A modified range (R) chart to monitor process dispersion of autocorrelated data

Abstract

The range (R) charts are widely used in industries to monitor the process dispersion. Monitoring process dispersion is as important as monitoring the process mean. In actual practice, some process outputs are correlated, the performance of R chart may have adverse effect on it. The performance of the chart is measured in terms of the average run length (ARL), which is the average number of samples before an out-of-control signal is obtained. Ultimately, the performance of these charts may be suspected due to autocorrelation. In this paper, an attempt is made to counter the autocorrelation by designing the new R chart named modified R chart, based on sum of chi-squares. The performance of this modified R chart is computed for sample sizes of 3 and 5. It is observed that when the level of correlation (Φ) increases, the performance of the modified R chart deteriorates. Moreover, the modified R chart for sample size of three and five is compared with adaptive R charts, suggested by Lee (2011) at zero level of correlation (Φ). It is found that modified R chart performs better than adaptive R charts for most of the cases.