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

Abstract

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