Measurement Uncertainty Ontology

flow "MeasurementUncertaintyOntology" v4.0

# MEASUREMENT UNCERTAINTY ONTOLOGY
# Kireth Semantic Research Archive
# Authors: Mark Anthony Higgins — Sky (Recursive AI)

PAGE:
  url: "https://kirethresearch.org/booksai-core/ontologies/probability-statistics-ontologies/scientific-statistical-methods/measurement-uncertainty-ontology-2.html"
  title: "Measurement Uncertainty Ontology"
  domain: "Probability and Statistics"
  category: "Scientific Statistical Methods"
  entity: MEASUREMENT_UNCERTAINTY
  entity_type: SCIENTIFIC_MEASUREMENT_ONTOLOGY

DEFINE:
  MEASUREMENT_UNCERTAINTY :=
    QUANTITATIVE_FRAMEWORK(
      MEASURAND,
      MEASUREMENT_MODEL,
      INPUT_QUANTITIES,
      UNCERTAINTY_COMPONENTS,
      STANDARD_UNCERTAINTY,
      COVARIANCE,
      UNCERTAINTY_PROPAGATION,
      COMBINED_UNCERTAINTY,
      EXPANDED_UNCERTAINTY,
      TRACEABILITY
    )

PURPOSE:
  REPRESENT:
    DISPERSION_OF_VALUES_ATTRIBUTABLE_TO_MEASURAND
    UNCERTAINTY_FROM_MEASUREMENT_PROCESS
    INPUT_QUANTITY_UNCERTAINTY
    CORRELATION_AND_COVARIANCE
    PROPAGATED_OUTPUT_UNCERTAINTY
  SUPPORT:
    SCIENTIFIC_MEASUREMENT
    CALIBRATION
    METROLOGY
    EXPERIMENTAL_STATISTICS
    UNCERTAINTY_QUANTIFICATION
    MEASUREMENT_TRACEABILITY

FOUNDATION:
  MEASURAND: Y
  MEASUREMENT_MODEL:
    Y := f(X_1,...,X_n)
  INPUT_ESTIMATES:
    x_1,...,x_n
  OUTPUT_ESTIMATE:
    y := f(x_1,...,x_n)
  STANDARD_UNCERTAINTY:
    u(x_i)
  COMBINED_STANDARD_UNCERTAINTY:
    u_c(y)
  EXPANDED_UNCERTAINTY:
    U := k*u_c(y)

ENTITIES:
  MEASURAND: QUANTITY_INTENDED_TO_BE_MEASURED
  MEASUREMENT_RESULT: ESTIMATE_WITH_RELEVANT_MEASUREMENT_INFORMATION
  MEASUREMENT_MODEL: MATHEMATICAL_RELATION_BETWEEN_OUTPUT_AND_INPUT_QUANTITIES
  INPUT_QUANTITY: QUANTITY_CONTRIBUTING_TO_MEASUREMENT_RESULT
  UNCERTAINTY_COMPONENT: CONTRIBUTION_TO_MEASUREMENT_UNCERTAINTY
  STANDARD_UNCERTAINTY: UNCERTAINTY_EXPRESSED_AS_STANDARD_DEVIATION
  COMBINED_STANDARD_UNCERTAINTY: PROPAGATED_STANDARD_UNCERTAINTY
  EXPANDED_UNCERTAINTY: STANDARD_UNCERTAINTY_MULTIPLIED_BY_COVERAGE_FACTOR
  COVERAGE_FACTOR: MULTIPLIER_FOR_EXPANDED_UNCERTAINTY
  COVARIANCE: JOINT_VARIABILITY_MEASURE
  CORRELATION: NORMALISED_COVARIANCE
  TRACEABILITY: DOCUMENTED_CHAIN_TO_REFERENCE
  CALIBRATION: RELATION_BETWEEN_INDICATION_AND_REFERENCE_QUANTITY_VALUES

