I just realised that I did not describe the math behind my calculations. Here it goes ...

To calculate the Cpk value, we use the concept of

**tolerance intervals**. For a

**single-sided** specification we use the non-central t-distribution,

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As you can see, we need three inputs to calculate the k_1:

(a) the coverage p = 1 - RQL,

(b) the confidence level 1-alpha, and

(c) the sample size n.

Hence, we just pick a sequence of sample sizes and redo the calculation until we are satisfied. E.g. for n=20, p=0.99, alpha=0.05 we get k_1=3.295157.

Next, we user the relationship Cpk = k_1/3. This yields the required (minimal) Cpk-value. In the above example we get Cpk=1.098386. This number is always rounded upwards. I round to the second digit, which yields Ppk >= 1.10.

Note, that translating the RQL=1% value directly into a Cpk-value would yield Cpk=0.7754493. By using the tolerance interval method we "add the required 95% confidence" into the result. Hence, the Cpk-value 1.10 is an upper limit of the corresponding tolerance interval.

Finally, I use the "common approximation" of the uncertainty of the Cpk value (see NIST link above), and calculate the single-sided confidence interval. This yields 1.416078 as an upper limit. This corresponds to the value you stated in your pre-PQ column.

Please note, that k_1 is for a single sided specification. The calculation is similar for two-sided specifications, but we are not allowed to use the non-central t-distribution.