3Statistical Considerations
3.1 Introduction
When designing a mechanical element, we must consider that most dimensions, geometry elements, and physical properties show variability as a result of, e.g. a manufacturing process. For instance, if we manufacture 100 mechanical elements with length 
, diameter 
, and yield stress 
, we expect that not all values of 
, 
, and 
are identical because of imperfections of the stock material and finite accuracy of the manufacturing process. Thus, it is important to understand probability theory and statistics to account for the uncertainty associated with the actual values of 
, 
, and .
3.2 Random Variables and Distributions
Probability theory and statistics ...
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