Title: Optimal schemes of standard range chart for auto-correlated observations

Authors: D.R. Prajapati; Sukhraj Singh

Addresses: Department of Mechanical Engineering, PEC University of Technology (formerly Punjab Engineering College), Chandigarh-160012, India ' Department of Mechanical Engineering, BBSBEC, Fatehgarh Sahib – 140407, Punjab, India

Abstract: In order to ensure homogeneous quality of the manufactured products, monitoring the process variance is as important as monitoring the process mean. Monitoring of process dispersion is also as important as monitoring the process mean. In actual practice, some process outputs are correlated, the performance of the (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. 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 chisquares. The performance of this modified (R) chart is computed for sample size of 4 and compared with conventional (R) chart. It is observed that when the level of correlation (Φ) increases, the performance of the conventional as well as modified (R) chart deteriorates. It is found that modified (R) chart performs much better than a conventional (Shewhart) (R) chart for all the cases.

Keywords: range charts; average run length; ARL; sample size; correlation level; autocorrelation; process variance; process monitoring; control charts; statistical process control; SPC.

DOI: 10.1504/IJQET.2014.059849

International Journal of Quality Engineering and Technology, 2014 Vol.4 No.1, pp.81 - 96

Received: 22 Apr 2013
Accepted: 13 Aug 2013
Published online: 17 May 2014 *

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