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

Abstract

Control charts (CCs) are one of the main tools in Statistical Process Control that 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, which can effect the CC’s performance. The authors explored the impact of a linear model with additive covariate M.E on the multivariate cumulative sum (CUSUM) CC 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 CCs. The authors have used the Markov chain method to study the impact of different involved parameters using six different cases for the variance-covariance matrix (VCM) (i.e., uncorrelated with equal variances, uncorrelated with unequal variances, positively correlated with equal variances, positively correlated with unequal variances, negatively correlated with equal variances and negatively correlated with unequal variances). The authors concluded that the error VCM has a negative impact on the performance of the multivariate CUSUM-CoDa CC, as the ARL increases with an increase in the value of the error VCM. The subgroup size m and powering operator b positively impact the proposed CC, as the ARL decreases with an increase in m or b. The number of variables p also has a negative impact on the performance of the proposed CC, as the values of ARL increase with an increase in p. For the implementation of the proposal, two illustrated examples have been reported for multivariate CUSUM-CoDa CCs in the presence of M.E’s. One deals with the manufacturing process of uncoated aspirin tablets, and the other is based on monitoring the machines involved in the muesli manufacturing process.