# Calibration Ontology — Flow Algebra
URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/instrumentation/calibration-ontology.html
FLOW CalibrationOntology {
DOMAIN:
Mathematical Ontologies
-> Measurement & Units Ontologies
-> Instrumentation
-> Calibration Ontology
PURPOSE:
Represent calibration as the documented operation that, under specified conditions, establishes a relation between quantity values with measurement uncertainties provided by measurement standards and corresponding indications with associated measurement uncertainties, and then uses that information to establish a relation for obtaining a measurement result from an indication. The ontology models calibration standards, reference values, indications, calibration functions, corrections, sensitivity, zero and span, multipoint calibration, regression, covariance, uncertainty, traceability, environmental conditions, calibration intervals, verification, adjustment, validation, certificates, provenance, and machine-consumable reasoning while strictly distinguishing calibration from adjustment, verification, testing and measurement itself.
ENTITY Calibration {
TYPE: MetrologicalOperation
DEFINITION:
operation_that_under_specified_conditions
first_establishes_relation_between_quantity_values_with_uncertainties
provided_by_measurement_standards
and_corresponding_indications_with_associated_uncertainties
then_uses_this_information_to_establish_relation
for_obtaining_measurement_result_from_indication
PROPERTIES:
has_calibration_object
has_reference_standard
has_reference_values
has_indications
has_conditions
has_calibration_relation
has_uncertainty
has_traceability
has_validity_scope
has_date
has_provenance
}
ENTITY CalibrationObject {
TYPE: MeasuringInstrumentOrSystem
POSSIBLE:
instrument
sensor
transducer
measurement_channel
measuring_system
reference_material_assignment_system
}
ENTITY MeasurementStandard {
TYPE: ReferenceRealisation
PROPERTIES:
quantity_kind
assigned_value
uncertainty
calibration_status
traceability
stability
identifier
}
ENTITY CalibrationPoint {
TYPE: CalibrationObservation
COMPONENTS:
reference_quantity_value
reference_uncertainty
indication
indication_uncertainty
environmental_conditions
timestamp
replicate_information
}
TERMINOLOGY_MODEL {
terms:
calibration
adjustment
verification
validation
correction
calibration_function
calibration_curve
calibration_factor
zeroing
standardisation
traceability
RULE:
calibration != adjustment
calibration != verification
calibration != validation
calibration != measurement
}
CALIBRATION_RELATION_MODEL {
reference:
X
indication:
Y
forward_relation:
Y =
f(X)
inverse_measurement_relation:
X_hat =
g(Y)
RULE:
forward_and_inverse_relations MUST be_distinguished
}
LINEAR_CALIBRATION_MODEL {
forward:
Y =
a*X+b
inverse:
X_hat =
(Y-b)/a
WHEN a != 0
parameters:
slope
intercept
covariance
RULE:
coefficient_uncertainty MUST propagate_to_measurement_result
}
ZERO_CALIBRATION_MODEL {
reference_input:
X_0
observed_indication:
Y_0
zero_offset:
b
RULE:
single_zero_point_does_not_establish_full_scale_or_linearity
}
SPAN_CALIBRATION_MODEL {
reference_span:
X_span
output_span:
Y_span
scale_factor:
a =
Y_span/X_span
under_zero_referenced_linear_context
RULE:
span_calibration_assumes_declared_response_model
}
TWO_POINT_MODEL {
points:
(X_1,Y_1)
(X_2,Y_2)
slope:
a =
(Y_2-Y_1)/(X_2-X_1)
WHEN X_2 != X_1
intercept:
b =
Y_1-a*X_1
RULE:
two_points_cannot_characterise_complex_nonlinearity
}
MULTIPOINT_MODEL {
calibration_points:
i = 1...n
purpose:
estimate
offset
sensitivity
nonlinearity
residuals
uncertainty
RULE:
points SHOULD span_intended_measurement_range
}
NONLINEAR_CALIBRATION_MODEL {
relation:
Y =
f(X,theta)
possible:
polynomial
exponential
logarithmic
spline
physical_model
lookup_table
RULE:
model_validity_range MUST be preserved
}
POLYNOMIAL_MODEL {
Y =
