A simple and effective R chart to monitor the process variance

Abstract

Purpose

The purpose of this paper is to introduce a new design of an R chart to catch smaller shifts in the process dispersion as well as maintaining the simplicity so that it may be applied at shopfloor level.

Design/methodology/approach

Here a new R chart has been proposed which can overcome the limitations of Shewhart, CUSUM and EWMA range charts. The concept of this R chart is based on chi‐square (χ²) distribution. Although CUSUM and EWMA charts are very useful for catching the small shifts in the mean or standard deviation, they can catch the process shift only when there is a single and sustained shift in process average or standard deviation.

Findings

It was found that the proposed chart performs significantly better than the conventional (Shewhart) R chart, CUSUM range schemes proposed by Chang and Gan for most of the process shifts in standard deviation. The ARLs of the proposed R chart is higher than ARLs of CUSUM schemes for only ten cases out of 40. The performance of the proposed R chart has also been compared with the variance chart proposed by Chang and Gan for various shifts in standard deviation. The ARLs of the proposed R chart are compared with Chang's R chart for sample sizes of 3 and it can be concluded from the comparisons that the proposed R chart is much better than Chang's variance chart for all shift ratios for sample size of three. Many difficulties related to the operation and design of CUSUM and EWMA control charts are greatly reduced by providing a simple and accurate proposed R chart scheme. The performance characteristics (ARLs) of the proposed charts are very comparable to a great degree with FIR CUSUM, simple CUSUM and other variance charts. It can be concluded that, instead of considering many parameters, it is better to consider single sample size and single control limits because a control chart loses its simplicity with a greater number of parameters. Moreover, practitioners may also find difficulty in applying it in production processes. On the other hand, CUSUM control charts are not effective when there is a single and sustained shift in the process dispersion.

Research limitations/implications

A lot of effort has been done to develop the new range charts for monitoring the process dispersion. Various assumptions and factors affecting the performance of the R chart have been identified and taken into account. In the proposed design, the observations have been assumed independent of one another but the observations may also be assumed to be auto‐correlated with previous observations and the performance of the proposed R chart may be studied.

Originality/value

The research findings could be applied to various manufacturing and service industries as it is more effective than the conventional (Shewhart) R chart and simpler than CUSUM charts.

Citation

Prajapati, D.R. and Mahapatra, P.B. (2009), "A simple and effective R chart to monitor the process variance", International Journal of Quality & Reliability Management, Vol. 26 No. 5, pp. 497-512. https://doi.org/10.1108/02656710910956210