Investigating zero-state and steady-state performance of MEWMA-CoDa control chart using variable sampling interval

Traditional process monitoring control charts (CCs) focused on sampling methods using fixed sampling intervals ($$s). The variable sampling intervals ($$s) scheme is receiving increasing attention, in which the sampling interval ($$) length varies according to the process monitoring statistics. A shorter $$ is considered when the process quality indicates the possibility of an out-of-control (OOC) situation; otherwise, a longer $$ is preferred. The $$ multivariate exponentially moving average for compositional data ($$-$$) CC based on a coordinate representation using isometric log-ratio ($$) transformation is proposed in this study. A methodology is proposed to obtain the optimal parameters by considering the zero-state ($$) average time to signal ($$) and the steady-state (SS) average time to signal ($$). The statistical performance of the proposed CC is evaluated based on a continuous-time Markov chain ($$) method for both cases, the $$ and the SS using a fixed value of in-control (IC) $$. Simulation results demonstrate that the $$-$$ CC has significantly decreased the OOC average time to signal ($$) than the $$ CC. Moreover, it is found that the number of variables (d) has a negative impact on the $$ of the $$-$$ CC, and the subgroup size (n) has a mildly positive impact on the $$ of the $$-$$ CC. At the same time, the $$ of the $$-$$ CC is less than the $$ of the $$-$$ CC for all the values of n and d. The proposed $$-$$ CC under steady-State performs effectively compared to its competitors, such as the $$-$$ CC, the $$-$$ CC and the $$-$$ CC. An example of an industrial problem from a plant in Europe is also given to study the statistical significance of the $$-$$ CC.