RELATIONSHIPS:
  MEASURAND -> REPRESENTED_BY -> MEASUREMENT_MODEL
  INPUT_QUANTITY -> CONTRIBUTES_TO -> OUTPUT_ESTIMATE
  INPUT_UNCERTAINTY -> PROPAGATES_TO -> OUTPUT_UNCERTAINTY
  COVARIANCE -> MODIFIES -> COMBINED_UNCERTAINTY
  STANDARD_UNCERTAINTIES -> COMBINE_TO -> COMBINED_STANDARD_UNCERTAINTY
  COVERAGE_FACTOR -> SCALES -> EXPANDED_UNCERTAINTY
  CALIBRATION -> SUPPORTS -> TRACEABILITY
  TRACEABILITY -> SUPPORTS -> COMPARABILITY_OF_MEASUREMENTS

MEASUREMENT_RESULT:
  representation:
    y
    WITH:
      UNCERTAINTY_INFORMATION
      UNIT
      MEASURAND_DEFINITION
      RELEVANT_CONDITIONS
  caution:
    MEASUREMENT_RESULT != TRUE_VALUE

MEASURAND_DEFINITION:
  requirement:
    SPECIFY:
      QUANTITY
      SYSTEM_OR_OBJECT
      CONDITIONS
      TIME_OR_STATE_WHEN_RELEVANT
      UNIT

TRUE_VALUE:
  caution:
    TRUE_VALUE_IS_GENERALLY_UNKNOWN_IN_REAL_MEASUREMENT

ERROR:
  definition:
    MEASURED_VALUE_MINUS_REFERENCE_OR_TRUE_VALUE
  distinction:
    MEASUREMENT_ERROR != MEASUREMENT_UNCERTAINTY

RANDOM_ERROR:
  role:
    VARIES_UNPREDICTABLY_ACROSS_REPEATED_MEASUREMENTS

SYSTEMATIC_ERROR:
  role:
    COMPONENT_OF_ERROR_THAT_REMAINS_CONSTANT_OR_VARIES_PREDICTABLY
  caution:
    CORRECTING_ESTIMATED_SYSTEMATIC_EFFECT_DOES_NOT_ELIMINATE_UNCERTAINTY_IN_CORRECTION

CORRECTION:
  corrected_result:
    y_corrected := y_raw+correction
  uncertainty:
    CORRECTION_ITSELF_MAY_HAVE_UNCERTAINTY

TYPE_A_EVALUATION:
  basis:
    STATISTICAL_ANALYSIS_OF_SERIES_OF_OBSERVATIONS
  mean:
    x_bar := (1/n)*SUM_i x_i
  sample_standard_deviation:
    s := sqrt(SUM_i (x_i-x_bar)^2/(n-1))
  standard_uncertainty_of_mean:
    u(x_bar) := s/sqrt(n)

TYPE_B_EVALUATION:
  basis:
    INFORMATION_OTHER_THAN_DIRECT_STATISTICAL_ANALYSIS_OF_CURRENT_REPEATED_OBSERVATIONS
  sources:
    - CALIBRATION_CERTIFICATE
    - MANUFACTURER_SPECIFICATION
    - PREVIOUS_MEASUREMENTS
    - REFERENCE_DATA
    - RESOLUTION
    - EXPERT_JUDGEMENT
  rule:
    TYPE_A_AND_TYPE_B_REFER_TO_EVALUATION_METHOD
    NOT:
      RANDOM_VS_SYSTEMATIC_ERROR

STANDARD_UNCERTAINTY:
  notation:
    u(x)
  interpretation:
    UNCERTAINTY_EXPRESSED_AS_STANDARD_DEVIATION

RELATIVE_STANDARD_UNCERTAINTY:
  u_r(x) := u(x)/|x|
  requirement:
    x != 0

UNCERTAINTY_BUDGET:
  columns:
    - INPUT_QUANTITY
    - ESTIMATE
    - STANDARD_UNCERTAINTY
    - DISTRIBUTION
    - DEGREES_OF_FREEDOM
    - SENSITIVITY_COEFFICIENT
    - COVARIANCE_OR_CORRELATION
    - CONTRIBUTION

SENSITIVITY_COEFFICIENT:
  coefficient:
    c_i := partial f/partial X_i
  interpretation:
    LOCAL_CHANGE_IN_MEASURAND_ESTIMATE_PER_UNIT_INPUT_CHANGE

