THE NEW VARIABLE SAMPLE SIZE SCHEMES TO MONITOR THE PROCESS MEAN OF AUTOCORRELATED TIME SERIES DATA
The variable sample sizes (VSS) approach to monitor the process mean of autocorrelated (within sub-group) samples using the supplementary runs-rules and synthetic schemes is proposed. To maximize the detection ability of these proposed VSS schemes, we mainly focus on the modified side-sensitive (MSS) design approach for the charting regions as it is shown that it yields the best possible performance out of all the four available design approaches. These new monitoring schemes incorporate the first-order autoregressive (i.e. AR(1)) model to the computation of the standardized charting statistics in order to account for autocorrelation. To reduce the negative effect of autocorrelation, a non-neighboring sampling method is used. Moreover, to construct dedicated Markov chain matrices, the AR(1) model and non-neighboring sampling method are incorporated into the values of probability elements to evaluate the zero- and steady-state run-length distribution. The main finding of this study is that, the proposed VSS schemes yield a uniformly better run-length performance than the existing VSS Â scheme and other Shewhart competitors. A real life example is used to illustrate the practical implementation of the proposed schemes.
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