  Control charts, one of the main tools in Statistical Process Control (SPC),
have been widely adopted in manufacturing sectors as an effective strategy for
malfunction detection throughout the previous decades. Measurement errors
(M.E's) are involved in the quality characteristic of interest. The authors
explored the impact of a linear covariate error model on the multivariate
cumulative sum (CUSUM) control charts for a specific kind of data known as
compositional data(CoDa). The average run length ARL is used to assess the
performance of the proposed chart. The results indicate that M.E's
significantly affects the multivariate CUSUM-CoDa control charts. The authors
have used the Markov chain method to study the impact of different involved
parameters using four different cases for the variance-covariance matrix (i.e.
uncorrelated with equal variances, negatively correlated with equal variances,
uncorrelated with unequal variances, positively correlated with unequal
variances). The authors concluded that the ARL of the multivariate CUSUM-CoDa
chart increase with an increase in the value of error variance-covariance
matrix, while the ARL decreases with an increase in the subgroup size m or the
constant powering b. For the implementation of the proposal, two illustrated
examples have been reported for multivariate CUSUM-CoDa control charts in the
presence of M.E's. One deals with the manufacturing process of uncoated aspirin
tablets, and the other is based on monitoring machines in the muesli
manufacturing process.
