Apply control limits to a non-normal distribution

Hello

I have a process parameter that is controlled this way:

If the equipment signal response is below a certain level, we know for sure that the result will be lower than 10% and thus reported as <10.

However, if a signal response is a little bit higher, then I have to actually quantify the value. In this cases, I usually get results around 5-6, which are still below the 10.

My data distbitution is something like this:

Sample size - 126
Analysis result | Number of events | Cumulative Count | Cumulative %
<10 | 97 | 97 | 77%
5 | 16 | 113 | 90%
6 | 9 | 122 | 97%
7 | 3 | 125 | 99%
8 | 1 | 126 | 100%

What would be the best distribution to fit this data? Exponential? Weibull? Gamma?

The purpose is to define an upper control limit, as the ones used for normal distributions in SixSigma (average+3sigma). How should I proceed in this case?

Thanks in advance for your support

 

For the sake of a capability study, you need to quantify all your points - even though the data may (or may not be) handy for ongoing control. Then you can establish an accurate model of your data and calculate the control limits based on that model. It may mean transformation - it depends on the distribution model you end up with.