Effect of Measurement Error on the Multivariate CUSUM Control Chart for?ompositional Data

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