Looks at the Cpk first. If the Cpk goes beyond 1.77 or even 2. It means the current tolerance spec is too tight! Don't make me wrong. It would not degrade the final product. Then you can set up a meeting with quality engineers and product design engineers to decide to "loose" the tolerance spec. which enlarges the tolerance range and then lower the Cpk to 1.5 around. By doing so, your manufacturing vendor can still provide the "meet the quality" parts to you. You can also benefit from leveraging the price with vendors.