Repeatability Ontology
Measurement Uncertainty
Authors: MArk Anthony Higgins - Sky Recursive Ai
Revised Date: 16 September 2026
Audio Overview
# Repeatability Ontology — Flow Algebra
URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/measurement-uncertainty/repeatability-ontology.html
FLOW RepeatabilityOntology {
DOMAIN:
Mathematical Ontologies
-> Measurement & Units Ontologies
-> Measurement Uncertainty
-> Repeatability Ontology
PURPOSE:
Represent measurement repeatability as measurement precision under a defined set of repeatability conditions, including replicate measurements, repeatability conditions, repeatability standard deviation and variance, repeatability limits, within-run variation, short-term instrument and method behaviour, sample size, degrees of freedom, heteroscedasticity, time dependence, random effects, quality control, uncertainty contributions, provenance, and strict distinctions between repeatability, reproducibility, intermediate precision, measurement uncertainty, accuracy, trueness and repeated observations themselves.
ENTITY Repeatability {
TYPE: MeasurementPrecisionCharacteristic
DEFINITION:
repeatability :=
measurement_precision
under_a_set_of_repeatability_conditions
PROPERTIES:
requires_replicate_measurements
requires_defined_conditions
describes_short_term_or_declared_within_condition_dispersion
may_be_expressed_by_standard_deviation
may_depend_on_quantity_level
may_contribute_to_measurement_uncertainty
is_not_accuracy
is_not_reproducibility
}
ENTITY RepeatabilityCondition {
TYPE: PrecisionConditionSet
TYPICAL_COMPONENTS:
same_measurement_procedure
same_operator_or_operating_system
same_measuring_system
same_location
same_or_similar_object
repetition_over_short_period
stable_environment_or_declared_environment
same_calibration_state
RULE:
actual_repeatability_conditions MUST be explicitly_preserved
}
ENTITY ReplicateMeasurement {
TYPE: RepeatedMeasurementObservation
REQUIRE:
measurand
value
unit
timestamp
replicate_identifier
repeatability_condition_identifier
}
ENTITY RepeatabilityStandardDeviation {
TYPE: PrecisionDispersionQuantity
SYMBOL: s_r
UNIT:
same_as_measurand
}
ENTITY RepeatabilityVariance {
TYPE: SquaredDispersionQuantity
SYMBOL: s_r^2
}
TERMINOLOGY_MODEL {
terms:
repeatability
repeatability_precision
repeatability_condition
replicate
repeated_measurement
within_run_precision
repeatability_standard_deviation
repeatability_limit
RULE:
repeated_measurement != repeatability
and_repeatability_is_property_inferred_from_replicate_results
}
CONDITION_MODEL {
dimensions:
procedure
operator
instrument
laboratory
location
environment
time_window
calibration_state
sample_preparation
object_identity
RULE:
if_material_condition_changes
then_result_may_no_longer_represent_repeatability
}
REPLICATE_MODEL {
replicate_set:
x_1,...,x_n
REQUIRE:
n >= 2
common_repeatability_condition
RULE:
technical_replicates_and_independent_samples MUST be distinguished
}
MEAN_MODEL {
sample_mean:
x_bar =
sum(x_i)/n
RULE:
mean_is_location_estimate_not_repeatability_metric
}
VARIANCE_MODEL {
sample_repeatability_variance:
s_r^2 =
sum((x_i-x_bar)^2)/(n-1)
under_simple_single_group_model
WHEN n > 1
RULE:
more_complex_designs_may_require_pooled_or_variance_component_estimation
}
STANDARD_DEVIATION_MODEL {
s_r =
sqrt(s_r^2)
interpretation:
dispersion_of_results_under_repeatability_conditions
RULE:
smaller_s_r_generally_indicates_better_repeatability
for_same_measurand_scale_and_level
}
RELATIVE_REPEATABILITY_MODEL {
RSD_r =
s_r/abs(x_bar)
WHEN x_bar != 0
percent_RSD_r =
100*RSD_r
RULE:
relative_repeatability_is_dimensionless
}
COEFFICIENT_OF_VARIATION_MODEL {
CV_r =
s_r/abs(x_bar)
WHEN x_bar != 0
RULE:
CV_is_unstable_near_zero_mean
}
REPEATABILITY_LIMIT_MODEL {
definition:
value_below_which_absolute_difference_between_two_single_results
obtained_under_repeatability_conditions
is_expected_to_lie_with_declared_probability
