Introduction: The hidden problem of productivity
Convert time proportions into equivalent hours using an explicit time base without treating them as realised savings.
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An observed share can be converted into equivalent hours if it represents the same population and period as the time base. Calling them “lost” does not establish avoidability, uselessness or recoverable production.
From readings to hours
Define person-time or machine-time and do not mix them. With a compatible known base H:category hours=p̂×H.
Across strata: category hours=Σp̂ₕHₕ. Do not multiply an unweighted global share by incompatible exposures.
If the proportion interval is [L,U] and H is known and compatible, transform it to [LH,UH]. Uncertainty in H or dependence needs consideration too. These are not standard times: standardisation also requires method, output, temporal reference, rating and allowances where applicable.
Sample and calculated example
Under independent simple sampling, n₀=ceiling(z²p₀(1−p₀)/e²). For p₀=0.25, z=1.96 and e=0.04, n₀=451 because the unrounded result is 450.1875. Do not round down to meet a target.
In a teaching example with 112 of 450 readings, p̂=24.8889%. On 400 represented person-hours this gives 99.56 equivalent hours. Using 450 does not invalidate everything, but report intended and achieved precision without promising an exact margin. The interval needs a suitable method and actual design.
Absences and exposure
Choose planned capacity, actual attendance or scheduled equipment time as the base. Vacation already excluded must not be deducted again through an arbitrary correction factor. Do not sample attendance and then apply an absence category to another denominator.
Covering an absence does not guarantee zero plant-wide capacity loss; work may be displaced elsewhere. Sickness is not automatically unproductive conduct. Separate uncovered capacity, incremental cost and flow effects without blaming the person.
Event records
For a confirmed stop:affected person-hours=minutes×people actually blocked/60.
Split events when affected headcount changes. Exclude useful alternative work and overlaps. One person in two simultaneous incidents does not generate two hours per clock hour.
Simulated example: 240 planned person-hours less eight vacation hours gives a 232-hour base. Assume ten uncovered absence hours, 130 stop minutes affecting four people (8.67 h) and non-overlapping incidents totalling 440 person-minutes (7.33 h).
| Item | Assumed person-hours |
|---|---|
| Uncovered absence | 10.00 |
| Stops | 8.67 |
| Incidents | 7.33 |
| Non-overlapping total | 26.00 |
26/232=11.21%; against 240 it is 10.83%. These are different denominators and must be stated. The example does not establish all 26 hours as removable or convertible to output.
Reconciliation and cost
Do not add sampling estimates to event losses already represented in them. Compare compatible scopes and investigate differences: error, coverage or definitions can explain gaps, not only incomplete incident reports.
Hours times a rate gives a cost equivalent, not automatic cash saving. Assess incremental benefits and implementation costs without double-counting payroll, lost margin and penalties.
Responsible use
Sampling alone does not certify ISO 9001, grant eligibility or labour compliance, or replace individual daily working-time records. OEE needs ideal cycle and counts, not activity hours alone. Worksamp supports planning and capture; this article does not establish an automated equivalent-hours module or undocumented integrations. Check exports, pending records and report calculations.
Sources: NIST, NIST intervals. Worksamp.