AbstractTwo problems greatly affect the use of capability indices such as $C_p$, $C_{pk}$ and $C_{pkm}$: the lack of affinity with the process fraction defective π and the difficulty of dealing with the sampling distributions of their natural estimators. In this paper, a capability index which is in one‐to‐one correspondence with π is introduced and simple inferential procedures under a Bayesian perspective are developed to facilitate its use in industrial applications. Copyright © 2001 John Wiley & Sons, Ltd.