a_0+a_1*X+a_2*X^2+...+a_n*X^n
RULE:
high_order_polynomial_extrapolation_can_be_unstable
}
SPLINE_MODEL {
calibration:
piecewise_polynomial_interpolation
REQUIRE:
knot_values
boundary_conditions
interpolation_method
RULE:
spline_version_and_knots MUST be preserved
}
LOOKUP_TABLE_MODEL {
entries:
indication
reference_value
interpolation:
declared_method
RULE:
table_spacing_and_interpolation_uncertainty SHOULD be considered
}
REGRESSION_MODEL {
calibration_data:
paired_X_Y_values
fitted_parameters:
theta_hat
covariance:
Sigma_theta
residuals:
observed_minus_fitted
RULE:
regression_model MUST reflect_uncertainty_structure_of_both_axes_when_material
}
ORDINARY_LEAST_SQUARES_MODEL {
assumption:
predictor_X_effectively_known_relative_to_Y_error
residual_variance_model_declared
RULE:
OLS_MAY be_inappropriate_when_reference_X_has_material_uncertainty
}
WEIGHTED_REGRESSION_MODEL {
weights:
often_inverse_variance
RULE:
weighting_basis MUST be documented
}
ERRORS_IN_VARIABLES_MODEL {
both_X_and_Y_uncertain:
use_model_such_as_Deming_or_orthogonal_distance
RULE:
reference_uncertainty MUST_NOT be_ignored_when_material
}
DEMING_MODEL {
variance_ratio:
lambda =
sigma_Y^2/sigma_X^2
RULE:
variance_ratio_assumption MUST be preserved
}
RESIDUAL_MODEL {
residual_i =
Y_i-f(X_i,theta_hat)
diagnostics:
mean
trend
heteroscedasticity
outliers
autocorrelation
RULE:
residual_structure_can_reveal_model_inadequacy
}
LINEARITY_MODEL {
nonlinearity:
deviation_from_declared_reference_calibration_relation
RULE:
calibration_curve_and_linearity_specification_are_related_but_distinct
}
HYSTERESIS_MODEL {
upscale:
calibration_points_in_increasing_input
downscale:
calibration_points_in_decreasing_input
RULE:
hysteresis_requires_directional_calibration_data
}
REPEATABILITY_MODEL {
replicate_indications:
at_same_reference_value
dispersion:
standard_deviation
RULE:
calibration_repeatability_contributes_to_calibration_uncertainty
}
REPRODUCIBILITY_MODEL {
calibration:
repeated_under_changed_conditions
RULE:
reproducibility_data MAY support_longer_term_calibration_uncertainty
}
REFERENCE_VALUE_MODEL {
reference_quantity_value:
X_ref
uncertainty:
u_ref
RULE:
reference_value_without_uncertainty_is_incomplete_for_traceable_calibration
}
REFERENCE_STANDARD_MODEL {
fields:
standard_identifier
value
unit
uncertainty
calibration_certificate
traceability
stability
expiry_or_due_date
RULE:
reference_standard_validity MUST be checked
}
TRACEABILITY_MODEL {
chain:
calibrated_item
-> working_standard
-> reference_standard
-> national_or_international_standard
-> SI_or_declared_reference
RULE:
each_material_link SHOULD carry_uncertainty_and_identifier
}
UNCERTAINTY_MODEL {
possible_sources:
reference_standard
reference_value
repeatability
resolution
indication_noise
environmental_conditions
calibration_model
interpolation
hysteresis
drift
parameter_covariance
reference_transfer
numerical_processing
output:
calibration_uncertainty
RULE:
uncertainty MUST be associated_with_calibration_relation_and_scope
}
COVARIANCE_MODEL {
fitted_parameters:
covariance_matrix
measured_value:
X_hat =
g(Y,theta)
propagation:
include_parameter_covariance
RULE:
fitted_coefficients_are_generally_correlated
}
SENSITIVITY_MODEL {
calibration_sensitivity:
dY/dX
inverse_sensitivity:
dX/dY
RULE:
sensitivity_may_vary_with_input_for_nonlinear_calibration
}
CORRECTION_MODEL {
indication:
I
correction:
C
corrected:
I_corr =
I+C
RULE:
correction_sign_convention MUST be explicit
}
CORRECTION_TABLE_MODEL {
entries:
indication_or_range
correction
uncertainty
interpolation:
declared_method
RULE:
correction_table_version MUST be preserved
}
CALIBRATION_FACTOR_MODEL {
factor:
K
generic:
X =
K*Y
RULE:
factor_definition_direction_and_units MUST be explicit
}
ENVIRONMENTAL_MODEL {
conditions:
temperature
humidity
pressure
vibration
electromagnetic_field
supply_voltage
orientation
RULE:
