Statistical Development of the V S Q -Control Chart for Extreme Data with an Application to the Carbon Fiber Industry

Abstract

The normality assumption is a significant part of the development of control charts. This underlying assumption of normality most likely does not hold true in real scenarios. One of such designs usually devised to observe the target parameter ${\sigma }^2$ of the Maxwell quality characteristics is the $V$ -control chart. In general, quality practitioners preferably have to observe the scale parameter $\sigma$ rather than ${\sigma }^2$ in examined processes. The contemporary $V$ -control chart is relying on the $V$ -statistic which does not hold the unbiasedness property with respective to parameter $\sigma$ of the Maxwell probability model. In view of this, implementation of the $V$ -chart is not an appropriate design in monitoring a real parameter of the underlying Maxwell data. To accommodate the monitoring of the parameter $\sigma$ of the Maxwell model, a novel design of the $V_{SQ}$ -chart is mainly proposed in this work. To support a statistical understanding of the $V_{SQ}$ -chart, power function, characteristic function, and the average run length $\left(\text{ARL}\right)$ have been essentially established. The parameters of the $V_{SQ}$ -chart are determined from the results of the sampling distribution of the derived statistic. Analytical findings are further applied to determine the performance of the study proposal with its existing counterpart. Substantially, the better performance of the proposed technique has been observed because of statistical power used as a performance measure. Eventually, the computational plan of the $V_{SQ}$ -chart is considered both for the simulated and real datasets with the aim of illustrating the theory of the proposed design.