Statistical Methods
Audit denominators before comparing inspection fractions
Establish the unit at risk
Suppose a data team inspects exported records for a formatting defect. A record with three formatting defects still contributes one affected record to a fraction chart. A separate count of individual defects answers a different question. Retain inspected records and affected records for each batch, along with the sampling rule.
Calculate the center from counts
Use the total affected across the baseline divided by the total inspected. For period size n, the binomial standard deviation of its fraction under the baseline is the square root of p(1−p)/n. Larger samples therefore have narrower limits. If inspection expands specifically after an alert, examine selection changes before interpreting the resulting series.
Hypothetical contrast
Two baseline batches have 2 affected records of 20 and 3 of 80. The combined fraction is 5/100 or 5%. Averaging the two batch percentages gives 6.875%, which gives the small batch as much influence as the large one. At a common reference fraction of 5%, the standard deviations for future batches of 20 and 80 are approximately 4.87 and 2.44 percentage points.
Document the numerator definition, inspection denominator and any repeated records. Classical three-standard-deviation limits use a normal approximation that can perform poorly with rare events and small denominators. A batch with zero inspected records contributes no observed fraction. Preserve its status in the timeline.
Method checked 9 November 2026. NIST/SEMATECH Engineering Statistics Handbook, 6.3.3.2. Proportions Control Charts.