Cells grown in culture can be tracked for several generations and measurements taken on size or age at division and other cell characteristics. The observations for the offspring of each cell form a family tree of dependent data. Such cell lineage data are here modeled as repeated measurements on different family trees arising from individual ancestor cells selected at random from a population of cultured cells. The bifurcating autoregression model is embedded in a process that allows for measurement error and variation from tree to tree. Robust methods are presented that accommodate outliers in this time-dependent and branching environment while allowing the statistician to interactively build a variance components model for the process. The methodology is illustrated on a substantial data set of 41 trees of EMT6 cells, with the surprising conclusion that after removing measurement error, sister-cell lifetimes are nearly identical.