several questions: what is this data? is it in process data or is it final product data?
what structure was used to generate the data? Bob is correct in that your process perfromance will be affected by set up to set up variation, raw material variation, tooling or other consumable variation, operator variation, time of day, cold equipment hot equipment, etc. Without understandign the process and it's components of variation, we cannot be sure if you have captured the full range of variation one can expect under normal conditions (without process improvements)
As for specifications - They alwasy come from the customer. even in process or input factor tolerances as these all compbine to create teh final product tolerances which must meet custoemr needs. (Now of course teh customer doesn't always tell us directly what they want.)
Bob - please clarify for everyone what you mean by "process specifications" and how are they different from product specifications