Hi all,

Someone can comment this:
How do we calculate capabilty indicators in case of non normality of a distribution for a bilateral characteristic? E.g: ø200±1.
Thanks for all comments.

You calculate them as normal.

But just to clear things up what do you mean by non-nomal distribution? I you talking about a binomial distrubution or one that shows a skewed population?

The variance will be that Cp / Cpk or Pp / Ppk will start to diverge as with a normal distribution they will be very close to each other and as the population gets more away from the nominal the two indices will start to diverge

I agree with Andy that you can just calculate the indices as normal. The definitions of these capability indices is relatively straightforward based on specs, mean, & St dev.

The problem with non-normal data is that you then lose much of the predictive value of the indices. They will still give rough estimates of capability, but the less normal, the leas accurate. A strongly skewed or strongly bimodal distribution will not allow accurate predictions of PPM defective or similar metrics.

If you truly want to predict defect then you might have to get more clever. Perhaps you can transform the data into something closer to normal that then use that distribution for calculations.

Tim F

First thanks for your comments,
Yes, the distribution I talked about follows the normal law, I gave the example of the Diameter 200 +/-1. So I'm not talking about a distribution that shows a skewed population.

In fact, in the french automotive standard Q544000 it's precised that in case of non-normality of the characteristic the capability indicators should be calculated with 8 Sigma insted of 6 Sigma. This way the indicators will be more strict than they've been calculated with a dispersion of 6 Sigma.
So I'm looking for a rule of a suggestion that takes into account the mentioned case.

Thanks in advance. :bigwave:

Not knowing that standard, an English PDF on here woudl be great, but the tolerance band you show has nothing to do with the population being skewed or not.

The results can be influenced by the set up and as such sked to the positive or negative and tip wear as well causing a bi-nomial distribution or a skewed population from this I can see the point of using 8 sigma as this is an attempt to get more in to the control limits but I still suggest that you look at Cp Vs Cpk and use this, and common scence, to make your decision. Sorry I can't be of any more help.

After all as the late Mark Twain said there are lies, dam lies and statistics.

Hi all,

Someone can comment this:
How do we calculate capabilty indicators in case of non normality of a distribution for a bilateral characteristic? E.g: ø200±1.
Thanks for all comments.

If the diameter is non-normal because it is the result of precision machining, that is, is has the sawtooth curve for tool wear, and its distribution is the uniform or rectangular distribution, then

capability=(USL-LSL)/(UCL-LCL)

Why? Because the capability is the spread of the tolerance over the spread of the process. The process spread for the rectangular distribution is the control limits. For a normal process 6 sigma is used to estimate the endpoints of a distribution with ongoing tails. The uniform distribution stops abruptly, and it stops right at the control limits. In fact, it is more predictive than the normal distribution because the distribution is so consistent, and the endpoints are very specific - theoretically.

see http://elsmar.com/Forums/showthread.php?p=187696#post187696 for more detail.