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

Abstract

ABSTRACT Conventionally, the standard process monitoring control charts (s) focused on fixed sample size (). An optimal statistical scheme is proposed in this study using a variable sample size to enhance the performance of a multivariate exponentially weighted moving average () control chart () for compositional data () (i.e. - ) based on a coordinate representation using isometric log-ratio transformation (). A methodology is proposed to obtain the optimal parameters by considering the zero-state () average run length () and the steady-state () average run length () conditions of the process. The statistical performance of the proposed is evaluated based on a continuous-time Markov chain () method for both cases (i.e. the and the ) using a fixed value of in-control (IC) average run length . For benchmarking reasons, the out-of-control () performance of the - is compared against the traditional - with in terms of ; the proposed shows better performance than the - . The and of the - are always less than that of the - at some certain level of shifts. The proposed - performs, on average, () and (for ) more effectively than - . Moreover, it is found that the number of variables (d) has a negative impact on the run length characteristics of the - . When the value of d increases, the and of the - also increase. The of the - is less than the of the - for all the combinations of sample size (n) and d, i.e. under , the proposed performs on average (for d = 3) and (for d = 5) better than the 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 - over the existing - .