Work Measurement, Learning and Forgetting: From Stopwatch Time to Retained Proficiency
Observed time, rating, allowances, takt, staffing and a sequential learn–decay–relearn model.
From observed time to standard time
The showcase starts with ten observed cycle times. Their average is observed time. Performance rating converts that observation to normal time: Tnormal = Tobserved × rating. Allowance then converts normal time to standard time using Tstandard = Tnormal / (1 − allowance).
The allowance formulation treats the allowance as a fraction of total allowed time. Organizations sometimes use different conventions, so the denominator convention must match the governing work-measurement standard.
Takt and staffing
For a 480-minute available day, takt = 480 / daily demand. The simplified staffing requirement is ceil(standard time / takt). This is a deterministic workload balance, not a queueing or variability model.
Changing demand therefore changes takt rather than the elemental work content. Changing rating or allowance changes standard work and can push the staffing ratio across an integer boundary.
Classical unit learning curve
The no-gap baseline uses Tₙ = T₁ nᵇ, where b = log(r)/log(2) and r is the learning-curve percentage. An 85% curve means that when cumulative production doubles, modeled unit time becomes 85% of its previous level.
This is a unit learning-curve convention. Cumulative-average learning curves use a different interpretation and should not be mixed with it.
Why forgetting needs state
Spacing cannot be represented faithfully by applying one discount after all repetitions. The revised showcase updates experience sequentially. Before each new repetition, accumulated experience above the novice baseline decays according to R(Δt)=exp(−kΔt); the new repetition then adds experience. Conceptually: perform → learn → wait → decay → perform/relearn.
The implemented state recurrence is Eₙ = 1 + (Eₙ₋₁ − 1)R(Δt) + 1, followed by Tₙ = Tstandard Eₙᵇ. With Δt=0, R=1 and Eₙ=n exactly, so the model collapses to the classical no-gap learning curve. That identity is an explicit validation check.
Controls and interpretation
Performance rating and allowance move the time build-up. Demand moves takt and staffing. Learning percentage changes the learning exponent. Days between repetitions changes how much accumulated experience survives between trials. Forgetting sensitivity k controls the assumed decay rate.
The comparison panel reports projected T@100 for no-gap, 1-day, 7-day and 30-day spacing. Equal repetition counts can therefore end at different modeled performance levels because retained experience differs.
What the forgetting coefficient is not
The forgetting sensitivity is a scenario parameter, not a universal human-memory constant. Actual retention depends on task complexity, procedural versus cognitive content, prior mastery, operator experience, cues, tooling and many other conditions. Operational use requires calibration against longitudinal performance data.
The model also does not yet include a separate permanent-memory state or empirically faster relearning after long layoffs. Those are reasonable extensions when data justify the additional parameters.
Validation checks
At zero forgetting sensitivity, spacing must have no effect. At zero gap, the sequential model must equal the classical learning curve. At a 100% learning rate, repetitions should not reduce modeled task time. Increasing gap or decay sensitivity must not improve projected performance while all else is fixed. Rating and allowance should scale the projected time baseline without changing those logical invariants.