# Tolerance Analysis Methodology

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- This topic has 11 replies, 5 voices, and was last updated 14 years, 6 months ago by Michael Schlueter.

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- August 11, 2005 at 12:22 am #40312

NJINIYELAParticipant@NJINIYELA**Include @NJINIYELA in your post and this person will**

be notified via email.I am performing tolerance analysis on a product that I am working on. I have used RSS analysis for fairly large tolerance loops (i.e. 6 features), but I have gotten feedback from my customer and some co-workers that this analysis is not adequate. Does anyone know of a better statistical method that is practical to use? Monte Carlo simulations, etc are not feasible at this point.

0August 11, 2005 at 1:50 am #124758

tol_sigmaMember@tol_sigma**Include @tol_sigma in your post and this person will**

be notified via email.Njiniyela,

Why does your customer think that analysis is not adequate? RSS analysis assumes, following:

1. Tolerances follow a normal distribution

2. Parts produced are mean centered

3. Tolerances are independent of each other

As long as these three assumptions are realistic in your situation, it is OK to use RSS method to evaluate variation.

Other options you have:

1. Worst case analysis (Straight stack)

2. Benderizer method (a variation of RSS method, recommended for sheet metal stampings)

3. Monte Carlo simulation method (where you can assign distributions to each tolerance, based on historical data)

If there are 3-dimensional interactions, such as moment arms or gravity related shifts play a role then 3D analysis should be considered. However in my experience, I found that a well done RSS stack will be very close to a 3D analysis (80 to 90% close).

Jean0August 11, 2005 at 6:56 am #124768Njiniyela,

To build upon Jean’s response, (you left your name at the end of you response), there is actually a third option which integrates Worst-case and Statistical tolerancing together called Process tolerancing.

If you have knowledge of the transfer function between the critical inputs and the output of interest, and you have an understanding of the variation of each of the critical inputs, or can acquire that understanding, then there is a fairly new method called “Robust Tolerancing” that can be done with some easy to use software to allow a complete tolerancing of the process to be done. If you’re interested in more details, then simply respond to this post.

Ken0August 11, 2005 at 2:04 pm #124814

NJINIYELAParticipant@NJINIYELA**Include @NJINIYELA in your post and this person will**

be notified via email.Thanks Jean for your response. One of the reasons why RSS is viewed as inadequate is that it assumes a normal distribution and does not take into account biases or shifted distributions.

0August 11, 2005 at 2:06 pm #124815

NJINIYELAParticipant@NJINIYELA**Include @NJINIYELA in your post and this person will**

be notified via email.Ken.

I am not familiar with process tolerancing. Is it the same as estimated mean shift? Please explain or direct me to a resource.0August 11, 2005 at 2:35 pm #124821Jean:Tolerance analysis falls into two categories with associated methodologies for each:Linear:- Worst case analysis- General Root Sum Squares (RSS)- Classical RSSNon-linear:- Worst case analysis- Partial derivative analysis- Monte Carlo (MC) simulation- Exact analysisWorst case analysis usually results in over design and is conservative unless the process capability is less than about 1.5 sigma.RSS assumes normally distributed and usually independent Xs – correlations are included by modifying the expression for summing variances. General RSS is similar, but allows weighting of variables.Partial derivative analysis requires an exact equation relating the Xs to the Y. It can appear similar to the general RSS above, where the partial derivatives replace the weighting coefficients of the equation for the calculation of the standard deviation of Y, but still assumes normality.Monte Carlo can be used with non-normal distributions determined by fitting with measurements from a sample of existing parts. Correlations between variables are easy to include and are specified in terms of Spearman’s r (for non-normal distributions). In limited circumstances MC can be used with 2D data. There are some software packages available that allow for the use of MC with 3D data and run with Unigraphics. These can be used to satisfy Geometric Dimensioning and Tolerancing (GD&T) requirements from ASME and ISO standards.When you list the reasons why your customers are dissatisfied with RSS, then MC is the next superior technique. Why do you say it is not feasible?BTDT

0August 11, 2005 at 2:36 pm #124822Jean:Tolerance analysis falls into two categories with associated methodologies for each:Linear:- Worst case analysis- General Root Sum Squares (RSS)- Classical RSSNon-linear:- Worst case analysis- Partial derivative analysis- Monte Carlo (MC) simulation- Exact analysisWorst case analysis usually results in over design and is conservative unless the process capability is less than about 1.5 sigma.RSS assumes normally distributed and usually independent Xs – correlations are included by modifying the expression for summing variances. General RSS is similar, but allows weighting of variables.Partial derivative analysis requires an exact equation relating the Xs to the Y. It can appear similar to the general RSS above, where the partial derivatives replace the weighting coefficients of the equation for the calculation of the standard deviation of Y, but still assumes normality.Monte Carlo can be used with non-normal distributions determined by fitting with measurements from a sample of existing parts. Correlations between variables are easy to include and are specified in terms of Spearman’s r (for non-normal distributions). In limited circumstances MC can be used with 2D data. There are some software packages available that allow for the use of MC with 3D data and run with Unigraphics. These can be used to satisfy Geometric Dimensioning and Tolerancing (GD&T) requirements from ASME and ISO standards.When you list the reasons why your customers are dissatisfied with RSS, then MC is the next superior technique. Why do you say it is not feasible?BTDT

0August 11, 2005 at 3:20 pm #124833

NJINIYELAParticipant@NJINIYELA**Include @NJINIYELA in your post and this person will**

be notified via email.We are currently designing the product and therefore do not have any sample parts to analyze. This is why I said that the Monte Carlo method was not feasible.

0August 11, 2005 at 3:28 pm #124834Njiniyela:Do you have a linear stack-up, or is this a more complex geometry?BTDT

0August 11, 2005 at 4:51 pm #124847N,Try this link: http://www.variation.com/techlib/ta-2full.htmlCheers,Ken

0August 12, 2005 at 3:30 am #124899

tol_sigmaMember@tol_sigma**Include @tol_sigma in your post and this person will**

be notified via email.Njiniyela,

Don’t rule out Monte Carlo simulations, yet. You don’t need to have sample parts data to perform Monte Carlo simulations. You can use historical capability data for tolerances, or you can use realistic assumptions based on experience to assign distributions.

Also the more number of tolerance contributions you have towards a stack, the output will be closer to a normal distribution.

Jean0August 12, 2005 at 7:57 am #124904

Michael SchlueterParticipant@Michael-Schlueter**Include @Michael-Schlueter in your post and this person will**

be notified via email.Hello Njiniyela,

The most practical one I know is Dr. Taguchi’s Tolerance design approach. You do not need distribution data, just objectives (targets).

Inputs:target (output) value for your customer [nominal value]

tolerable tolerance for your customer

monetary loss associated for your customer

monetary loss for you, the supplier

Output:a tolerance for you, the supplier

which minimzes overall economic loss (for you and your customer).

Example:assume you manufacture windows (those with the glas panes ;-)

the target outer dimension is 1 m (so your customer can mount it into a house)

his bearable tolerance is +- 0.1 m (if it’s > 1.1 m it cuases rework; if its < 0.9 m it calls for improvisations)

the avarage loss associated to it is $ 22

by adjusting your process you can prevent deviations from the target dimensions

adjustment would cost you $3.

So your in-house tolerance should be +- 0.036 m

So your manufacturing department has to check and adjust the process when the dimensions differ from (1 – 0.036) to (1 + 0.036) m.

This way economic loss will be minimum for you (less warranties) and your customer (fewer problems).

Repeat this process for each parameter you have to tolerance.

Hope this helps, Michael Schlueter

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