The following variables represent the fractional components of the Cost of Quality model:

They add to 100% so:

We want to calculate the relative increase in production when rework is reduced:

The ratio of appraisal to production costs is assumed to be the same in both cases. This assumes that, on average, appraisal hours are proportional to development effort.

A₂ can be replaced by:

Let

Therefore,

Solving for x gives:

Since x is the ratio of the increase in production, x − 1 is the productivity improvement. For example, if production rises by a factor of 1.25, the productivity improvement is 25%.