common_normal_95_percent_approximation:
r approximately_equals
2.8*s_r
derivation_context:
standard_deviation_of_difference =
sqrt(2)*s_r
approximate_95_percent_factor:
1.96*sqrt(2) approximately_equals 2.77
RULE:
2.8_factor_requires_normality_independence_and_declared_coverage_context
}
PAIRWISE_DIFFERENCE_MODEL {
two_results:
x_1
x_2
difference:
d =
x_1-x_2
independent_equal_repeatability_variance:
Var(d) =
2*s_r^2
RULE:
correlation_between_replicates_changes_difference_variance
}
WITHIN_RUN_MODEL {
run:
group_of_measurements_under_tightly_controlled_conditions
within_run_variance:
estimates_short_term_repeatability_component
RULE:
run_definition MUST be preserved
}
POOLED_REPEATABILITY_MODEL {
groups:
i = 1...g
pooled_variance:
s_p^2 =
sum((n_i-1)*s_i^2)/
sum(n_i-1)
CONDITIONS:
group_variances_estimate_common_repeatability_variance
RULE:
pooling_requires_compatibility_across_groups
}
DEGREES_OF_FREEDOM_MODEL {
single_group:
nu =
n-1
pooled:
nu =
sum(n_i-1)
ANOVA:
depends_on_design
RULE:
degrees_of_freedom_quantify_information_for_variance_estimate
}
VARIANCE_UNCERTAINTY_MODEL {
normal_model:
confidence_interval_for_population_variance
may_use_chi_square_distribution
RULE:
estimated_repeatability_standard_deviation_has_sampling_uncertainty
}
SAMPLE_SIZE_MODEL {
n:
replicate_count
effect:
small_n_produces_imprecise_variance_estimate
RULE:
repeatability_estimate SHOULD report_sample_size
}
HETEROSCEDASTIC_MODEL {
repeatability:
s_r =
f(quantity_level)
possible:
constant_absolute_SD
constant_CV
mixed_variance_model
RULE:
repeatability_at_one_level MUST_NOT automatically_be_applied_to_all_levels
}
PRECISION_PROFILE_MODEL {
model:
s_r(x)
or
CV_r(x)
REQUIRE:
validated_measurement_range
fitted_parameters
uncertainty
RULE:
precision_profile_version MUST be preserved
}
LOG_SCALE_MODEL {
multiplicative_variability:
may_be_more_constant_in_log_space
transformed:
y =
ln(x)
RULE:
repeatability_on_log_scale MUST be_transformed_carefully_for_original_scale_reporting
}
NORMALITY_MODEL {
common_assumption:
replicate_errors_approximately_normal
diagnostics:
histogram
Q_Q_plot
residual_analysis
robust_comparison
RULE:
normality_should_not_be_assumed_without_context
}
OUTLIER_MODEL {
outlier:
unusual_replicate
possible_causes:
gross_error
instrument_fault
contamination
transcription_error
legitimate_extreme_random_value
RULE:
exclusion_requires_documented_criterion
and_original_value_must_remain_in_provenance
}
ROBUST_REPEATABILITY_MODEL {
possible_estimators:
MAD
robust_scale
Qn
robust_ANOVA
RULE:
robust_repeatability_metric MUST identify_estimator_and_scaling
}
AUTOCORRELATION_MODEL {
sequential_replicates:
may_not_be_independent
autocorrelation:
rho(k)
effect:
can_bias_or_change_interpretation_of_standard_deviation_and_mean_precision
RULE:
sequential_measurements SHOULD be_checked_for_dependence
}
DRIFT_MODEL {
short_term_drift:
can_inflate_repeatability_dispersion
deterministic_drift:
may_be_modelled_and_corrected
stochastic_drift:
may_require_time_series_model
RULE:
repeatability_study_duration_should_be_short_relative_to_unmodelled_drift_when_repeatability_is_intended
}
WARMUP_MODEL {
instrument:
may_change_response_during_warmup
RULE:
warmup_state SHOULD be_standardised_or_recorded
}
ENVIRONMENTAL_MODEL {
variables:
temperature
humidity
pressure
vibration
electromagnetic_interference
RULE:
repeatability_conditions_require_environment_to_be_stable_or_declared
}
OPERATOR_MODEL {
same_operator:
typical_repeatability_condition
automation:
software_or_robotic_operator_may_define_operating_system
RULE:
operator_identity_or_operating_configuration SHOULD be preserved
}
INSTRUMENT_MODEL {
same_measuring_system:
typical_repeatability_condition
RULE:
changing_instrument_may_shift_context_to_intermediate_precision_or_reproducibility
}
CALIBRATION_STATE_MODEL {
calibration:
should_remain_same_or_stable_during_repeatability_study
RULE:
