Formal concept analysis has been proved to be useful to support knowledge discovery from boolean matrices. In many applications, such 0/1 data have to be computed from experimental data and it is common to miss some one values. Therefore, we extend formal concepts towards fault-tolerance. We define the DR-bi-set pattern domain by allowing some zero values to be inside the pattern. Crucial properties of formal concepts are preserved (number of zero values bounded on objects and attributes, maximality and availability of functions which "connect" the set components). DR-bi-sets are defined by constraints which are actively used by our correct and complete algorithm. Experimentation on both synthetic and real data validates the added-value of the DR-bi-sets.