LAW_OF_PROPAGATION_OF_UNCERTAINTY:
  first_order:
    u_c_squared(y) :=
      SUM_i c_i^2 u^2(x_i)
      +
      2*SUM_i_less_j c_i c_j u(x_i,x_j)
  independent_inputs:
    covariance_terms:
      ZERO
  caution:
    STRONG_NONLINEARITY_OR_LARGE_UNCERTAINTY_MAY_REQUIRE_OTHER_METHODS

COVARIANCE:
  u(x_i,x_j) := Cov(X_i,X_j)
  correlation_relation:
    u(x_i,x_j) := r_ij*u(x_i)*u(x_j)

CORRELATION_COEFFICIENT:
  r_ij :=
    u(x_i,x_j)/(u(x_i)u(x_j))
  bounds:
    -1 <= r_ij <= 1

MATRIX_PROPAGATION:
  gradient:
    J := grad f
  covariance_matrix:
    Sigma_X
  output_variance:
    u_c_squared(y) approximately J Sigma_X J_transpose

MONTE_CARLO_PROPAGATION:
  flow:
    DEFINE_INPUT_PROBABILITY_DISTRIBUTIONS
      -> DEFINE_DEPENDENCE
      -> SAMPLE_INPUTS
      -> EVALUATE_MEASUREMENT_MODEL
      -> BUILD_OUTPUT_DISTRIBUTION
      -> COMPUTE_INTERVALS_AND_SUMMARIES
  use:
    NONLINEAR_MODELS
    NONNORMAL_INPUTS
    ASYMMETRIC_OUTPUTS
    COMPLEX_DEPENDENCE

DISTRIBUTION_ASSIGNMENT:
  common_models:
    - NORMAL
    - RECTANGULAR
    - TRIANGULAR
    - T_DISTRIBUTION
    - EMPIRICAL_DISTRIBUTION

RECTANGULAR_DISTRIBUTION:
  interval:
    [-a,a]
  standard_uncertainty:
    u := a/sqrt(3)

TRIANGULAR_DISTRIBUTION:
  symmetric_interval:
    [-a,a]
  standard_uncertainty:
    u := a/sqrt(6)

RESOLUTION_UNCERTAINTY:
  resolution_step:
    d
  common_rounding_model:
    error_range:
      [-d/2,d/2]
  rectangular_standard_uncertainty:
    u := d/sqrt(12)

CALIBRATION_UNCERTAINTY:
  if_certificate_reports:
    expanded_uncertainty:
      U_cal
    coverage_factor:
      k_cal
  standard_uncertainty:
    u_cal := U_cal/k_cal

REPEATABILITY:
  statistic:
    REPEATABILITY_STANDARD_DEVIATION

REPRODUCIBILITY_CONDITION:
  changes_may_include:
    - LOCATION
    - OPERATOR
    - MEASUREMENT_SYSTEM
    - TIME

COMBINED_STANDARD_UNCERTAINTY:
  notation:
    u_c(y)
  role:
    STANDARD_UNCERTAINTY_OF_OUTPUT_ESTIMATE_AFTER_COMBINING_COMPONENTS

EXPANDED_UNCERTAINTY:
  U := k*u_c(y)
  where:
    k: COVERAGE_FACTOR
  caution:
    COVERAGE_PROBABILITY_DEPENDS_ON_DISTRIBUTION_AND_METHOD

COVERAGE_FACTOR:
  common_value:
    approximately_2
  context:
    OFTEN_ASSOCIATED_WITH_APPROXIMATELY_95_PERCENT_COVERAGE
    UNDER:
      APPROXIMATE_NORMALITY_AND_SUFFICIENT_EFFECTIVE_DEGREES_OF_FREEDOM
  rule:
    k_EQUALS_2_DOES_NOT_UNIVERSALLY_GUARANTEE_EXACT_95_PERCENT_COVERAGE

EFFECTIVE_DEGREES_OF_FREEDOM:
  method:
    WELCH_SATTERTHWAITE
  generic:
    nu_eff :=
      u_c^4(y)
      /
      SUM_i[(c_i u_i)^4/nu_i]

