Performance of the hotelling T² control chart for compositional data in the presence of measurement errors

ABSTRACT

In statistical process monitoring, the presence of measurement errors is known to impact the performance of control charts. This paper makes an attempt to investigate the performance of the Hotelling CoDa (Compositional Data) $T^2$ control chart in the presence of measurement errors. A linearly covariate measurement error model for CoDa is introduced to study the influence of the measurement device parameters (${\sigma }_{\mathrm{M}}$ and b) and the number of independent observations m on the performance of the Hotelling CoDa $T^2$ control chart in the in- and out-of-control cases. A realistic illustrative example based on the production of muesli is used to illustrate the estimation of the measurement device parameters and the in-control process parameters, as well as to demonstrate the ability of this control chart to efficiently detect changes in the muesli composition.

KEYWORDS:

• Monitoring
• compositional data
• measurement errors

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

P. Castagliola http://orcid.org/0000-0002-9532-4029

K. P. Tran http://orcid.org/0000-0002-6005-1497

M. B. C. Khoo http://orcid.org/0000-0002-3245-1127