Six Sigma: Statistical Tolerancing

In this quick lesson, we go over Six Sigma statistical tolerancing and how to easily do this using QuikSigma. Have any questions? Please leave a comment below!




The basic idea of statistical tolerancing is to put items, such as these yellow boxes, inside an envelope such as this red outline here. Now, these can be actual mechanical things, or you can do it with time, or you can do with anything that you can translate so that all of the things that have to fit in, have the same dimension. I’ve seen this applied, for example, to the motors that run disk drives. Now, the standard is that the envelope giveth and the boxes taketh away. So the envelope, the space is positive and the things that are taking up space are negative. Usually, what we’re really interested in here is the gap, what’s left over. If we’re trying to fit things and we don’t want the gap to be less than 0. If we want our assembly to be tight, we also don’t want that to be very large. So let’s go into QuikSigma and apply those ideas.

Under toolbox, I’ve opened the statistical tolerance tool and I’ve loaded some data here and I’ve done the exact opposite of what I told you a minute ago. This will this will help keep the demonstration a little simpler so bear with me. I’ve made the boxes positive. Normally, they would be negative. For simplicity, I’ve chosen boxes that have a mean dimension of ten, just as we did in the visual aid and I’ve given each of them a standard deviation of .0167. I’ve also set an upper spec limit and a lower spec limit for my stack of boxes. So all I have to do now is click calculate and we’re not looking very good. How are we doing? Well, maybe we’re being just a little strict with ourselves. It says that our Ppk of our stack against our limits is going to be about 1.5, that’s really not very bad, that’s quite good. I’m going to have a mean of 40 and i’m going to have a standard deviation of .033. I can use this to see how many standard deviations there are between the mean and the upper spec limit and the mean in this lower spec limit. This process is perfectly centered. Gee, I wonder what the probability of that is? Now I’m going to go back and change the set up just a little bit.

Here’s that other data set and what I’ve done is gone and made the boxes negative like they’re supposed to be and made the envelope positive. The question is, will these boxes generally fit within this envelope? Now, if you do this with just a maximum specification approach, you’ll almost always end up with a loose assembly. This tends to work a lot better. So let’s look at what we’ve done. Now, we’re reporting the size of the gap. Before we were reporting the stack up of the boxes. So, my mean gap is .025 with a sigma of .009. Six thousand times roughly out of a million, I’m going to have an assembly that doesn’t fit and that’s a Ppk .9. So maybe that’s not very good, not horrible, but not great and according to these, once again, I’ve succeeded in exactly centering my process. Now, what this lets you do in addition to the obvious, is if you have some parts that it’s easy to keep tolerances on, you can be tighter on those. If you have other parts that are harder to be accurate on, then you can intelligently allocate your variation for maximum ease of manufacturing and this deceptively simple-looking tool does about as much as many of the very expensive packages that do nothing but statistical tolerancing.

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