# What is Statistical Tolerancing? How to apply it to a product?

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#### lee01

I need some help?

People have been asking about Statistical Tolerance and how to apply it to a product?

We are currently manufacturing ‘test’ products that will be used to ascertain our capabilities etc. A member of our team has heard about Statistical Tolerancing and wishes to use it to allow for various errors including, measurement inaccuracy stack, inability to manufacture to design standards due to machine capability etc.

Therefore the idea is to have a design standard and a Statistical Tolerance that could be used to allow for these errors and use the measured capability as either the design standard and/ or backup or fall back standard to pass fail the product.

Please note that we are in a design stage and the ability to implement such a methodology would be useful.

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#### M Greenaway

Statistical tolerancing is based on the concept that it is highly unlikely that you will get mating pieces both at maximum material condition.

All manufacturing processes subject to common cause variation will produce parts that vary in size around a nominal value. The distribution of this variation will be a 'normal' curve. If your process is just 'perfectly' capable, in that +/- 3 standard deviations of the nominal size fits the tolerance spread perfectly, then very few pieces will be at the extremities of the curve, i.e. max or min material conditions.

If the mating piece is similarly produced with regard to capability then the chances of getting, for example, a shaft a maximum material condition, and a hole at maximum material condition are very small.

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#### lee01

I think I have the wrong interpretation of ST, I’m of the understanding that it can be used to, well, increase the design tolerance, or at least provide a ‘back-up’ tolerance?

I thought (I’m being told elsewhere) that ST is a method of applying a tolerance to a part based on proven studies regarding the manufacturing capability. And as a result applies to achievable result/ tolerances, is this not the case.

We are going to use an ST in addition to the design standard to create a way of accounting for the odd measured point falling outside the ‘+/- curve’. And therefore not failing a part and encouraging cost due to gaining a concession. (a full-back tolerance)

I have only just been informed of this proposed system and would like more information big time!

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#### M Greenaway

Lee

I think that is what I said - in perhaps a roundabout way.

Traditional tolerancing is based on the assumption that a piece of a certain size can only be a certain maximum dimension to fit into another piece of a certain minimum dimension. This theory is based on the likelihood of all variations of size occuring equally often.

As such a shaft is often a nominal size with a minus tolerance, and a hole is a nominal size with a plus tolerance.

Statistical tolerancing realises that manufacturing capability is such that a capable process, well centred, will produce very fex pieces of maximum or minimum size. As such you can relax the tolerances based on this.

This looks like a good link

http://www.qfm.uni-erlangen.de/gps/content/Chapters/chapter_21.htm#21.1 Introduction

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#### Paul F. Jackson

##### Quite Involved in Discussions
You can read a description of Statistical Tolerancing (What it is, What it is used for, Benefits, Limitations and cautions, and Examples of applications) in the Technical Report publication ISO/TR 10017 Guidance on statistical techniques for ISO 9001:1994 Section 4.12 Page 18.

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#### Bill Ryan - 2007

We are going to use an ST.......
I may be mistaken, but I don't think you can "decide" to use ST without your customer's approval.

Bill

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#### Ravi Khare

Statistical tolerancing does depend on the fact that it is very unlikely that all the dimensions contributing to a tolerance stack up would swing to their worst case condition in the same assembly.

The popular method of evaluation of Statistical tolerance Stack ups is the RSS (Root Sum Square) method where the variance of the total stacked up tolerance is calculated as the sum of variances on individual contributing dimensions. This method however works well when we are assured that al contributing dimensions have a Normally distributed variation.

For cases of non normal distributions Monte Carlo Simulation method (Similar to those used in Risk analysis) are used to evaluate a realistic tolerance stack up.

Statistical tolerance in any case can be used to relax individual tolerances in a calculated manner.

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