What kind of data is usually considered for Shewhart charts i.e. cross-sectional data or longitudinal data. Because, if it is longitudinal data then usual techniques are no longer valid. A common feature of repeated measurements on an individual is correlation; that is, knowledge of the value of the response on one occasion provides information about the likely value of the response on a future occasion. Another common feature of longitudinal data is heterogeneous variability; that is, the variance of the response changes over the duration of the study. These 2 features of longitudinal data violate the fundamental assumptions of independence and homogeneity of variance that are at the basis of many standard techniques (eg, t test, ANOVA, and multiple linear regression). Typically, longitudinal study designs call for a fixed number of repeated measurements on all study participants at a set of common time points. When all individuals have the same number of repeated measurements, obtained on a common set of occasions, the study is said to be “balanced” over time.

Thus, i am confused that we are taking repeated sample in time and for construction they are iid. How this point is valid? Also, what is main point of difference between control charts and hypothesis testing especially multiple comparison?