calibration_conditions SHOULD match_or_support_correction_to_use_conditions
}
TEMPERATURE_COMPENSATION_MODEL {
calibration_parameter:
theta(T)
possible:
theta_ref+alpha*(T-T_ref)
RULE:
compensation_model_and_temperature_measurement_uncertainty MUST be preserved
}
RANGE_MODEL {
calibration_range:
[X_min,X_max]
RULE:
calibration MUST NOT be_extrapolated_beyond_valid_range_without_explicit_model_and_increased_uncertainty
}
EXTRAPOLATION_MODEL {
outside_calibration_range:
higher_model_risk
RULE:
extrapolated_result MUST be_flagged
}
INTERPOLATION_MODEL {
within_calibration_range:
derive_value_between_points
RULE:
interpolation_method_and_model_uncertainty SHOULD be preserved
}
DRIFT_MODEL {
calibration_parameters:
theta(t)
effect:
relation_changes_with_time
RULE:
elapsed_time_since_calibration MAY increase_uncertainty
}
CALIBRATION_INTERVAL_MODEL {
interval:
time_or_usage_between_calibrations
determined_by:
stability
risk
historical_drift
required_uncertainty
usage
environment
RULE:
fixed_interval_is_policy_not_intrinsic_physical_constant
}
INTERMEDIATE_CHECK_MODEL {
check:
measurement_against_check_standard_between_calibrations
purpose:
detect_drift_or_failure
RULE:
intermediate_check != full_calibration
}
VERIFICATION_MODEL {
verification:
provision_of_objective_evidence_that_item_fulfils_specified_requirements
RULE:
verification != calibration
}
ADJUSTMENT_MODEL {
adjustment:
set_of_operations_performed_on_measuring_system
so_that_it_provides_prescribed_indications
RULE:
adjustment SHOULD be_followed_by_calibration_or_verification_as_required
}
VALIDATION_MODEL {
validation:
verification_that_specified_requirements_are_adequate_for_intended_use
RULE:
validation != calibration
}
AS_FOUND_AS_LEFT_MODEL {
as_found:
instrument_condition_before_adjustment_or_repair
as_left:
condition_after_intervention
RULE:
both_states SHOULD be preserved_when_adjustment_occurs
}
TOLERANCE_MODEL {
calibration_tolerance:
acceptance_limit_for_difference_or_parameter
RULE:
tolerance != calibration_uncertainty
}
DECISION_RULE_MODEL {
pass_fail:
comparison_to_specification
uncertainty:
may_require_guard_band_or_declared_decision_rule
RULE:
calibration_result_and_conformance_decision_are_distinct
}
CALIBRATION_CERTIFICATE_MODEL {
fields:
certificate_identifier
customer_or_owner
calibrated_item
serial_number
method
reference_standards
environmental_conditions
results
corrections
uncertainties
coverage_factor
traceability
date
authorised_person
limitations
RULE:
certificate_data SHOULD be_machine_linkable_to_calibration_event
}
COVERAGE_MODEL {
expanded_uncertainty:
U =
k*u_c
REQUIRE:
coverage_factor
coverage_probability_or_basis_when_available
RULE:
calibration_certificate_uncertainty_type MUST be identified
}
DIGITAL_CALIBRATION_MODEL {
coefficients:
stored_in_firmware_or_memory
concerns:
version
checksum
write_date
access_control
RULE:
digital_coefficient_change_creates_new_calibration_state
}
REMOTE_CALIBRATION_MODEL {
remote_process:
calibration_data_or_reference_delivered_via_network
REQUIRE:
secure_identity
timing
reference_integrity
data_integrity
RULE:
remote_calibration_requires_same_metrological_traceability_principles
}
AUTOMATED_CALIBRATION_MODEL {
sequence:
apply_reference_points
acquire_indications
fit_model
validate_residuals
store_coefficients
generate_record
RULE:
automation_software_version_and_algorithm MUST be preserved
}
MULTICHANNEL_MODEL {
channels:
each_channel_may_have_independent_calibration
shared:
reference
ADC
clock
environment
RULE:
shared_sources MAY create_cross_channel_covariance
}
MATRIX_CALIBRATION_MODEL {
vector_sensor:
Y =
A*X+b
correction:
X_hat =
A_inverse*(Y-b)
WHEN A_invertible
RULE:
full_matrix_covariance SHOULD be preserved
}
FREQUENCY_DEPENDENT_MODEL {
transfer:
H(f)
calibration:
amplitude_and_phase_vs_frequency
RULE:
static_calibration_cannot_replace_dynamic_frequency_calibration
