The Permit Processing Comparison
Three months of permit-processing data are tabled for a service review. Office North: January, 420 applications completed with a mean processing time of 11.2 days; February, 380 applications at 12.6 days; March, 460 applications at 9.8 days. Office South: January, 310 applications at 13.4 days; February, 340 applications at 12.1 days; March, 300 applications at 14.0 days. Mean processing time is calculated only for completed applications. At the review, the South manager states that her office is 'faster overall and improving month on month', and proposes transferring two processing officers from North to South. The North manager counters that his March figure proves his team is the stronger performer. A separate audit note records that 6% of North's applications were returned as incomplete, which pauses the processing clock, and that South handles a higher share of applications requiring a site inspection. Neither manager has supplied staffing numbers.
1. Calculate a weighted mean processing time for each office and explain why the simple average of monthly means would give a different answer.
Read the worked answer
North - total applications 420 + 380 + 460 = 1,260. (420 × 11.2) + (380 × 12.6) + (460 × 9.8) = 4,704 + 4,788 + 4,508 = 14,000 14,000 ÷ 1,260 = 11.11 days
South - total 310 + 340 + 300 = 950. (310 × 13.4) + (340 × 12.1) + (300 × 14.0) = 4,154 + 4,114 + 4,200 = 12,468 12,468 ÷ 950 = 13.12 days
Simple averages for comparison: North 11.20, South 13.17.
The unweighted mean treats a 300-application month as equal in importance to a 460-application month. North's busiest month (March, 460 cases) was also its fastest, so the simple average understates North's true speed; South's quietest month (March, 300) was its slowest, so its simple average overstates its speed. The weighted figure answers 'how long does a typical application take', which is the question the review is actually asking.
2. Evaluate the South manager's claim and her proposal using only the data given.
Read the worked answer
Claim 1 - 'faster overall': false. South's weighted mean is 13.12 days against North's 11.11, so South is about 2.0 days slower, roughly 18% longer.
Claim 2 - 'improving month on month': false. South's sequence is 13.4 → 12.1 → 14.0: February improved, March reversed and ended worse than January. That is not a trend, and three data points cannot establish one in any case.
Claim 3 - the North manager's counter is equally weak. One good March (9.8 days) in the office's highest-volume month may reflect volume, staffing or case mix; it does not prove North is 'stronger' in general.
The proposal is not supported. Before moving two officers, three confounders must be resolved: South's higher share of site-inspection cases, which legitimately lengthens processing; North's 6% incomplete-return rate, which pauses the clock and so flatters North's mean; and the absence of staffing numbers, without which no per-officer productivity comparison exists.
Better next step: a like-for-like comparison banded by application type, measuring from valid submission to decision with paused days included, plus FTE per office. Transferring staff on a two-day gap driven by case mix would move the problem, not fix it.
3. What further data would you require before any decision on redeploying staff, and how would you use it?
Read the worked answer
Required data, with the use of each:
- FTE per office per month - converts raw output into cases per officer, which is the only basis for a redeployment decision.
- Application mix by type and complexity, plus the site-inspection share - lets the two offices be compared on matched case types rather than a blended average.
- Clock-stop reasons and durations - isolates the effect of the 6% incomplete returns at North from genuine processing speed.
- Backlog at the start of each month - a large carried-over backlog depresses throughput without reflecting effort.
- Quality measures - error rate, overturn rate on appeal, complaints - so speed is not improved by cutting corners.
- Absence, vacancies and overtime - a two-day gap may be a temporary staffing artefact.
How to use it. Rebuild the comparison as a matched-case measure (valid submission to decision, pauses excluded) per FTE. If South remains slower after matching, the cause is process or staffing and one officer on a time-limited secondment with a review date is a proportionate test. If the gap disappears, the proposal should be dropped and the review should instead target the incomplete-application rate, which is the one defect the data clearly identifies.