The bivariate generalized variance |S| control chart with runs rules

This work studies the effect of incorporating the 2-of-k, 3-of-k, and k-of-k runs rules into the one-sided bivariate generalized variance |S| control chart, in terms of the average run length (ARL). The Markov chain approach is used to obtain the ARL profiles for the proposed chart. From the ARL comparisons, the control charts with runs rules detect the process change faster than the corresponding chart without runs rules. The results also indicate that the out-of-control ARL of the chart with 2-of-k runs rule decreases with increasing values of k up to a point beyond which the ARL increases. This is also the case for the 3-of-k runs rule. Meanwhile, the out-of-control ARL of chart with k-of-k runs rule increases as the value of k increases. The chart with 2-of-k runs rule gives better ARL performance than the charts with 3-of-k and k-of-k runs rules.