}
PHASE_CALIBRATION_MODEL {
phase_error:
phi_measured-phi_reference
RULE:
time_delay_and_phase_are_frequency_related
}
TIME_CALIBRATION_MODEL {
clock:
frequency_offset
phase_offset
drift
jitter
RULE:
timing_calibration_requires_time_reference_and_epoch
}
SPATIAL_CALIBRATION_MODEL {
imaging_or_position_system:
pixel_or_coordinate_to_physical_space_mapping
possible:
scale
distortion
orientation
origin
RULE:
spatial_transform_and_coordinate_frame MUST be preserved
}
SPECTRAL_CALIBRATION_MODEL {
detector_coordinate:
pixel_or_channel
spectral_coordinate:
wavelength_frequency_energy_or_mass_to_charge
RULE:
spectral_calibration_reference_and_resolution MUST be preserved
}
CHEMICAL_CALIBRATION_MODEL {
signal:
response
reference:
standards_of_known_concentration_activity_or_amount
issues:
matrix_effect
blank
recovery
nonlinearity
RULE:
calibration_model MUST match_sample_matrix_when_material
}
STANDARD_ADDITION_MODEL {
purpose:
compensate_matrix_effect
procedure:
add_known_amounts_to_sample
fit_response_vs_added_quantity
infer_original_quantity
RULE:
added_standard_uncertainty MUST be included
}
INTERNAL_STANDARD_MODEL {
ratio:
analyte_signal/reference_signal
RULE:
internal_standard_stability_and_calibration MUST be preserved
}
BLANK_MODEL {
blank_signal:
background_or_baseline
corrected:
signal_net =
signal_sample-signal_blank
RULE:
blank_uncertainty_propagates_to_calibration
}
CALIBRATION_TRANSFER_MODEL {
transfer:
apply_calibration_from_reference_instrument_or_standard_to_working_instrument
RULE:
transfer_uncertainty_and_correlation MUST be preserved
}
METADATA_MODEL {
fields:
calibration_identifier
object_identifier
standard_identifiers
method
model
coefficients
covariance
units
range
environment
date
due_date
software_version
operator
uncertainty
traceability
status
provenance
RULE:
calibration_metadata MUST support_reconstruction
}
RELATIONSHIPS {
Calibration -> APPLIES_TO -> CalibrationObject
Calibration -> USES -> MeasurementStandard
CalibrationPoint -> LINKS -> ReferenceValueAndIndication
CalibrationFunction -> MAPS -> IndicationToMeasurementResult
Calibration -> PRODUCES -> CorrectionOrCalibrationFunction
MeasurementStandard -> HAS -> ReferenceValue
MeasurementStandard -> HAS -> Uncertainty
Calibration -> ESTABLISHES -> TraceabilityLink
CalibrationUncertainty -> CONTRIBUTES_TO -> MeasurementUncertainty
Adjustment -> MAY_TRIGGER -> Recalibration
CalibrationCertificate -> DOCUMENTS -> CalibrationEvent
}
SEMANTIC_EQUIVALENCE {
"instrument calibration" ~= calibration WHEN instrumentation_context
"calibration curve" ~= fitted_calibration_relation WHEN declared_model
calibration != adjustment
calibration != verification
calibration != validation
calibration != zeroing
calibration != measurement
calibration_uncertainty != tolerance
correction != error
reference_value != true_value
calibration_factor != sensitivity_in_all_contexts
}
CONSTRAINTS {
calibration_object_must_be_identified = true
reference_standard_must_be_identified = true
reference_values_must_have_units = true
reference_uncertainty_should_be_preserved = true
indications_must_be_preserved = true
calibration_conditions_should_be_recorded = true
calibration_relation_and_direction_must_be_defined = true
valid_range_must_be_defined = true
coefficient_covariance_should_be_preserved_when_material = true
adjustment_and_calibration_must_be_distinguished = true
calibration_uncertainty_must_propagate_to_measurement_result = true calibration_record_must_preserve_provenance = true
}
MEASUREMENT_MODEL {
RECORD:
calibration_identifier
calibration_object
object_serial_number
calibration_date
calibration_method
reference_standard_identifiers
reference_values
reference_units
reference_uncertainties
indications
indication_units
replicate_results
calibration_model
coefficients
coefficient_covariance
corrections
