A new approach to monitor the process dispersion

Abstract

Purpose

The concept of the proposed R chart is based on the sum of chi squares (χ²). The average run lengths (ARLs) of the proposed R chart are computed and compared with the ARLs of a standard R chart, Shewhart variance chart proposed by Chang and Gan, a CUSUM range chart (with and without FIR feature) proposed by Chang and Gan and also with an EWMA range chart proposed by Crowder and Hamilton for various chart parameters. This paper aims to show that only FIR CUSUM schemes perform better than the proposed R chart but other CUSUM and EWMA schemes are less efficient than the proposed R chart.

Design/methodology/approach

The concept of the proposed R chart is based on the sum of chi squares (χ²). The proposed R chart divides the plot area into three regions, namely: outright rejection region; outright acceptance region; and transition region. The NULL hypothesis is rejected if a point falls beyond the control limit, and accepted if it falls below the warning limit. However, when a point falls beyond the warning limit, but not beyond the control limit, the decision is taken on the basis of individual observations of the previous H samples, which are considered to evaluate statistic U, that is the sum of chi squares. The NULL hypothesis is rejected if U exceeds a predefined value (U*) and accepted otherwise.

Findings

The comparisons also show that the CUSUM, EWMA and proposed R charts outperform the Shewhart R chart by a substantial amount. It is concluded that only FIR CUSUM schemes perform better than the proposed R chart, as it is second in ranking. The other CUSUM and EWMA schemes are less efficient than the proposed R chart.

Research limitations/implications

CUSUM and EWMA charts can catch a small shift in the process average but they are not efficient to catch a large shift. Many researchers have also pointed out that these charts' applicability is limited to the chemical industries. Another limitation of CUSUM and EWMA charts is that they can catch the shift only when there is a single and sustained shift in the process average. If the shift is not sustained, then they will not be effective.

Practical implications

Many difficulties related to the operation and design of CUSUM and EWMA control charts are greatly reduced by providing a simple and accurate proposed scheme. The performance characteristics (ARLs) of the proposed charts described in this paper are very much comparable with FIR CUSUM, CUSUM, EWMA and other charts. It can be concluded that, instead of considering many chart parameters used in CUSUM and EWMA charts, it is better to consider a simple and more effective scheme, because a control chart loses its simplicity with multiple parameters. Moreover, practitioners may also experience difficulty in using these charts in production processes.

Originality/value

It is a modification of the Shewhart Range Chart but it is more effective than the Shewhart Range chart, as shown in the research paper.

Citation

Prajapati, D.R. (2011), "A new approach to monitor the process dispersion", International Journal of Quality & Reliability Management, Vol. 28 No. 3, pp. 280-297. https://doi.org/10.1108/02656711111109892