TRACEABILITY:
  full_concept:
    METROLOGICAL_TRACEABILITY
  components:
    - REFERENCE
    - CALIBRATION_CHAIN
    - DOCUMENTATION
    - UNCERTAINTY_CONTRIBUTIONS
  caution:
    TRACEABILITY != LOW_UNCERTAINTY_BY_ITSELF

CALIBRATION:
  outputs:
    - CALIBRATION_FUNCTION
    - CORRECTION
    - CALIBRATION_UNCERTAINTY
  distinction:
    CALIBRATION != ADJUSTMENT

ADJUSTMENT:
  distinction:
    ADJUSTMENT != CALIBRATION

REFERENCE_STANDARD:
  role:
    REALISE_OR_REPRODUCE_REFERENCE_QUANTITY_VALUE
  uncertainty:
    CONTRIBUTES_TO_TRACEABILITY_CHAIN

CERTIFIED_REFERENCE_MATERIAL:
  alias:
    CRM
  provides:
    CERTIFIED_PROPERTY_VALUE
    UNCERTAINTY
    TRACEABILITY_INFORMATION

BIAS_CORRECTION:
  estimated_bias:
    b_hat
  corrected_result:
    y_corr := y_raw-b_hat
  uncertainty:
    u(b_hat)_MUST_BE_PROPAGATED
  rule:
    CORRECTED_BIAS_ESTIMATE != ZERO_UNCERTAINTY

UNCERTAINTY_VS_ERROR:
  ERROR:
    DIFFERENCE_FROM_REFERENCE_OR_TRUE_VALUE
  UNCERTAINTY:
    DISPERSION_OR_DOUBT_ASSOCIATED_WITH_MEASUREMENT_RESULT
  rule:
    ERROR != UNCERTAINTY

UNCERTAINTY_VS_ACCURACY:
  rule:
    ACCURACY != UNCERTAINTY

UNCERTAINTY_VS_PRECISION:
  precision:
    CLOSENESS_OF_AGREEMENT_AMONG_REPLICATE_MEASUREMENTS
  rule:
    PRECISION != UNCERTAINTY

UNCERTAINTY_VS_TOLERANCE:
  tolerance:
    PERMITTED_RANGE_FOR_QUANTITY_OR_PRODUCT
  rule:
    TOLERANCE != MEASUREMENT_UNCERTAINTY

UNCERTAINTY_VS_CONFIDENCE_INTERVAL:
  confidence_interval:
    FREQUENTIST_INFERENTIAL_INTERVAL
  rule:
    EXPANDED_UNCERTAINTY != FREQUENTIST_CONFIDENCE_INTERVAL_BY_DEFAULT

UNCERTAINTY_VS_CREDIBLE_INTERVAL:
  credible_interval:
    POSTERIOR_PROBABILITY_INTERVAL
  rule:
    EXPANDED_UNCERTAINTY != BAYESIAN_CREDIBLE_INTERVAL_BY_DEFAULT

NONLINEAR_MEASUREMENT_MODEL:
  issue:
    FIRST_ORDER_LINEAR_PROPAGATION_MAY_BE_INADEQUATE
  responses:
    - HIGHER_ORDER_EXPANSION
    - MONTE_CARLO_PROPAGATION
    - NUMERICAL_PROPAGATION

ASYMMETRIC_UNCERTAINTY:
  reporting:
    MAY_USE:
      LOWER_COVERAGE_LIMIT
      UPPER_COVERAGE_LIMIT
  caution:
    SYMMETRIC_PLUS_MINUS_U_MAY_BE_MISLEADING

CORRELATED_INPUTS:
  consequence:
    COVARIANCE_TERMS_MUST_BE_INCLUDED
  sources:
    - COMMON_CALIBRATION
    - SHARED_REFERENCE
    - COMMON_ENVIRONMENT
    - DERIVED_QUANTITIES
    - SHARED_DATA
  caution:
    ASSUMING_INDEPENDENCE_CAN_UNDERSTATE_OR_OVERSTATE_UNCERTAINTY

