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A possible origin story of OOT-limits - part 2

Updated: Jun 18, 2023

In the first part, after the introduction we discussed mostly where we should look around searching for OOT-limits. This second part is about how to prepare before calculating the OOT-limits.

How to determine OOT-limit

Let's start the legwork and do some statistics. But what, how many data can I use? and what can I do with the results?

1. Number of results to apply

If you ask a statistician, what is the minimal number of data to use for +/-3sigma evaluation, they will say 'at least 50'. OK, then you may laugh, because either you implemented 4 changes in your manufacturing process during the last 50 batches, or maybe you have 3-4 batches per year of a product.

On the other hand, I had the pleasure of discussing this through with an inspector from the Far East, who wanted to see statistics from the first 3 validation batches.

Let me suggest the golden mean: if you want to set up OOT limits from scratch, choose last year's batches, but at least 10, if you manufactured less than 10.

2. What to calculate first - capability index

I don't plan to go in details on calculating capability index, but since there are a lot of different equations out there, let me clarify to suggest Cpk = (USL-LSL)/6s. If you have a one-side specification limit, just mirror the USL to get the LSL, or vice versa (if you have a NMT 3000 ppm acetone content limit for you API, your USL is 3000 and your LSL is -3000).

So first determine this value to know what the next step is going to be. Because if it is less or equal than 1.0, you won't determine any limits, since your control range is equal or even wider than your specification range. You might suggest some improvement in your process to achieve smaller standard deviation, but that is outside of the range of this post :)

But let's not forget the other end of the scale: if your Cpk is too big (like more than 20), don't use the +/-3s approach, you would be oversensitive, and your risk of getting false alarms would increase. Instead, choose a limit using a fraction of your specification range (e.g., one fifth of your specification limit).

3. What to calculate now

Now we arrived: we can go forward and determine the OOT-limit using the +/-3sigma approach.

We won! Or do we? Let's discuss that in Part 3.