Introducing measurement system analysis (MSA) with single variable examples is good for communicating basic concepts of the subject. After practitioners are comfortable with the single variable case, graduating to the multiple variable one is the next logical step. Understanding measurement variation in two or more dimensions simultaneously is a regularly occurring need. For a flavor of the multiple dimensional case, consider the example of a metal fabricator producing rectangular components with tolerances for length and width to yield a desired surface area. The variation in surface area is a function of the joint variation of length and width, and the measurement variation of surface area is a function of the measurement variations of length and width, and their interplay.
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