The purpose of this paper is to study the performance of the X‐bar chart on the basis of average run lengths (ARLs) for the positively correlated data. The ARLs at various sets of parameters of the X‐bar chart are computed by simulation. The performance of the chart at the various shifts in the process mean is compared with the X‐bar chart suggested by Zang and residual chart proposed by Zang. The optimal schemes suggested in this paper are also compared with variable parameters (VP) chart and double sampling (DS) X‐bar chart suggested by Costa and Machado.
Positively correlated observations having normal distribution are generated with the help of the MATLAB software. The performance of the X‐bar chart in terms of ARLs at the various shifts in the process mean is compared with the X‐bar chart suggested by Zang and residual chart proposed by Zang. The optimal schemes are also compared with VP X‐bar chart and DS X‐bar chart suggested by Costa and Machado.
The suggested optimal schemes of X‐bar chart perform better at the various shifts in the process mean than the X‐bar chart suggested by Zang and residual chart suggested by Zang. It was concluded that, although the suggested schemes for X‐bar chart detect shifts later than the VP and DS X‐bar charts proposed by Costa and Machado, they involved a much smaller number of parameters that are to be adjusted. So the time required for adjustment in case of optimal scheme is very small compared to the VP and DS charts.
The optimal schemes of X‐bar chart are developed for the normally distributed autocorrelated data. But this assumption may also be relaxed to design these schemes for autocorrelated data. Moreover, the optimal schemes for chart can be developed for variable sample size and for variable sampling intervals.
Although it is the extension of previous work, it can be applied to various manufacturing industries as well as service industries where the data is positively correlated and normally distributed.
