A process variability control chart
Construction of a Shewhart-type control chart is considered for the variance (deviation) of a monitored process \(Y\) in the case when some information on an auxiliary characteristic X is available. The chart utilizes a ratio type estimator for the variance \(V_t\) of \(Y\) at the moment \(t\), i.e., \(\hat V_t=s^2_Y(\sigma^2_x/s^2_x)^{\rho^2_{xy}}\), where \(s_y^2\), \(s^2_x\) are the sample variances of \(Y\) and \(X\), \(\sigma_x^2\) is the true variance of \(X\) (known) and \(\rho^2_{xY}\) is the known true correlation between \(X\) and \(Y\). The authors construct the center line, and lower and upper control limits for their control chart, basing on Monte Carlo approximations for the corresponding constants. The performance of the constructed \(V_t\) chart is compared to the performance of the classical Shewhart \(S^2\)-chart and some other charts by simulated data.
scientific article; zbMATH DE number 5925222
scientific article