On designing efficient multivariate exponentially weighted moving average control chart for compositional data using variable sample size.

Conventionally, the standard process monitoring control charts ( CC s) focused on fixed sample size ( FSS ). An optimal statistical scheme is proposed in this study using a variable sample size (VSS) to enhance the performance of a multivariate exponentially weighted moving average ( MEWMA ) control chart ( CC ) for compositional data ( CoDa ) (i.e. VSSMEWMA - CoDa CC ) based on a coordinate representation using isometric log-ratio transformation ( ilrt). A methodology is proposed to obtain the optimal parameters by considering the zero-state ( ZS ) average run length ( ZARL ) and the steady-state ( SS ) average run length ( SARL ) conditions of the process. The statistical performance of the proposed CC is evaluated based on a continuous-time Markov chain ( CTMC ) method for both cases (i.e. the ZS and the SS ) using a fixed value of in-control (IC) average run length ARL 0 . For benchmarking reasons, the out-of-control ( OOC ) performance of the VSSMEWMA - CoDa CC is compared against the traditional MEWMA - CoDa CC with FSS in terms of ARL ; the proposed CC shows better performance than the FSSMEWMA - CoDa CC . The SARL and ZARL of the VSSMEWMA - CoDa CC are always less than that of the FSSMEWMA - CoDa CC at some certain level of shifts. The proposed VSSMEWMA - CoDa CC performs, on average, 15.25 % ( SS ) and 18.28 % (for ZS ) more effectively than FSSMEWMA - CoDa CC . Moreover, it is found that the number of variables (d) has a negative impact on the run length characteristics of the VSSMEWMA - CoDa CC . When the value of d increases, the OOC SARL and ZARL of the VSSMEWMA - CoDa CC also increase. The SARL of the VSSMEWMA - CoDa CC is less than the ZARL of the VSSMEWMA - CoDa CC for all the combinations of sample size (n) and d, i.e. under SS , the proposed CC performs on average 5.19 % (for d = 3) and 28.8 % (for d = 5) better than the ZS situation. An example of an industrial problem of grid production for a European plant is also given to study the statistical significance and implementation of the VSSMEWMA - CoDa CC over the existing FSSMEWMA - CoDa CC . [ABSTRACT FROM AUTHOR]