Study Validity with Missing Observations

A reading is missing when the selected resource cannot be classified at the intended moment. A stopped machine that can be observed is not missing data: it is a valid state when within study scope. An absent person may be an observable state or an incident depending on the agreed definition; do not automatically label absence as a break, productivity or misconduct.

Distinguish coverage from response

Keep an attempt log with target, scheduled time, actual time, valid reading and documented reason for a loss. Distinguish notification failure, blocked access, an out-of-scope resource and an undetermined state. A missing reading does not establish a worker's intention.

An inaccessible work area may cause undercoverage: part of the population has no real chance of inclusion. More readings in accessible areas do not repair that problem.

Effects on estimation

For a category, p̂=x/n uses valid readings contributing to that estimate, not all scheduled alerts. Under approximate independent binomial sampling, SE≈√(p̂(1−p̂)/n). Clustered rounds or weights may require a different standard error.

Fewer responses usually reduce precision. Bias is also possible when response depends on the state. Its direction depends on which states are missed: omitting breakdowns may inflate the running share, while missing mobile productive work may reduce it. There is no universal direction.

Missing-data assumptions matter:

• MCAR: loss does not depend on observed or missing values.
• MAR: observed variables correctly included in analysis can explain the loss mechanism.
• MNAR: loss still depends on the missing state after considering observed information.

These are assumptions about a mechanism, not labels established by a simple test.

An example of the information limit

In a simulated teaching example, 1000 readings are planned, 900 completed and 360 indicate direct work. Among responses, p̂=360/900=40%. The remaining 100 states are unknown.

If every missing reading were non-direct, the share over all 1000 attempts would be 36%; if all were direct it would be 46%. The 36–46% range is a worst-case analysis of the attempted set, not a population confidence interval. It shows why a small sampling margin among respondents does not resolve missing-state uncertainty. Unequally weighted attempts also require weighted bounds.

Plan and prevent

To obtain an expected n valid readings with anticipated missing rate r, plan ceil(n/(1−r)) attempts. For n=1000 and r=0.10, this is 1112. That is an expectation, not a guarantee or bias correction.

Arrange safe access and shift/area coverage before collection. Stratification uses known characteristics such as shift or area; it cannot assign a missing reading to its unknown actual activity. Allocate readings and weights according to the population being represented.

Do not replace each failed alert with the next convenient moment: that may select different states. Define replacement scheduling and retain the original incident.

Imputation does not recover an observed state

Replacing a missing binary state with the shift mean creates a fractional value and can artificially reduce variability. Do not count a prediction as an independent observed reading.

Response-probability weighting, multiple imputation or explicit models can help when assumptions are defensible. They require relevant auxiliary variables, adequate support and uncertainty propagation. MNAR requires further assumptions and sensitivity analysis. Attendance records provide context, not the task at the missing instant.

Comparing complete-case and imputed results is informative; a difference below 5% does not automatically validate a model. Explore plausible alternative assumptions and explain their effect on decisions.

Reactivity, safety and privacy

Explaining the purpose and training observers may help. No universal number of initial readings must be discarded, and familiarization does not guarantee normalized behavior. Define pilot exclusions before interpreting findings.

Covert observation or security cameras are not automatic substitutes. Where personal data are processed, assess legal basis, purpose, information, proportionality and retention. Aggregating a report does not guarantee anonymity of the original records.

Reporting and tools

Report attempts, valid readings, losses by stratum, exclusion rules, weights, assumptions and sensitivity. A study can usefully describe the observed population if conclusions are limited accordingly. Documenting an imputation does not make it statistically valid or an ISO 9001 requirement.

WorkSamp supports planning and recording visits; do not assume built-in multiple imputation or automatic missingness diagnostics. Check locally pending records before declaring an observation absent. Induly provides working-time context and Cronometras supports specific duration studies. Complete OEE also needs production counts, ideal cycle and good units, not sampled states alone.

Sources and foundations

• National Research Council: preventing and treating missing data. Its principles of assumptions, uncertainty and sensitivity are general; industrial application needs a design-specific adaptation.
• NIST: planning proportion samples.
• GDPR: official text.