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).