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 ( $ \mathrm {FSI} $ FSI s). The variable sampling intervals ( $ \mathrm {VSI} $ VSI s) scheme is receiving increasing attention, in which the sampling interval ( $ \mathrm {SI} $ SI ) length varies according to the process monitoring statistics. A shorter $ \mathrm {SI} $ SI is considered when the process quality indicates the possibility of an out-of-control (OOC) situation; otherwise, a longer $ \mathrm {SI} $ SI is preferred. The $ \mathrm {VSI} $ VSI multivariate exponentially moving average for compositional data ( $ \mathrm {VSI} $ VSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa ) CC based on a coordinate representation using isometric log-ratio ( $ \operatorname {ilr} $ ilr) transformation is proposed in this study. A methodology is proposed to obtain the optimal parameters by considering the zero-state ( $ \mathrm {ZS} $ ZS ) average time to signal ( $ \mathrm {ZATS} $ ZATS ) and the steady-state (SS) average time to signal ( $ \mathrm {SATS} $ SATS ). The statistical performance of the proposed CC is evaluated based on a continuous-time Markov chain ( $ \mathrm {CTMC} $ CTMC ) method for both cases, the $ \mathrm {ZS} $ ZS and the SS using a fixed value of in-control (IC) $ \mathrm {ATS}_0 $ ATS 0 . Simulation results demonstrate that the $ \mathrm {VSI} $ VSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa CC has significantly decreased the OOC average time to signal ( $ \mathrm {ATS} $ ATS ) than the $ \mathrm {FSI}\,\mathrm {MEWMA}\,\mathrm {CoDa} $ FSI MEWMA CoDa CC. Moreover, it is found that the number of variables (d) has a negative impact on the $ \mathrm {ATS} $ ATS of the $ \mathrm {VSI} $ VSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa CC, and the subgroup size (n) has a mildly positive impact on the $ \mathrm {ATS} $ ATS of the $ \mathrm {VSI} $ VSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa CC. At the same time, the $ \mathrm {SATS} $ SATS of the $ \mathrm {VSI} $ VSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa CC is less than the $ \mathrm {ZATS} $ ZATS of the $ \mathrm {VSI} $ VSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa CC for all the values of n and d. The proposed $ \mathrm {VSI} $ VSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa CC under steady-State performs effectively compared to its competitors, such as the $ \mathrm {FSI} $ FSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa CC, the $ \mathrm {VSI} $ VSI - $ T^2\,\mathrm {CoDa} $ T 2 CoDa CC and the $ \mathrm {FSI} $ FSI - $ T^2\,\mathrm {CoDa} $ T 2 CoDa CC. An example of an industrial problem from a plant in Europe is also given to study the statistical significance of the $ \mathrm {VSI} $ VSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa CC. [ABSTRACT FROM AUTHOR]