The usual Hotelling T² control chart is not appropriate for monitoring processes where the quality characteristic is a mixture. The composition of mixtures are vectors of positive elements that represent parts of a whole, to which standard multivariate techniques are not appropriate due to their restricted sample space. There are many applications where a mixture is monitored against time, such as in the chemical industry, product composition, impurity profile, or gas components analysis. In this paper, a multivariate control chart for individual compositional observations based on the T² statistic is proposed and compared with the typical one in terms of average run length. We show how results are more consistent with compositional data nature and illustrate implementation in a real-world example.

Objective: To assess whether alcohol intake is associated with the onset of migraine attacks up to 2 days after consumption in individuals with episodic migraine (EM). Background: Although alcohol has long been suspected to be a common migraine trigger, studies have been inconclusive in proving this association. Methods: This was an observational prospective cohort study among individuals with migraine who registered to use a digital health platform for headache. Eligible individuals were aged ≥18 years with EM who consumed alcohol and had tracked their headache symptoms and alcohol intake for ≥90 days. People who did not drink any alcohol were excluded. The association of alcohol intake (“Yes/No”) and of the number of alcoholic beverages in the 2 days preceding a migraine attack was assessed accounting for the presence of migraine on day‐2 and its interaction with alcohol intake on day‐2, and further adjusted for sex, age, and average weekly alcohol intake. Results: Data on 487 individuals reporting 5913 migraine attacks and a total of 40,165 diary days were included in the analysis. Presence of migraine on day‐2 and its interaction with alcohol intake on day‐2 were not significant and removed from the model. At the population level, alcohol intake on day‐2 was associated with a lower probability of migraine attack (OR [95% CI] = 0.75 [0.68, 0.82]; event rate 1006/4679, 21.5%), while the effect of alcohol intake on day‐1 was not significant (OR [95% CI] = 1.01 [0.91, 1.11]; event rate 1163/4679, 24.9%) after adjusting for sex, age, and average weekly alcohol intake. Similar results were obtained with the number of beverages as exposure. Conclusions: In this English‐speaking cohort of individuals with EM who identified themselves as mostly low‐dose alcohol consumers, there was no significant effect on the probability of a migraine attack in the 24 h following consumption, and a slightly lower likelihood of a migraine attack from 24 to 48 h following use.