An image-forming system includes a determining section that, for each type of malfunction in image-forming apparatuses, determines a reference number of occurrences of the type of malfunction based on at least one of (1) a distribution of the number of apparatuses in which the type of malfunction has occurred against the number of occurrences of the type of malfunction and (2) a distribution of the number of apparatuses on which maintenance has been carried out against the number of occurrences of the type of malfunction; an extracting section that extracts a subgroup of apparatuses in which the malfunction has occurred a number of times larger than or equal to the reference number of occurrences; and a setting section that sets a criterion for maintenance based on a time series tendency of occurrence of the malfunction in an apparatus on which maintenance has been carried out in the subgroup.