Four Offices: Is the Region Really Getting Faster?
Four processing offices report the following for the month just ended, with the previous month for comparison.
| Office | Cases cleared (this month) | Average days (this month) | Cases cleared (last month) | Average days (last month) |
|---|---|---|---|---|
| North | 1,240 | 4.2 | 1,100 | 4.4 |
| South | 860 | 6.5 | 900 | 6.2 |
| East | 2,050 | 3.8 | 1,700 | 4.0 |
| West | 640 | 5.1 | 700 | 4.9 |
The regional director wants a one-line summary: are we getting faster? She also wants to know whether any gain is real effort or just a shift in where the work sits. Total cases cleared rose from 4,400 to 4,790.
1. Compute the correct average handling time for each month and explain the trap in averaging the four office figures.
Read the worked answer
Weight by cases (case-days ÷ cases).
This month: 1,240×4.2 = 5,208; 860×6.5 = 5,590; 2,050×3.8 = 7,790; 640×5.1 = 3,264. Total 21,852 case-days over 4,790 cases = 4.56 days.
Last month: 1,100×4.4 = 4,840; 900×6.2 = 5,580; 1,700×4.0 = 6,800; 700×4.9 = 3,430. Total 20,650 over 4,400 cases = 4.69 days.
So the region improved by 0.13 days (about 2.8%).
Trap: the unweighted mean is (4.2+6.5+3.8+5.1)/4 = 4.90 this month against (4.4+6.2+4.0+4.9)/4 = 4.875 last month - a slight worsening. That reverses the truth because it gives East's 2,050 cases the same weight as West's 640.
2. Split the 0.13-day improvement into a mix effect and a genuine within-office effect.
Read the worked answer
Hold handling times at last month's levels but use this month's case volumes: 1,240×4.4 = 5,456; 860×6.2 = 5,332; 2,050×4.0 = 8,200; 640×4.9 = 3,136. Total 22,124 over 4,790 = 4.62 days.
- Mix effect: 4.69 − 4.62 = 0.07 days.
- Within-office effect: 4.62 − 4.56 = 0.06 days.
So roughly half the headline gain is composition, not effort. East's share of all cases rose from 1,700/4,400 = 38.6% to 2,050/4,790 = 42.8%, and East is by far the fastest office.
On their own numbers, only North (4.4 → 4.2) and East (4.0 → 3.8) improved. South (6.2 → 6.5) and West (4.9 → 5.1) got slower.
3. What should the director be told, and which office should be challenged first?
Read the worked answer
Report two figures, not one: overall 4.69 → 4.56 days, of which about 0.06 is operational improvement and 0.07 is the work shifting towards the fastest office. Unweighted averages would have shown a deterioration and should be rejected.
Challenge South first. Its time rose 0.3 days on 860 cases while its volume fell 4.4%, and at 6.5 days it is 2.7 days slower than East - the largest absolute gap in the region, so the biggest available saving.
West also worsened but on only 640 cases, where a 0.2-day move is within normal noise. Praise East, which absorbed 350 extra cases and still cut 0.2 days, but check its rework or appeal rate before treating that as pure productivity.