The MEboost tolerance calculator allows you to see the potential rejection rate given a probability distribution for a dimension. This allows you to estimate rejection rate while balancing the necessary tolerance for functionality.

A tolerance range is specified by a range of sigmas (standard deviation) around the nominal dimension, or you can directly specify the dimensional tolerance limits.

Prior to using the tool you need to have an understanding of the manufacturing process used to create the part. In order to determine rejection rate, a probability distribution of the dimension must be specified.

Consider a part whose nominal dimension is 1.000 and the standard deviation of the manufacturing process is .005 and is normally distributed. The probability density function is shown below. We can specify the tolerance limits at +/-3 standard deviations and determine the percentage of parts rejected for being out of tolerance.

Alternatively, you may have tolerance limits that are required for fit, performance, etc. The rejection rate is determined for parts outside the limits.

There is often a trade-off between tolerances and reject rate. If the tolerance limits are too tight, reject rate increases and therefore increases cost. When reject rate is too high, a costlier manufacturing method may have to be used. If the tolerance limits are too loose, performance or fit may suffer.

## The MEboost Tolerance Calculator

To open the tolerance calculator, click on the *Tolerance Calculator* button in the MEboost ribbon.

### Specify by Sigma Range

Using the example part, we select a normal distribution with a mean of 1 and standard deviation of .005. We will use a range of 6 standard deviations (+/- 3σ).

Clicking the *Calculate* button will show the following results.

For tolerance limits at +/-3σ, we can expect a reject rate of 0.27%. If we increase the sigma range, we could lower the reject rate. A smaller sigma range would result in a higher reject rate.

### Specify by Tolerance Limits

Now let's assume that we need the tolerance limits to be +/- 0.010. We enter the dimension's upper and lower values as shown below.

Clicking the *Calculate* button will show the following results.

For tolerance limits at +/- 0.010, we can expect a reject rate of 4.55%.

## Other Distributions

MEboost allows for the following probability distributions:

- Normal
- Uniform
- Triangular
- Trapezoidal
- PERT

The normal distribution is generally used when there is data available on the manufacturing process and is normally distributed. The uniform distribution might be used to model machine tool wear. The remaining distributions are generally used when you can only estimate the parameters of the distribution.

MEboost is an Excel add-in that includes a suite of mechanical engineering tools for analysis and charting.

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