A plate is to be placed into a bracket where the dimensions

A plate is to be placed into a bracket where the dimensions with natural statistical tolerances of the plate and bracket are hp = u(hp) + t(hp) = 2.435 (+ or -) 0.120 in and hb = u(hb) + t(hb) = 2.455 (+ or -) 0.150in.

What is the percentage of assemblies that will have clearances less than c = hb - hp = .005 in?

For this question we took 40 data points for the thickness of 10 separate plates (4 per plate) and 3 measurements for the slot. I have the average as well as standard deviation etc. I am wondering if I would use a Z score here and then simply look up 1 - alpha in a table? If so, how do I take tolerances into account? Thank you!

Solution

Tolerance limits for hp:

Lower Limit: 2.435-0.120=2.315

Upper Limit: 2.435+0.120=2.555

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Tolerance limits for hb:

Lower Limit: 2.455-0.150=2.305

Upper Limit: 2.455+0.150=2.605

I think here you have to first identified the plates which are with in tolerance limit of hp and hb. Then for selected plates in the previous step, you will have to find c.