For the repeated measures design D.C.Montgomery in his "Design and Analysis of Experiments" classic book provides the mathematical / statistical (linear) model: $y_{ij} = \mu + \tau_i+ \beta_j + \epsilon_{ij}$, where $\tau$ is the effect of the $i$th treatment, $\beta$ is a parameter associated with the $j$th subject, and $\epsilon_{ij}$ is the independent error.
In a (document, p. 2) it is stated that to check the model's assumptions we should operate with residuals calculated as (A): $$\hat\epsilon_{ij} = Y_{ij} - \bar Y_{i.} - \bar Y_{.j} + \bar Y.$$

The formula (B) on Wikipedia is $$\hat\epsilon_i = Y_i - \bar Y.$$

My question is:
what formula is used to correctly calculate residuals in the model describing a single-factor repeated measures design to check its assumptions (multivariate normality, homoscedasticity, sphericity, linearity, additivity)?

Thank you.

EDIT
E.Vonesh and V.M.Chinchilli in their "Linear and Nonlinear Models for the Analysis of Repeated Measurements" monograph state that the single-sample RM design may be written as $y_{i} = \mu + \epsilon_{j}$.