EFFECT OF CORRELATION ON STATISTICAL PERFORMANCE OF X AND HOTELLING’S T QUALITY CONTROL CHARTS USING AVERAGE RUN LENGTH OF TYPE I ERROR

Abstract

The effect of correlation on statistical performance of X and Hotelling’s T
quality control charts were examined. Two random variables from normal distribution were generated at a specified level of correlations ranging from -0.9 to +0.9 for 5000 data points having repeated samples of size five each were simulated using
R 10.2 software. Simulated data were analyzed using Shewart X -chart and Hotelling T
2
chart to investigate
for Type I error (α). It was observed that the average probability of Type I error for univariate vary as the level
of correlation increases where as the average of Type I error for multivariate did not varied as a result of change in the level of correlation. It has been observed also that multivariate chart yielded less error compared to univariate and therefore performed better. It has also been observed from Average Run Length (ARL) of Type I error that multivariate performed better than univariate because the multivariate takes more samples compare to univariate before recording an out –of – control signal. Finally, it is recommended that level of correlation should be examined when subjecting several variable characteristics for quality testing.