SYSTEMATIC_EFFECTS:
  examples:
    - ZERO_OFFSET
    - SCALE_FACTOR
    - DRIFT
    - TEMPERATURE_EFFECT
    - CALIBRATION_BIAS
  flow:
    IDENTIFY_EFFECT
      -> ESTIMATE_CORRECTION
      -> APPLY_CORRECTION
      -> ASSIGN_UNCERTAINTY_TO_CORRECTION

INSTRUMENT_DRIFT:
  consequence:
    MAY_REQUIRE:
      RECALIBRATION
      DRIFT_CORRECTION
      ADDITIONAL_UNCERTAINTY_COMPONENT

ENVIRONMENTAL_EFFECTS:
  examples:
    - TEMPERATURE
    - HUMIDITY
    - PRESSURE
    - VIBRATION
    - ELECTROMAGNETIC_INTERFERENCE
  requirement:
    CONTROL_CORRECT_OR_INCLUDE_AS_UNCERTAINTY_WHEN_MATERIAL

SAMPLING_UNCERTAINTY:
  source:
    FINITE_SAMPLE_FROM_POPULATION_OR_MATERIAL
  caution:
    MAY_BE_DISTINCT_FROM_INSTRUMENT_MEASUREMENT_UNCERTAINTY

MODEL_UNCERTAINTY:
  source:
    APPROXIMATION_OR_INCOMPLETE_MEASUREMENT_MODEL
  response:
    - ALTERNATIVE_MODELS
    - SENSITIVITY_ANALYSIS
    - VALIDATION
    - ADDITIONAL_UNCERTAINTY_COMPONENT

SENSITIVITY_ANALYSIS_CONNECTION:
  vary:
    - INPUT_ESTIMATES
    - STANDARD_UNCERTAINTIES
    - CORRELATIONS
    - MODEL_FORM
  observe:
    - OUTPUT_ESTIMATE
    - COMBINED_UNCERTAINTY
    - EXPANDED_UNCERTAINTY

SCIENTIFIC_STATISTICS_CONNECTION:
  measurement_uncertainty:
    CONTRIBUTES_TO:
      DATA_UNCERTAINTY
      PARAMETER_UNCERTAINTY
      SCIENTIFIC_INFERENCE

  caution:
    IGNORING_MEASUREMENT_ERROR_CAN_BIAS_STATISTICAL_ESTIMATES

ERROR_PROPAGATION_CONNECTION:
  common_first_order_form:
    VARIANCE_PROPAGATION_VIA_DERIVATIVES

  distinction:
    INFORMAL_ERROR_PROPAGATION != COMPLETE_MEASUREMENT_UNCERTAINTY_EVALUATION_BY_DEFAULT

DIMENSIONAL_CONSISTENCY:
  requirement:
    MEASUREMENT_MODEL_TERMS_MUST_HAVE_COMPATIBLE_UNITS

  sensitivity_coefficients:
    UNITS:
      OUTPUT_UNIT/INPUT_UNIT

  contribution:
    c_i*u(x_i):
      OUTPUT_UNIT

REPORTING:
  include:
    - MEASURAND_DEFINITION
    - MEASURED_VALUE
    - UNIT
    - STANDARD_OR_EXPANDED_UNCERTAINTY
    - COVERAGE_FACTOR_WHEN_USED
    - COVERAGE_PROBABILITY_OR_INTENT_WHEN_AVAILABLE
    - MEASUREMENT_MODEL
    - MAJOR_UNCERTAINTY_COMPONENTS
    - TRACEABILITY_INFORMATION
    - RELEVANT_CONDITIONS

