sampling interval to be varied in the VSSI MCV chart, process engineers will have better control in process monitoring and at the same time are able to detect an out-of-control signal quicker. Illustrative examples are presented by considering the VSSI MCV chart to show the chart’s implementation.

Multivariate coefficient of variation control charts in phase I of SPC

Multivariate control charts are mostly available for monitoring the process mean vector or the covariance matrix. Recently, work has been done on monitoring the multivariate coefficient of variation (CV) in phase II of the statistical process control (SPC). However, no study has investigated the performance of the multivariate CV charts in phase I. The phase I procedures are more important and involve the estimation of the charts’ limits from a historical or reference dataset that represents the in-control state of the process. In real life, contaminations are mostly present in the historical samples; hence, the phase I procedures are mostly adopted to get rid of these contaminated samples. In this study, we investigate the performance of a variety of multivariate CV charts in phase I considering both diffuse symmetric and localized CV disturbance scenarios, using probability to signal as a performance measure. A real-life application, concerning carbon fiber tubing, is also provided to show the implementation of the proposed charts in phase I. The findings of this study will be useful for practitioners in their selection of an efficient phase I control chart for monitoring multivariate CV.

One-sided control charts for monitoring the multivariate coefficient of variation in short production runs

In production, it is common to deal with short production runs, where flexibility is required in the built-up of parts to produce numerous variants of manufactured goods. Monitoring the multivariate coefficient of variation (MCV) is an effective method to monitor the relative multivariate variability compared with the mean. Monitoring the relative multivariate variability is important when practitioners are not interested in the changes in the mean vector or the covariance matrix. Monitoring the univariate coefficient of variation in short production runs has already been successfully executed. In this paper, the statistical performance of one-sided charts for monitoring the MCV of a multivariate process with finite horizon is investigated. Prior to this work, no attempt has been made to study process monitoring of MCV in short production runs. Investigations are made when the exact shift size can be specified and when there is a random shift size. It is found that the proposed upward chart detects an increasing shift in the MCV quicker than its downward counterpart detects a decreasing shift, for the same shift size (from the nominal value). An example is presented to illustrate the implementation of the new method.

Run sum chart for monitoring multivariate coefficient of variation

Coefficient of variation (CV) is an important quality characteristic to take into account when the process mean and standard deviation are not constants. A setback of the existing chart for monitoring the multivariate CV is that the chart is slow in detecting a multivariate CV shift in the Phase-II process. To overcome this problem, this paper proposes a run sum chart for monitoring the multivariate CV in the Phase-II process. The average run length (ARL), standard deviation of the run length (SDRL) and expected average run length (EARL), under the zero state and steady state cases, are used to compare the performance of the proposed chart with the existing multivariate CV chart. The proposed chart’s optimal parameters are computed using the Mathematica programs, based on the Markov chain model. Two one-sided run sum charts for monitoring the multivariate CV are considered, where they can be used simultaneously to detect increasing and decreasing multivariate CV shifts. The effects of different in-control CV values, number of regions, shift and sample sizes, and number of variables being monitored are studied. The implementation of the proposed chart is illustrated with an example using the data dealing with steel sleeve inside diameters.

The multivariate coefficient of variation for comparing serum protein electrophoresis techniques in external quality assessment schemes

External quality assessment (EQA) schemes are national or transnational programmes designed to control the analytical performance of clinical laboratories and to maintain inter-laboratory variability within acceptable limits. In such EQA programmes, participants are usually grouped by the type of assay technique/equipment they use. The coefficient of variation (CV) is a simple tool for comparing the inter-laboratory reproducibility of such techniques: the lower the CV, the better the analytical performance. Serum protein electrophoresis, a laboratory test profile consisting of five fractions (albumin, α 1, α 2, β and γ globulins) summing up to 100% of total proteins, can also be assayed in different ways depending on the media or the analytical principle. We propose a multivariate CV for comparing the performance of electrophoretic techniques in EQA, thus extending the univariate CV concept. First, the compositional nature of electrophoretic data requires a one-to-one transformation from the five-dimensional to the four-dimensional space. Next, robust estimations of the mean and the covariance matrix are needed to avoid the effect of outliers. The new approach is illustrated on electrophoretic datasets from the French and Belgian national EQA programmes.