Family deductibles were designed so that large families wouldn’t be burdened with paying individual health insurance deductibles for each family member. 

Each time an individual within the family pays toward their individual deductible, that amount is also credited toward the family deductible. Coverage begins for any particular individual as soon as they have met their individual deductible. Coverage begins for the entire family, even those family members who haven’t met their individual deductibles yet, as soon as the family deductible is met.