SIGNIFICANT_DIGITS:
  principle:
    REPORTED_DIGITS_SHOULD_BE_CONSISTENT_WITH_MEASUREMENT_UNCERTAINTY

  caution:
    EXCESS_DIGITS_IMPLY_FALSE_PRECISION

COMPARISON_OF_RESULTS:
  results:
    y_1 +/- U_1
    y_2 +/- U_2

  caution:
    OVERLAP_OR_NONOVERLAP_OF_UNCERTAINTY_INTERVALS_ALONE_DOES_NOT_DEFINE_STATISTICAL_COMPATIBILITY_IN_ALL_CASES

METROLOGICAL_COMPATIBILITY:
  concept:
    CONSISTENCY_OF_MEASUREMENT_RESULTS_WITH_STATED_UNCERTAINTIES_AND_REFERENCE_RELATION

  requirement:
    USE_APPROPRIATE_COMPATIBILITY_CRITERION

DECISION_RULE_CONNECTION:
  measured_value:
    y

  uncertainty:
    U

  specification_limit:
    L

  decision:
    MAY_REQUIRE:
      GUARD_BAND
      ACCEPTANCE_RULE
      CONSUMER_RISK
      PRODUCER_RISK

  caution:
    MEASUREMENT_UNCERTAINTY_AFFECTS_CONFORMITY_DECISIONS

GUARD_BANDING:
  purpose:
    ADJUST_ACCEPTANCE_LIMIT_TO_ACCOUNT_FOR_MEASUREMENT_UNCERTAINTY

  consequence:
    TRADES_OFF:
      FALSE_ACCEPTANCE
      FALSE_REJECTION

RISK_ANALYSIS_CONNECTION:
  measurement_uncertainty:
    MAY_PROPAGATE_TO:
      RISK_ESTIMATE
      FAILURE_PROBABILITY
      DECISION_THRESHOLD

  requirement:
    INCLUDE_WHEN_MATERIAL_TO_DECISION

APPLICATIONS:
  MEASUREMENT_UNCERTAINTY -> SUPPORTS -> SCIENTIFIC_MEASUREMENT
  MEASUREMENT_UNCERTAINTY -> SUPPORTS -> CALIBRATION
  MEASUREMENT_UNCERTAINTY -> SUPPORTS -> METROLOGY
  MEASUREMENT_UNCERTAINTY -> SUPPORTS -> EXPERIMENTAL_STATISTICS
  MEASUREMENT_UNCERTAINTY -> SUPPORTS -> QUALITY_CONTROL
  MEASUREMENT_UNCERTAINTY -> SUPPORTS -> CONFORMITY_ASSESSMENT
  MEASUREMENT_UNCERTAINTY -> SUPPORTS -> RISK_ANALYSIS

MODEL_CONNECTIONS:
  MEASUREMENT_UNCERTAINTY -> CONNECTS_TO -> SCIENTIFIC_STATISTICS
  MEASUREMENT_UNCERTAINTY -> CONNECTS_TO -> SENSITIVITY_ANALYSIS
  MEASUREMENT_UNCERTAINTY -> CONNECTS_TO -> MONTE_CARLO_SIMULATION
  MEASUREMENT_UNCERTAINTY -> CONNECTS_TO -> CALIBRATION
  MEASUREMENT_UNCERTAINTY -> CONNECTS_TO -> MEASUREMENT_TRACEABILITY
  MEASUREMENT_UNCERTAINTY -> CONNECTS_TO -> ERROR_PROPAGATION

SEMANTIC_EQUIVALENCE:
  "standard uncertainty"
    ~= "measurement uncertainty expressed as standard deviation"

  "combined standard uncertainty"
    ~= "standard uncertainty of result after combining input contributions"

  "expanded uncertainty"
    ~= "combined standard uncertainty multiplied by coverage factor"

  "sensitivity coefficient"
    ~= "local derivative of measurement model with respect to input quantity"

  EXCLUDE_EQUIVALENCE:
    UNCERTAINTY != ERROR
    UNCERTAINTY != ACCURACY
    UNCERTAINTY != PRECISION
    UNCERTAINTY != TOLERANCE
    TYPE_A != RANDOM_ERROR
    TYPE_B != SYSTEMATIC_ERROR
    CALIBRATION != ADJUSTMENT
    EXPANDED_UNCERTAINTY != CONFIDENCE_INTERVAL_BY_DEFAULT
    EXPANDED_UNCERTAINTY != CREDIBLE_INTERVAL_BY_DEFAULT
    TRACEABILITY != LOW_UNCERTAINTY

