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Finally, even dusts that don’t pose exposure risks can still be hazardous because, if allowed to accumulate, they can become combustible. In fact, the ACMA staff wrote in an article for Composites Manufacturing Magazine that they were “not aware of any composites dust that did not test as hazardous [meaning combustible] using OSHA’s approved test methods.”

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In the worst case example above, there was an extreme distribution of tolerances. The question now is what is a (more) realistic distribution. This is not an easy question to answer, but a better estimate would increase the accuracy of your analysis.

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A widely used method for performing a statistical stack-up tolerance analysis is the Root-Sum-Squares (RSS) method. Variances (the standard deviation is the square root of variance) can be added. This makes it easy to sum normally distributed tolerances: Ttot = √(T12 + T22 + …. Tn2).

It is clear that it is beneficial to consider the probability distribution of the tolerances and perform a statistical analysis

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Carbon nanotubes are 20 times stronger than carbon fiber. Unfortunately, research has shown that they’re also as dangerous to human lungs as asbestos. Carbon nanotubes can also irritate the eyes and the skin.

In the Worst-case Tolerance Stack-up Analysis article, you will read about worst-case or linear stack-up analysis. Such an analysis assumes that all dimensions in the tolerance chain have worst-case deviations from their nominal values. A statistical tolerance stack-up analysis considers the probability of a tolerance value and the combination of tolerances. It turns out that the probability of a worst-case combination is negligible for even a small number of parts. Let’s look at the following example. Suppose you are making a stack of 4 identical parts and you want to analyze the total height of the stack. The parts have a height specification of 10 +/-1. Now assume that all parts have a worst-case deviation and are either 9 (part ‘9’) or 11 (part ’11’) high (any dimension, mm, inch, meter, etc.). With only 4 parts, it is still possible to write down all possible combinations.

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If you don’t know the distribution of tolerances, you have to make an estimate. It is often assumed that tolerances have a normal (Gaussian) distribution. This is because the normal distribution seems to occur in “almost all cases”. In statistics, this is called the central limit theorem. Roughly speaking, this theorem states that “the sum of a large number of independent and identically distributed random variables, will be approximately normally distributed“. Since the manufacturing process of machined parts consists of many variables, it is safe to assume a normal distribution of tolerances. An added benefit is that it is relatively easy to add up normally distributed tolerances.

The probability of an extreme thickness is 2/16 = 12.5%. If, for example, only the top pile is problematic, the probability is only 6.25%. Note that this is an extreme tolerance distribution with a low probability itself. In practice, the probability of an extreme height is very low.

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Carbon fiber dust is well-known to be hazardous to electronics because carbon fibers are electrically conductive. If allowed to build up, this dust can short out computers and cause other digital device havoc. It’s also associated with lung damage in people.

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Dust is everywhere in composites manufacturing. If it’s not controlled, that dust can easily find its way into your eyes and lungs, causing irritation; into hard-to-reach areas, creating combustible dust hazards; and onto surfaces, leading to slip and fall incidents.

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Exposure to these and other composites dusts can cause serious adverse health effects, ranging from dermatitis to lung cancer. One of the best ways to keep these effects at bay is to eliminate hazardous dust at the source.

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A tolerance analysis spreadsheet is available in the Engineering Toolkit of Vink System Design & Analysis. This allows you to quickly start performing tolerance analysis, including the statistical method described here. The advanced method as described in ‘Advanced Method of Tolerance Analysis‘ is also possible.

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In small particles, crystalline silica becomes silica dust, which is respirable and is known to cause silicosis among other lung disorders.

As the American Composites Manufacturing Association (ACMA) notes, “Many composite raw materials and molded composite products contain crystalline silica.” These include: “sand, quartz, calcium carbonate, gypsum, dolomite, mica and other materials used in the production of cast polymer, engineered stone, tub/showers, and many other composite products.”

Several types of resin dusts are common in composites manufacturing, and they aren’t all created equal in terms of hazardousness. For example, there are no adverse health effects associated with thermoplastic resins. However, dust from heated bismaleimide resin products can cause eye, nose, and throat irritation. And dust from polyurethane resin is highly toxic.

A common assumption is that the tolerance limits coincide with the +/-3σ (3x standard deviation) values. As a reminder, the standard deviation is a measure of variation. 99.7% of the population falls within the +/-3σ limits.

If similar parts have been produced, you have important data to make a good estimate of the tolerance distribution. But what if you’re working on a new product and don’t have that kind of data to compare?

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“To reduce combustible dust hazards and avoid citations, composites manufacturers should employ regular housekeeping to keep dust levels below hazardous levels, use listed electrical equipment in dusty process areas, and locate cyclones and bag houses outdoors.” [emphasis added]

In the example above, all tolerances were +/-1, so the total height variation is: Ttot = √(12 + 12 + 12 + 12) = 2. The stack of parts will have a height of 40 +/-2. And 0.3% of the stacks will be smaller or larger (with a height of 36 .. 38 or 42 .. 44).