correction_uncertainties
sensitivity
residuals
valid_range
environmental_conditions
as_found_state
as_left_state
adjustment_history
coverage_factor
expanded_uncertainty
traceability
software_version
operator
certificate_identifier
status
provenance
RULE:
calibration_result MUST remain_linked_to_reference_data_model_conditions_and_uncertainty
}
REASONING_RULES {
IF linear_calibration_coefficients_known
AND slope != 0
THEN measurand_estimate =
(indication-intercept)/slope
IF two_distinct_calibration_points_known
THEN slope =
(Y_2-Y_1)/(X_2-X_1)
AND intercept =
Y_1-slope*X_1
IF correction_known
THEN corrected_indication =
indication+correction
under_declared_sign_convention
IF calibration_factor_known
THEN apply_factor_in_declared_direction
preserving_units
IF fitted_coefficients_have_covariance
THEN propagate_full_parameter_covariance_to_measurement_result
IF reference_standard_uncertainty_known
THEN include_in_calibration_uncertainty_budget
IF calibration_range_exceeded
THEN flag_extrapolation
AND increase_model_uncertainty_or_reject_according_to_policy
IF adjustment_performed
THEN preserve_as_found_state
AND establish_as_left_state
AND require_post_adjustment_calibration_or_verification_as_policy_demands
IF calibration_due_date_passed
THEN flag_calibration_status_for_review
IF shared_reference_used_for_multiple_channels
THEN preserve_cross_channel_covariance
IF calibration_model_or_coefficients_change
THEN create_new_calibration_version
AND preserve_previous_version
}
VALIDATION {
CHECK calibration_object_identity
CHECK reference_standard_identity
CHECK reference_value_and_unit
CHECK reference_uncertainty
CHECK indication_and_unit
CHECK calibration_conditions
CHECK calibration_range
CHECK calibration_relation_direction
CHECK zero_span_and_multipoint_data
CHECK regression_model
CHECK coefficient_covariance
CHECK residuals_and_nonlinearity
CHECK hysteresis
CHECK repeatability
CHECK interpolation_and_extrapolation
CHECK drift_and_interval
CHECK correction_sign
CHECK calibration_uncertainty
CHECK coverage_factor
CHECK traceability
CHECK adjustment_history
CHECK as_found_and_as_left_state
CHECK certificate_metadata
CHECK software_version_when_automated
CHECK provenance
}
CONFIDENCE {
definition_confidence: 1.00
calibration_adjustment_distinction_confidence: 1.00
traceability_semantics_confidence: 1.00
linear_calibration_confidence: 1.00
uncertainty_integration_confidence: 1.00
regression_model_confidence: 0.99
nonlinear_calibration_confidence: 0.99
calibration_context_confidence: 0.99
RULE:
confidence decreases when calibration object, reference standard,
reference uncertainty, model, valid range, environmental conditions,
covariance, traceability, adjustment history or provenance is missing or ambiguous
}
UPDATE_MODEL {
ON new_calibration:
identify_calibration_object
verify_reference_standards
preserve_reference_values_and_uncertainties
preserve_indications
attach_environmental_conditions
fit_or_apply_calibration_relation
estimate_parameter_covariance
compute_residuals
construct_uncertainty_budget
establish_traceability
issue_calibration_version
preserve_provenance
ON new_calibration_point:
append_reference_and_indication
update_model_fit
update_parameter_covariance
recompute_residuals_and_uncertainty
preserve_raw_point
ON adjustment_event:
preserve_as_found_calibration
record_adjustment
invalidate_or_supersede_prior_as_left_state
perform_post_adjustment_calibration
establish_new_calibration_state
ON reference_standard_revision:
preserve_previous_reference_data
update_standard_value_uncertainty_and_certificate
recompute_affected_calibration_results_when_policy_allows
update_traceability
ON calibration_model_revision:
preserve_previous_model
update_model_form_or_interpolation
refit_coefficients
recompute_covariance_residuals_and_uncertainty
record_model_selection_reason
