Work Measurement: Stopwatch Times, Practice and Forgetting

The problem

Picture someone standing next to a worker with a stopwatch, timing the same job ten times. The readings hover around five minutes. But you can’t drop that number straight into a plan. The worker you timed may be quicker or slower than most people. And nobody works every minute of a shift. People need rest and some personal time, and small delays happen. So planners need a fair time per job, called the standard time. It decides how many people it takes to fill a day’s orders.

Then practice changes things. People get faster each time they repeat a job. But when days go by between repeats, they forget some of what they learned. Take a job done every day and the same job done once a month. They start at the same time and can end up far apart. I built the lab so you can change each of these assumptions yourself. Then watch three things react: the planned time, the crew size and the time per job after 100 repeats.

The model has two halves. The first turns stopwatch readings into a standard time and a crew size. The second starts from that standard time and tracks how much practice a person carries from one repeat to the next.

From stopwatch time to standard time

The lab starts with ten stopwatch readings of the job, start to finish. Their average is the observed time. Next comes the performance rating. That’s the timekeeper’s judgment of how fast the worker was going compared with a typical pace. It turns the observed time into the normal time: Tnormal = Tobserved × rating. So a worker who was going fast gets their time stretched out to a typical pace. Then comes the allowance, the share of time set aside for rest, personal needs and delays nobody can avoid. It turns normal time into standard time: Tstandard = Tnormal / (1 − allowance).

This formula counts the allowance as a share of the total time allowed for the job. Not every company counts it that way. So the bottom of the fraction has to match whatever work-measurement standard your workplace follows.

Takt time and crew size

Takt is the pace the day’s orders set: one finished unit every so many minutes. With 480 working minutes in a day, takt = 480 / daily demand. The simple rule for crew size is ceil(standard time / takt). Here ceil means round up to the next whole number, since you can’t hire part of a person. This is plain math on the average workload. It doesn’t model waiting lines or the ups and downs of real work.

So changing demand changes the takt, not the work inside each job. Changing the rating or the allowance changes the standard time instead. That can nudge standard time ÷ takt past a whole number, which adds or drops a whole person.

The classic learning curve

A learning curve shows how people speed up with practice. With no gaps between repeats, the lab uses Tₙ = T₁ nᵇ. Here Tₙ is the time for repeat number n, and T₁ is the time for the first one. The exponent is b = log(r)/log(2), where r is the learning-curve percentage. An 85% curve means that each time the total number of repeats doubles, the time per job drops to 85% of what it was. So the second job takes 85% as long as the first, and the fourth takes 85% as long as the second.

This version tracks the time for each single job. Another common version tracks the running average of all the jobs so far. The two read the same percentage differently, so don’t mix them up.

Tracking forgetting one repeat at a time

You can’t capture the gaps between repeats by taking one discount off at the end. So the lab updates experience one repeat at a time. Think of experience as a running score, where a total beginner starts at the bottom. Before each new repeat, only part of the score above that beginner level survives. The share that survives is R(Δt)=exp(−kΔt). Here Δt is the days since the last repeat, and k is how fast people forget. The longer the gap, the less survives. Then the new repeat adds to the score. In short: do the job → learn → wait → forget a bit → do it again and relearn.

In symbols, the score updates as Eₙ = 1 + (Eₙ₋₁ − 1)R(Δt) + 1. The time for that repeat is then Tₙ = Tstandard Eₙᵇ. With no gap (Δt=0), nothing fades: R=1 and Eₙ=n exactly. Then the model turns back into the classic learning curve. The lab checks that this really happens.

Using the controls

Here’s what each control does. Performance rating and allowance change how the standard time is built up. Demand changes the takt and the crew size. The learning percentage sets the exponent b, which controls how steep the learning curve is. Days between repeats sets how much experience survives each gap. The forgetting rate k sets how fast it fades.

The comparison panel shows T@100, the time per job on the 100th repeat. It shows this for no gap, and for gaps of 1 day, 7 days and 30 days. The same number of repeats can end at different times, because people keep different amounts of what they learned. The learning landscape is a surface. It runs the same math for every whole-day gap from 0 to 30. It also covers repeats 1 to 100, on a log scale that gives the early repeats more room. The front edge is the classic no-gap curve. The gap you picked is drawn as a slice through the surface. The rise at repeat 100 is the T@100 penalty: how much slower the 100th repeat is than with no gap. With the same gap every time, experience creeps up toward a ceiling of 1 + 1/(1 − R). So the time per job levels off instead of continuing down the learning curve.

What the forgetting rate is not

The forgetting rate is a “what if” setting, not a fixed fact about human memory. How much people really remember depends on a lot. It depends on how hard the task is, and whether it’s mostly hands-on skill or mostly thinking. It also depends on how well they knew it before, how experienced they are, cues around them, their tools and much more. Before using the model for real planning, you’d have to tune it to data that tracks people’s performance over a long stretch of time.

The model also leaves out two things, for now. It has no separate long-term memory that never fades. And it doesn’t include the faster relearning after long layoffs that real data has shown. Both would be sensible to add once there’s data to support the extra settings.

How I check it

These checks have to pass. With the forgetting rate at zero, gaps between repeats must make no difference. With no gap, the step-by-step model must match the classic learning curve. With a 100% learning rate, practice must not make the job any faster. A longer gap or a higher forgetting rate must never make people faster, with everything else held the same. Rating and allowance should scale the times up or down without breaking any of those rules.