The Supervisor's 25% Productivity Claim
A DRDO-supported electronics workshop has 12 technicians assembling connector modules. In an 8-hour shift they produce 480 modules. After a process revision, 15 technicians work a 7-hour shift and produce 630 modules. The supervisor writes in his note: 'Output per technician-hour has risen by 25%, so the revised process is clearly better.' On the next day, 3 of the 15 technicians are absent, so only 12 work the 7-hour shift at the new rate. Separately, quality checks show the old process had a 2% rejection rate and the new process has a 5% rejection rate. The workshop head wants a short, defensible calculation before approving the revision; she is wary of percentage claims that compare total output instead of productivity, and she wants net good modules considered.
1. Calculate modules per technician-hour before and after the revision, and test the supervisor's 25% claim.
Read the worked answer
Old rate = 480 / (12 x 8) = 480 / 96 = 5 modules per technician-hour. New rate = 630 / (15 x 7) = 630 / 105 = 6 modules per technician-hour. The increase is (6 - 5) / 5 = 1/5 = 20%, not 25%. The supervisor probably compared total output, 630 against 480, which is a 31.25% rise, but that comparison ignores the extra workers and the shorter shift. His claim is false as stated.
2. How many modules should the 12 technicians produce in the 7-hour shift at the new rate, and how many good modules is that after 5% rejection?
Read the worked answer
At the new rate, 12 x 7 x 6 = 504 modules. A 5% rejection rate gives 504 x 0.05 = 25.2 rejected modules, so good modules are 504 - 25.2 = 478.8. Since modules are discrete, report about 479 if fractional output is being averaged, or 478 complete good modules if only whole modules count. State the rounding convention explicitly.
3. Compare net good modules per technician-hour before and after the revision. Does the revision still improve productivity after rejections, and what caution should the head add?
Read the worked answer
Old good output = 480 x 0.98 = 470.4 modules; per technician-hour = 470.4 / 96 = 4.90. New good output = 630 x 0.95 = 598.5 modules; per technician-hour = 598.5 / 105 = 5.70. The increase is 0.80 / 4.90 = 16.3%. The revision still improves net productivity, but the supervisor's 25% overstates it, and the higher rejection rate removes about 3.7 percentage points from the gross gain. The head should also check rework and scrap cost before approving.