Equivalences between multiple dependent state sampling, chain sampling, and control chart runs rules

Multiple dependent state sampling (MDSS) is a feature that was recently proposed for acceptance sampling plans. In addition, it is increasingly recommended to use this technique, and its generalization, with quality control charts. In our paper, we show that the MDSS feature is an extension of chain sampling in acceptance sampling applications. In addition, we show that use of the MDSS feature with control charts is equivalent to the use of standard supplementary runs rules. Analytical methods based on Markov chains for determining the performance of control charts with runs rules can also be applied to MDSS acceptance sampling applications. Additionally, we provide a derivation approach for some of the formulas for the performance measures for the MDSS charts and point out some incorrect derivations.