Statistical Tolerance Question 1

[KENAT]

I’m pretty sure I’m being a dullard but I can’t work it out and I don’t have any text books to hand and it’s a long time since I looked at statistics in any detail. Did a quick google search of this site and the web and although I found useful data I’m not smart enough to put it together.

I have a robot placing a square sample in a measuring device.

The square sample itself obviously has tolerance. There is the tolerance of the placement of the sample in X-Y and there is a contribution from the sample also having an angular off set in placement.

For calculating where the edges of the sample come I’m happy using worst case.

However, I’d also like to look at where the nominal center of the sample should end up. In this case the size variation of the sample is effectively insignificant and I only have to worry about the 2 placement accuracies.

I’m happy using RSS with normal distribution however this gives the zone that 99.73% of parts fall in.

I want to be able to calculate the zone that say, 98% of sample centers (should) fall in.

Can anyone point me to a website that will help me with this or even explain a method, my brain’s hurting!


KENAT, probably the least qualified checker you'll ever meet...

 

[PSE]

Kenat,

It sounds like you wish to assess the capability of the process. If you do a Google search using process capability study you will get many hits that you can follow for additional information. Searching using statistical analysis online also brought up some links though I did not see anything directly pertaining to process capability. They would be a couple of places to start.

Then to throw another wrinkle your way, has a gage R&R (repeatability and reproducibility study) been done on the test equipment to assess it's capability in providing the information you require?

http://www.aiag.org/scriptcontent/index.cfm

The Automotive Industry action group has (at least what I think) are some well written publications regarding statistical process capability/control and gage assessment.

Hope this helps a bit.

Regards,

 

[KENAT]

Thanks PSE. What I'm actually trying to do is improve placement repeatability.

This is my logic:

Although the worst case location zone is a certain size, if we assume something approaching a normal distribution then the majority of placements will be in a much smaller zone.

The samples are (or could be) loaded into some kind of pocket or fixture (3 point contact on bottom (z), 2 on one side (x) 1 on another type thing).

My thinking is load the sample into the fixture nominally centered with a slight clearance from the x & y stops at worst case and pause just before contacting z but after being within the height of the x & y stops. Move the sample slightly over toward x and then y before finishing lowering onto Z.

It's probably not acceptable to have the sample routinely hitting the stops and hence sliding on the robot due to contamination issues but if it happened say 1 in 100 or something that may be OK.

So my idea is to limit the distance we move in toward X & Y based on statistics such that the sample only moves so far as to touch the stops and start sliding say 1 in a 100 times.

Say worst case placement accuracy is +-.25mm. Statistically a lot of them will fall in a much smaller zone, say +-.15. If 98% of them fell into this zone, and then I pulled the zone into the corner by .1 in both x & y then I’d end up with all of them in +-.2 and almost 99% in +-.15. Basically any that were off set toward the corner would be pushed into the +-.15 zone by hitting the stops.

However, typing this out has just made me realize it may not simplistically work.

The size of the samples varies significantly (actually probably more than the simple x-y placement accuracy), to the extent that most of the time you could probably move them the small distance I was thinking of without them hitting the stops and so almost all of the time you’d just be moving the placement zone not really improving it.

I guess I’ll have to get a better definition of ‘repeatability of placement in x & y’ before I go further. Is it the placement of the theoretical center or the placement of the hard edge.

I know the answer will probably be the placement of the same feature on the sample but then you’ve got so many things to take into account it could blow your mind!


KENAT, probably the least qualified checker you'll ever meet...

 

[PSE]

Kenat,

Would a machine vision system perhaps work in this application? If there is a registration mark or similar feature on the component, you could perhaps excercise greater control. As you indicate, if the size of the components are varying and if you are relying on the "outside" of the component as registration points, you really may not have much control over the "center" which appears to be your feature of interest. Reducing size variation may prove to be more useful and perhaps easier to accomplish.

If I read correctly, you have a centered distribution in X and Y that you are trying to shift with likely adjusting either stops or placement coordinates on the robot. As you approach the stops, you will essentially skew your normal distribution by collapsing the curve (hitting the stops), which may not be a desirable thing as it could cause new or additional potential failure mechanisms within your process.

If it appears that your current placement process is optimal yet you need further improvement from it, the process or equipment capabilities likely need to change. Like moving from a ruler to calipers, you may need to upgrade the system itself or at least provide it better tools to use. An example might be replacing or supplementing a mechanical stop with a proximity sensor.

Hope this helps a bit.

Regards,

 

[KENAT]

Thanks very much PSE, star for you.

We have a machine vision system,trouble is we are measuring at the sub micron range so the field of vision of the camera is very limited in order to get resolution good enough to get our measurement head in position. This is why the concern over placement accuracy.

We have techniques for accomodating this but they may have a major impact on thruput (we're getting them tested) so we're looking at plan B as it were.

I don't know we have a normal distribution (we're still designing part of the tool) but was going to assume it for the sake of doing some calculations to see if the idea was even worth pursuing.

The size variation is from an industry standard so we need to support all sizes.

We're actually designing the metrology tool for customers, sorry if my earlier posts were misleading.

Once again thanks for the time to spent on this.

KENAT, probably the least qualified checker you'll ever meet...