Worst case tolerance analysis is the starting point when creating a tolerance specification. It is a conservative approach as it only considers the maximum or minimum values of part variation, whichever leads to the worst situation.
The worst case method simply adds the dimensions using the extreme values for those dimensions. Thus if a part is specified at 25mm +/- 0.1mm than use either 25.1mm or 24.9mm, whichever leads to the most unfavorable situation.
Tolerance and Reliability
Ideally, every part has the same dimensions, and each product created fits together the same, thus performing the same (and as expected.) Unfortunately, that doesn’t occur, and everything varies.
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Products fail due to variation that leads to excessive wear of parts that are too large, or due to electronics running hotter than expected, or connectors fitting too loosely, for example. There are many sources of the variation and if the design accommodates the expected range of variation, the product will not suffer adverse effects of the variation that occurs.
One of the signals that reliability engineers should consider is the parts that are difficult to manufacture within the specified tolerances. It is more likely to have parts at or beyond the tolerances. These can lead to premature failure, if not poor product performance.
By identifying the parts with tight tolerances or low process capability, we can work with the design team or supplier to improve the ability of the parts to meet the needs of the design. Or, as a minimum, we can take steps to monitor and control the process to create parts that are within tolerance specifications.
Simple example
Let’s consider a stack of five plates and we want to estimate the combined thickness. If each plate is 25mm +/- 0.1mm then the combined thickness will be 5 times 25mm, for 125mm for the nominal thickness. And the math for the minimum and maximum is about as simple.
The tolerance is +/- 0.1mm, thus combining five plates at maximum and minimum tolerances provide a tolerance for five plates of +/- 0.5mm.
Thus, the stack of five plates will have a thickness of 125mm +/- 0.5mm or range in thickness from 124.5mm to 125.5mm.
Best Practices and Assumptions
Worst case tolerance analysis is quick and easy.
You need just the tolerances of the components involved. No need for distributions or assumptions about distributions. We should have evidence that the part tolerances are real though. If the plate is specified as 25mm +/- 0.1mm, then verify that the range of measured values actually falls within the range of the tolerance.
If the design function and the manufacturing process work using the worst case tolerance analysis, then that is a safe way to set tolerances. There are cases where the tolerance stack is too large for the design or assembly process.
In that case, consider conducting the analysis using the root sum squared or Monte Carlo methods.
Related:
Why do Tolerance Analysis (article)
Root Sum Squared Tolerance Analysis Method (article)
Reliability as Part of Every Decision (article)
This quick introduction to three statistical analysis methods enables you to quickly determine or assess part tolerances. Plus, you will learn why tolerances are critical to achieving a reliability product or system.
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