This paper deals with an optimization problem, which arises when a new simple assembly line has to be designed subject to a fixed number of available workstations, cycle time constraint, and precedence relations between necessary assembly tasks. The studied problem consists in assigning a given set of tasks to workstations so as to find the most robust line configuration, which can withstand processing time uncertainty as much as possible. The line robustness is measured by a new indicator, called stability factor. In this work, the studied problem is proven to be strongly NP-hard, upper bounds are proposed, and the relation of the stability factor with another robustness indicator, known as stability radius, is investigated. A mixed-integer linear program (MILP) is proposed for maximizing the stability factor in the general case, and an alternative formulation is also derived when uncertainty originates in workstations only. Computational results are reported on a collection of instances derived from classic benchmark data used in the literature for the Simple Assembly Line Balancing Problem (SALBP).