Transition probabilities and ARL performance of Six Sigma zone control charts

In this article, Six Sigma zone control charts (SSZCCs) are proposed for world class organizations. The transition probabilities are obtained using the Markov chain approach. The Average Run Length (ARL) values are then presented. The ARL performance of the proposed SSZCCs and the standard Six Sigma control chart (SSCC) without zones or run rules is studied. The ARL performance of these charts is then compared with those of the other standard zone control charts (ZCCs), the modified ZCC and the traditional Shewhart control chart (SCC) with common run rules. As expected, it is shown that the proposed SSZCC outperforms the standard SSCC without zones or run rules for process shifts of any magnitude. When compared to the other standard ZCCs and the Shewhart chart with common run rules, it is observed that the proposed SSZCCs have much higher false alarm rates for smaller shifts and hence they prevent unwanted process disturbances. The application of the proposed SSZCC is illustrated using a real time example.