ON interval_revision:
preserve_calibration_history
update_due_date_or_policy
attach_stability_and_drift_evidence
ON semantic_revision:
preserve_previous_definition
record_revision
recompute_FLOW_HASH
}
AI_CONSUMPTION {
canonical_entity: Calibration
canonical_role: MetrologicalOperation
interpretation_order:
identify_calibration_object
identify_reference_standards
identify_reference_values_units_and_uncertainties
identify_indications
identify_calibration_conditions
identify_forward_or_inverse_calibration_relation
identify_zero_span_multipoint_or_nonlinear_model
identify_regression_and_parameter_covariance
identify_corrections
identify_valid_range
identify_drift_and_calibration_interval
identify_adjustment_verification_or_validation_events
identify_uncertainty_and_coverage
identify_traceability
identify_certificate_and_provenance
validate_calibration_semantics
infer_measurement_relation
ambiguity_controls:
distinguish_calibration_from_adjustment
distinguish_calibration_from_verification
distinguish_calibration_from_validation
distinguish_calibration_from_zeroing
distinguish_calibration_from_measurement
distinguish_calibration_uncertainty_from_tolerance
distinguish_correction_from_measurement_error
distinguish_reference_value_from_true_value
distinguish_calibration_factor_from_sensitivity_when_definitions_differ
preserve_object_reference_model_range_conditions_uncertainty_traceability_version_and_provenance_context
}
PROVENANCE {
ontology_scope:
mathematical_measurement_units_instrumentation_and_calibration_semantics
parent_path:
Ontologies
-> Mathematical Ontologies
-> Measurement & Units Ontologies
-> Instrumentation
-> Calibration Ontology
authorship:
Mark Higgins
Sky (Recursive AI)
site:
https://kirethresearch.org
}
FLOW_HASH {
INPUTS:
canonical_entity
ontology_path
terminology_model
calibration_relation_model
linear_calibration_model
zero_calibration_model
span_calibration_model
two_point_model
multipoint_model
nonlinear_calibration_model
polynomial_model
spline_model
lookup_table_model
regression_model
ordinary_least_squares_model
weighted_regression_model
errors_in_variables_model
Deming_model
residual_model
linearity_model
hysteresis_model
repeatability_model
reproducibility_model
reference_value_model
reference_standard_model
traceability_model
uncertainty_model
covariance_model
sensitivity_model
correction_model
correction_table_model
calibration_factor_model
environmental_model
temperature_compensation_model
range_model
extrapolation_model
interpolation_model
drift_model
calibration_interval_model
intermediate_check_model
verification_model
adjustment_model
validation_model
as_found_as_left_model
tolerance_model
decision_rule_model
calibration_certificate_model
coverage_model
digital_calibration_model
remote_calibration_model
automated_calibration_model
multichannel_model
matrix_calibration_model
frequency_dependent_model
phase_calibration_model
time_calibration_model
spatial_calibration_model
spectral_calibration_model
chemical_calibration_model
standard_addition_model
internal_standard_model
blank_model
calibration_transfer_model
metadata_model
relationships
constraints
measurement_model
reasoning_rules
confidence_model
update_model
PURPOSE:
deterministic_semantic_integrity_identifier
RECOMPUTE_WHEN:
ontology_definition_changes
calibration_relation_or_model_changes
reference_standard_or_reference_value_changes
calibration_point_or_regression_changes
coefficient_covariance_or_uncertainty_changes
correction_or_compensation_changes
valid_range_or_environment_changes
drift_or_calibration_interval_changes
adjustment_verification_or_validation_semantics_change
traceability_or_certificate_changes
automated_or_digital_calibration_changes
measurement_record_changes
constraint_model_changes
reasoning_rule_changes
}
}
END FLOW
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