posted 23 November 1999 12:09 PM               

Date: Tue, 14 Sep 1999 23:04:58 +0200
From: "Frans J.C. Martins" [email protected]
To: Greg Gogates
Subject: Re: Inspection Criteria

Dear Group,

SNIP
> The most common use in the US seems to be if the uncertainty (k=something,
> usually 2) is less than some fraction of the tolerance, commonly 25% (10%
> traditionally, 25% in Z540, 33% in ISO 10012, ...) then the tolerance is used
> as stated. This corresponds to the ISO 14253 standard used with k=0. I admit
> that using the expanded uncertainty with k=0 doesn't make sense at first (at
> least it didn't to me when Ralph Veale explained to me how k=0 would be a good
> idea), but in the language of ISO 14253 it is actually a sensible description
> of current US practice.
SNIP

I believe that the 33% limit is obtained by assuming the upper and lower spec limit to be 3 sigma. If we relate this back to SPC practically:

Specification: 100 ± 1

the ± 1 is assumed a three sigma value and the 100 as the mean, now.........

ZONE A (Stable zone) would be the mean ± 1 sigma thus 100 ± 0.333

ZONE B (Warning zone) would be the mean ± 2 sigma thus ± 100 ± 0.667

ZONE C (Action zone) would be the mean ± 3 sigma thus 100 ± 1

This theory then also traces back to the Process capability indices
calculation which are given by Relative capability or Process capability

Cp = USL - USL / 6 sigma NOTE: to manufacture within specifications the distance between the USL (upper specification limit) and the LSL (lower specification limit) must be less than the width of the base of the normal distribution thus the distance between -3 sigma and + 3 sigma) If Cp is < 1, the process is not capable

Cp = 1, the process is marginally capable
Cp > 1, it indicates a potential for higher capability

and

Capability index
Cpk = the lesser of: USL - mean / 3 sigma or mean - LSL / 3 sigma
If Cpk < 1, the process is incapable
Cpk = 1, still some undetected non-conforming output
Cpk > 1 but < 2, still some non-conforming output but with a good chance of
detection
Cpk > 2, total confidence in the process.

I trust that this helps and makes some sense.