recalibration_mid_study_may_create_multiple_precision_conditions
}
SAMPLE_PREPARATION_MODEL {
repeated_measurement_same_preparation:
technical_repeatability
repeated_independent_preparations:
may_include_preparation_variability
RULE:
preparation_level MUST be declared
}
DESTRUCTIVE_TEST_MODEL {
same_object:
may_not_be_remeasurable
solution:
use_similar_objects_or_specimens_under_defined_repeatability_design
RULE:
object_equivalence_assumption MUST be preserved
}
NATURAL_VARIABILITY_MODEL {
biological_environmental_or_material_objects:
may_vary_between_replicates
RULE:
true_object_variability MUST_NOT automatically_be_attributed_to_measurement_repeatability
}
RESOLUTION_MODEL {
coarse_resolution:
may_quantise_replicate_values
effect:
can_mask_or_inflate_observed_dispersion
RULE:
resolution SHOULD be considered_in_repeatability_interpretation
}
UNCERTAINTY_MODEL {
repeatability_standard_deviation:
may_contribute_to_standard_uncertainty
mean_of_n_independent_replicates:
u_repeat_mean =
s_r/sqrt(n)
single_result:
repeatability_component_may_use
s_r
under_declared_measurement_model
RULE:
repeatability != measurement_uncertainty
}
TYPE_A_MODEL {
repeated_measurements:
often_support_Type_A_evaluation
standard_uncertainty_of_mean:
u_A =
s_r/sqrt(n)
under_independent_stable_conditions
RULE:
Type_A_uncertainty != repeatability
}
PRECISION_MODEL {
hierarchy:
precision
-> repeatability
-> intermediate_precision
-> reproducibility
RULE:
hierarchy_represents_conditions_not_simple_numeric_ordering
}
INTERMEDIATE_PRECISION_DISTINCTION_MODEL {
intermediate_precision:
same_laboratory_but_one_or_more_conditions_changed
repeatability:
tighter_same_condition_set
RULE:
intermediate_precision != repeatability
}
REPRODUCIBILITY_DISTINCTION_MODEL {
reproducibility:
precision_under_reproducibility_conditions
often_between_laboratories_or_locations
RULE:
reproducibility != repeatability
}
ACCURACY_DISTINCTION_MODEL {
accuracy:
closeness_to_reference_or_true_value
repeatability:
agreement_among_replicates
RULE:
excellent_repeatability_can_coexist_with_systematic_bias
}
TRUENESS_DISTINCTION_MODEL {
trueness:
closeness_of_average_to_reference
repeatability:
within_condition_dispersion
RULE:
repeatability_does_not_establish_trueness
}
BIAS_DISTINCTION_MODEL {
bias:
systematic_difference
repeatability:
random_dispersion_under_conditions
RULE:
bias != repeatability
}
CONTROL_CHART_MODEL {
repeated_control_results:
monitor_short_term_precision
possible:
range_chart
standard_deviation_chart
RULE:
control_limits_are_not_repeatability_limits_unless_defined_as_such
}
VALIDATION_MODEL {
method_validation:
repeatability_study
design:
levels
replicates
runs
operators
days
RULE:
study_design MUST support_claimed_repeatability_scope
}
REPORTING_MODEL {
REQUIRED:
measurand
repeatability_metric
unit_or_relative_form
repeatability_conditions
sample_size
measurement_level_or_range
RECOMMENDED:
degrees_of_freedom
study_design
normality_assumption
outlier_handling
confidence_interval
instrument
environment
calibration_state
provenance
RULE:
repeatability_value_without_conditions_is_incomplete
}
RELATIONSHIPS {
Repeatability -> IS_A -> MeasurementPrecision
Repeatability -> REQUIRES -> RepeatabilityConditions
ReplicateMeasurement -> SUPPORTS -> RepeatabilityEstimate
RepeatabilityStandardDeviation -> QUANTIFIES -> RepeatabilityDispersion
RepeatabilityVariance -> SQUARE_OF -> RepeatabilityStandardDeviation
RepeatabilityLimit -> DERIVED_FROM -> RepeatabilityStandardDeviation
Repeatability -> MAY_CONTRIBUTE_TO -> MeasurementUncertainty
TypeAEvaluation -> MAY_USE -> RepeatabilityData
InstrumentResolution -> MAY_AFFECT -> ObservedRepeatability
Drift -> MAY_AFFECT -> RepeatabilityStudy
}
SEMANTIC_EQUIVALENCE {
"repeatability precision" ~= repeatability
"repeatability standard deviation" ~= s_r WHEN declared_context
repeatability != repeated_measurement
repeatability != reproducibility
