Performance of CUSUM and EWMA charts for serial correlation
Authors: Singh Sukhraj , Prajapati D.R. 
Published: April 2013

PurposeThe purpose of this paper is to study the effect of correlation on the performance of CUSUM and EWMA charts. The performance of the CUSUM and EWMA charts is measured in terms of average run lengths (ARLs) for the positively correlated data. The ARLs at various set of parameters of the CUSUM and EWMA charts are computed, using MATLAB. The behavior of the CUSUM and EWMA chart at the various shifts in the process mean is studied, analyzed and compared at different levels of correlation (Φ). The optimum schemes for both the charts are suggested for various levels of correlation (Φ).Design/methodology/approachPositively correlated observations having normal distribution are generated with the help of the MATLAB. Performance of both the charts in terms of ARLs is measured and compared at various levels of correlation (Φ). The optimal schemes of charts which give the desired in‐control ARLs are suggested for various levels of correlation (Φ).FindingsFor each level of correlation (Φ) various schemes of both the charts are suggested. Moreover those suggested schemes which give quick response to the shifts in the process mean is termed as optimal scheme. It is concluded that CUSUM schemes are preferred as compared to the EWMA schemes for quicker response. The optimal schemes of CUSUM and EWMA chart are also compared with the EWMAST chart suggested by Winkel and Zhang (2004).Research limitations/implicationsBoth the schemes are optimized by assuming the autocorrelated numbers to be normally distributed. But this assumption may also be relaxed to design these schemes for autocorrelated data. Moreover sample size of four is taken while developing these schemes; various other schemes can also be developed for different sample sizes. Control charts for attribute type of data can also be developed for different level of correlation (Φ).Practical implicationsFor a specific control chart, if the in‐control ARL of the process outputs of any industry is in accordance with the simulated in‐control ARL. It means the process outputs must have same level of correlation (Φ) corresponding to the simulated in‐control ARL and the suggested optimal schemes, corresponding to that level of correlation (Φ), must be adopted to avoid the false alarm rate. 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. Thus false alarms generated, will be minimum for the suggested schemes at different level of correlation (Φ).Social implicationsIf the optimal CUSUM schemes are employed in process/service industry, there will be a considerable amount of saving in time and money expended in search of causes behind frequent false alarms. 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.Originality/valueThe research findings could be applied to various manufacturing industries as well as service industries where the data is positively correlated and normally distributed.