Correction: SPC is not signaling that you don’t have what you are looking for. The Capability index is signaling that. But the capability index is NOT part of SPC (Shewhart would rollover in his grave and Deming certainly belittled this statistical malpractice).
@Jake with the Calipers You might try reading
Statistical Alchemy for a pretty cogent argument against capability indices. The paper also has a long list of references to further understand this abomination of the quality engineering discipline.