Every product quality of concern has a target goal, G, which defines the economically optimum value for that quality. The actual quality can vary above and/or below G by a small value, say g⁺ and g^- respectively, where either value can be zero and are not necessarily equal to one another. So, the key to achieving optimum Quality (Q) is to minimize all variations (g⁺ and g^-) from the goal (G): i.e.



Optimum Quality is achieved when all g_i are zero; i.e. there are no variations from the optimum goals, G_i. Optimum Quality calculates to Q = i, where i is the total number of defined qualities. As Quality strays from optimum, Q < i.

Acceptable Quality is defined as Q_An, where n < i and is the value calculated with the widest acceptable tolerances, g_n for each quality.

For example, if one defines 20 qualities as being critical and necessary for a Quality product (i = 20), then:

1. If all tolerances (g_i) are zero, optimum Quality is achieved and is equal to the total number of qualities, i.e. Q = i = 20.
2. If one or more of the tolerances are not zero (reality) then Q < 20; but the lowest acceptable value which yields a product of acceptable Quality must then be defined.

This arithmetic model allows a simple, analytical means to define, monitor and control Quality.

Note: The standard terms 'variation' and 'standard deviation' are not useful for this discussion since these statistical quantities are predicated on variations from a 'mean' value and presumed to be distributed about the 'mean' according to a Gaussian (bell) Curve. In fact many of the quality tolerances in this definition of Quality can be defined to approach the optimum goal from one direction only. For example: "FCC radiated emissions must be 10dB below the legal limit"