Modified chart with optimized ARLs in autocorrelated processes

Abstract

Purpose

The purpose of this paper is to counter autocorrelation by designing the chart, using warning limits. Various optimal schemes of modified chart are proposed for various sample sizes (n) at levels of correlation (Φ) of 0.00, 0.475 and 0.95. These optimal schemes of modified chart are compared with the double sampling (DS) chart, suggested by Costa and Claro (2008).

Design/methodology/approach

The performance of the chart is measured in terms of the average run length (ARL) that is the average number of samples before getting an out-of-control signal. Ultimately, due to the effect of autocorrelation among the data, the performance of the chart is suspected. The ARLs at various sets of parameters of the chart are computed by simulation, using MATLAB. The suggested optimal schemes are simpler schemes with limited number of parameters and smaller sample size (n=4) and this simplicity makes them very helpful in quality control.

Findings

The suggested optimal schemes of modified chart are compared with the DS chart, suggested by Costa and Claro (2008). It is concluded that the modified chart outperforms the DS chart at various levels of correlation (Φ) and shifts in the process mean. The simplicity in the design of modified chart, makes it versatile for many industries.

Research limitations/implications

Both the schemes are optimized by assuming the normal distribution. But this assumption may also be relaxed to design theses schemes for autocorrelated data. The optimal schemes for chart can be developed for variable sample size and for variable sampling intervals. The optimal schemes can also be explored for cumulative sum and exponentially weighted moving average charts.

Practical implications

The correlation among the process outputs of any industry can be find out and corresponding to that level of correlation the suggested control chart parameters can be applied. The understandable and robust design of modified chart makes it usable for industrial quality control.

Social implications

The rejection level of products in the industries can be reduced by designing the better control chart schemes which will also reduce the loss to the society, as suggested by Taguchi (1985).

Originality/value

Although it is the extension of previous work but it can be applied to various manufacturing industries as well as service industries, where the data are positively correlated and normally distributed.

Citation

Prajapati, D.R. and Singh, S. (2015), "Modified chart with optimized ARLs in autocorrelated processes", The TQM Journal, Vol. 27 No. 5, pp. 633-647. https://doi.org/10.1108/TQM-04-2013-0052