Q.Distinguish between control limits and tolerance (specification) limits.

One set of limits is calculated from the process's own recent behaviour and describes the process; the other is fixed externally by design and describes the product.

Control limits are computed from the process's own past data — the grand mean $\bar{\bar{X}}$ and average range $\bar{R}$ of samples actually drawn from the process, combined with standard factors like $A_2$, $D_3$, $D_4$. They are plotted on sample statistics ($\bar{X}$, $R$), not on individual items, and they answer the question: "Is the process behaving consistently, with chance causes only?"

Tolerance (specification) limits, in contrast, are fixed externally, by the product's design engineering or the customer's actual requirement, entirely independent of how the process happens to be performing. They apply to individual finished items, and answer a completely different question: "Is this particular item fit for use?" …

Treating 'in control' as automatically meaning 'meets specification' — the two are answering different questions, and a perfectly consistent (in-control) process can still be consistently producing items that …