repeatability != intermediate_precision
repeatability != accuracy
repeatability != trueness
repeatability != bias
repeatability != measurement_uncertainty
repeatability != Type_A_uncertainty
repeatability_standard_deviation != standard_error_of_mean
}
CONSTRAINTS {
repeatability_is_precision_characteristic = true
repeatability_requires_defined_conditions = true
repeatability_requires_replication = true
sample_size_must_be_at_least_two_for_simple_variance_estimate = true
repeatability_and_reproducibility_are_not_semantically_equivalent = true
repeatability_and_accuracy_are_not_semantically_equivalent = true
repeatability_and_uncertainty_are_not_semantically_equivalent = true
repeatability_and_Type_A_uncertainty_are_not_semantically_equivalent = true
measurement_level_or_range_should_be_preserved = true
outlier_handling_must_preserve_provenance = true
}
MEASUREMENT_MODEL {
RECORD:
measurand
replicate_values
unit
replicate_identifiers
timestamps
repeatability_condition_identifier
measurement_procedure
operator
instrument
laboratory
location
environment
calibration_state
sample_preparation
measurement_level
measurement_range
sample_size
mean
repeatability_variance
repeatability_standard_deviation
relative_repeatability
repeatability_limit
degrees_of_freedom
confidence_interval
outlier_rule
dependence_model
quality_control_state
provenance
RULE:
repeatability_statistics MUST remain_linked_to_replicate_data_and_conditions
}
REASONING_RULES {
IF replicate_values_known
AND n > 1
THEN mean =
sum(x_i)/n
AND repeatability_variance =
sum((x_i-mean)^2)/(n-1)
AND repeatability_standard_deviation =
sqrt(repeatability_variance)
IF mean != 0
AND repeatability_standard_deviation_known
THEN relative_repeatability =
repeatability_standard_deviation/abs(mean)
IF repeatability_standard_deviation_known
AND normal_independent_pairwise_95_percent_context
THEN repeatability_limit approximately_equals
2.8*repeatability_standard_deviation
IF multiple_compatible_groups_known
THEN pooled_repeatability_variance =
weighted_by_degrees_of_freedom(group_variances)
IF n_independent_replicates_averaged
THEN repeatability_standard_uncertainty_of_mean =
repeatability_standard_deviation/sqrt(n)
IF measurement_level_changes_and_dispersion_changes
THEN fit_or_apply_precision_profile
IF sequential_replicates_are_autocorrelated
THEN do_not_apply_independent_sample_formulas_without_adjustment
IF systematic_bias_present
THEN repeatability_may_still_be_high
and_accuracy_must_be_assessed_separately
}
VALIDATION {
CHECK measurand
CHECK replicate_count
CHECK replicate_type
CHECK repeatability_conditions
CHECK measurement_procedure
CHECK operator_and_instrument
CHECK environment
CHECK calibration_state
CHECK measurement_level_or_range
CHECK variance_and_standard_deviation
CHECK relative_repeatability_mean_nonzero
CHECK repeatability_limit_assumptions
CHECK degrees_of_freedom
CHECK heteroscedasticity
CHECK autocorrelation
CHECK drift
CHECK resolution
CHECK outlier_handling
CHECK natural_variability
CHECK repeatability_vs_reproducibility
CHECK repeatability_vs_uncertainty
CHECK repeatability_vs_accuracy
CHECK provenance
}
CONFIDENCE {
definition_confidence: 1.00
condition_semantics_confidence: 1.00
variance_relationship_confidence: 1.00
repeatability_limit_confidence: 0.99
uncertainty_distinction_confidence: 1.00
reproducibility_distinction_confidence: 1.00
accuracy_distinction_confidence: 1.00
measurement_context_confidence: 0.99
RULE:
confidence decreases when replicate type, repeatability conditions,
sample size, measurement level, instrument state, environment,
autocorrelation, drift, outlier treatment or provenance is missing or ambiguous
}
UPDATE_MODEL {
ON new_replicate:
identify_measurand
verify_repeatability_condition
append_raw_value_and_timestamp
update_sample_size
recompute_mean_variance_and_standard_deviation
update_relative_repeatability_when_valid
