Abstract:

The Average run lengths (ARLs) of the modified x? chart are computed by simulation using MATLAB software in this paper. The modified x? chart, based on sum of chi-squares theory is able to counter the autocorrelation in the observations. Various optimal schemes of modified x? chart for sample size (n) of 10 are proposed at different levels of correlation (Φ). The ARLs of the modified x? chart are also validated and compared with the ARLs obtained by Artificial Neural networks (ANNs). It is found that when the level of correlation (Φ) increases for a particular sample size (n), the performance of all the schemes deteriorates. It is concluded that the modified chart offers more robustness compared to Shewhart x? chart for autocorrelated data at various levels of correlation (Φ) and shifts in the process mean.