ABSTRACT
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.
Disclosure statement
No potential conflict of interest was reported by the author(s).