preserve_provenance
ON new_repeatability_study:
preserve_raw_design_and_replicates
identify_measurement_levels_and_groups
estimate_group_and_pooled_repeatability
assess_heteroscedasticity
attach_degrees_of_freedom_and_intervals
ON condition_change:
preserve_previous_repeatability_result
identify_changed_condition
reclassify_as_intermediate_precision_or_other_context_when_required
start_new_condition_set
ON drift_or_dependence_revision:
preserve_raw_time_series
update_drift_and_autocorrelation_models
recompute_valid_repeatability_statistics
update_confidence
ON outlier_revision:
preserve_original_data
apply_documented_rule
recompute_statistics
retain_exclusion_reason_and_provenance
ON semantic_revision:
preserve_previous_definition
record_revision
recompute_FLOW_HASH
}
AI_CONSUMPTION {
canonical_entity: Repeatability
canonical_role: MeasurementPrecisionCharacteristic
interpretation_order:
identify_measurand
identify_replicate_set
identify_repeatability_conditions
identify_replicate_type
identify_measurement_level_and_range
identify_sample_size
identify_variance_standard_deviation_or_relative_metric
identify_repeatability_limit_and_assumptions
identify_degrees_of_freedom
identify_heteroscedasticity
identify_autocorrelation_and_drift
identify_resolution_and_environment
identify_outlier_handling
identify_uncertainty_use_when_present
identify_provenance
validate_repeatability_semantics
infer_repeatability_statistics
ambiguity_controls:
distinguish_repeatability_from_repeated_measurement
distinguish_repeatability_from_reproducibility
distinguish_repeatability_from_intermediate_precision
distinguish_repeatability_from_accuracy
distinguish_repeatability_from_trueness
distinguish_repeatability_from_bias
distinguish_repeatability_from_measurement_uncertainty
distinguish_repeatability_from_Type_A_uncertainty
distinguish_repeatability_standard_deviation_from_standard_error
preserve_measurand_conditions_replicate_type_level_design_statistics_and_provenance_context
}
PROVENANCE {
ontology_scope:
mathematical_measurement_uncertainty_and_repeatability_semantics
parent_path:
Ontologies
-> Mathematical Ontologies
-> Measurement & Units Ontologies
-> Measurement Uncertainty
-> Repeatability Ontology
authorship:
Mark Higgins
Sky (Recursive AI)
site:
https://kirethresearch.org
}
FLOW_HASH {
INPUTS:
canonical_entity
ontology_path
terminology_model
condition_model
replicate_model
mean_model
variance_model
standard_deviation_model
relative_repeatability_model
coefficient_of_variation_model
repeatability_limit_model
pairwise_difference_model
within_run_model
pooled_repeatability_model
degrees_of_freedom_model
variance_uncertainty_model
sample_size_model
heteroscedastic_model
precision_profile_model
log_scale_model
normality_model
outlier_model
robust_repeatability_model
autocorrelation_model
drift_model
warmup_model
environmental_model
operator_model
instrument_model
calibration_state_model
sample_preparation_model
destructive_test_model
natural_variability_model
resolution_model
uncertainty_model
Type_A_model
precision_model
intermediate_precision_distinction_model
reproducibility_distinction_model
accuracy_distinction_model
trueness_distinction_model
bias_distinction_model
control_chart_model
validation_model
reporting_model
relationships
constraints
measurement_model
reasoning_rules
confidence_model
update_model
PURPOSE:
deterministic_semantic_integrity_identifier
RECOMPUTE_WHEN:
ontology_definition_changes
repeatability_condition_changes
replicate_definition_or_study_design_changes
variance_or_precision_profile_changes
repeatability_limit_model_changes
heteroscedasticity_or_dependence_model_changes
drift_environment_or_resolution_model_changes
uncertainty_or_Type_A_semantic_changes
reproducibility_or_accuracy_distinction_changes
measurement_record_changes
reporting_model_changes
constraint_model_changes
reasoning_rule_changes
}
}
END FLOW