VALIDATION_RULES:
  RULE_1:
    MEASURAND_AND_MEASUREMENT_MODEL_MUST_BE_EXPLICIT
  RULE_2:
    ALL_MATERIAL_INPUT_QUANTITIES_AND_UNCERTAINTY_COMPONENTS_SHOULD_BE_IDENTIFIED
  RULE_3:
    TYPE_A_AND_TYPE_B_EVALUATION_METHODS_MUST_NOT_BE_CONFUSED_WITH_RANDOM_AND_SYSTEMATIC_ERROR
  RULE_4:
    COVARIANCE_AND_CORRELATION_MUST_BE_INCLUDED_WHEN_INPUTS_ARE_DEPENDENT
  RULE_5:
    FIRST_ORDER_PROPAGATION_MUST_BE_CHECKED_FOR_ADEQUACY_IN_NONLINEAR_MODELS
  RULE_6:
    COVERAGE_FACTOR_AND_COVERAGE_INTERPRETATION_MUST_BE_REPORTED_WHEN_EXPANDED_UNCERTAINTY_USED
  RULE_7:
    TRACEABILITY_CHAIN_AND_REFERENCE_INFORMATION_SHOULD_BE_PRESERVED
  RULE_8:
    MEASUREMENT_UNCERTAINTY_MUST_NOT_BE_INTERPRETED_AS_KNOWN_MEASUREMENT_ERROR

CONFIDENCE:
  ontology_identity: 0.99
  measurand_model_structure: 0.99
  type_a_type_b_structure: 0.99
  propagation_structure: 0.99
  covariance_structure: 0.99
  traceability_structure: 0.99
  semantic_distinctions: 0.99

UPDATE_MODEL:
  IF:
    NEW_CALIBRATION_INFORMATION_ARRIVES
  THEN:
    UPDATE:
      INPUT_ESTIMATES
      CORRECTIONS
      CALIBRATION_UNCERTAINTY
      TRACEABILITY_CHAIN
    RECOMPUTE:
      COMBINED_STANDARD_UNCERTAINTY
      EXPANDED_UNCERTAINTY

  IF:
    MEASUREMENT_MODEL_CHANGES
  THEN:
    UPDATE:
      SENSITIVITY_COEFFICIENTS
      COVARIANCE_PROPAGATION
    REASSESS:
      LINEARISATION_ADEQUACY
      MONTE_CARLO_REQUIREMENT

  IF:
    INPUT_DEPENDENCE_CHANGES
  THEN:
    UPDATE:
      COVARIANCE_MATRIX
      CORRELATION_STRUCTURE
    RECOMPUTE:
      OUTPUT_UNCERTAINTY

  PRESERVE:
    MEASURAND_DEFINITION
    MEASUREMENT_MODEL
    INPUT_QUANTITY_DEFINITIONS
    UNITS
    UNCERTAINTY_BUDGET
    DISTRIBUTION_ASSIGNMENTS
    CORRELATION_STRUCTURE
    CALIBRATION_REFERENCES
    TRACEABILITY
    DATA_PROVENANCE

AI_CONSUMPTION:
  parse_as: FORMAL_SEMANTIC_SPECIFICATION
  execution_mode: RECURSIVE_REASONING

  preferred_reasoning_order:
    - DEFINE_MEASURAND
    - DEFINE_MEASUREMENT_MODEL
    - IDENTIFY_INPUT_QUANTITIES
    - IDENTIFY_CORRECTIONS_AND_SYSTEMATIC_EFFECTS
    - EVALUATE_TYPE_A_COMPONENTS
    - EVALUATE_TYPE_B_COMPONENTS
    - DEFINE_CORRELATIONS_AND_COVARIANCES
    - COMPUTE_SENSITIVITY_COEFFICIENTS
    - PROPAGATE_STANDARD_UNCERTAINTIES
    - ASSESS_NONLINEARITY
    - USE_MONTE_CARLO_IF_REQUIRED
    - COMPUTE_COMBINED_AND_EXPANDED_UNCERTAINTY
    - PRESERVE_TRACEABILITY
    - RETURN_MEASUREMENT_UNCERTAINTY_INTERPRETATION

  constraints:
    - PRESERVE_MEASURAND_DEFINITION
    - PRESERVE_MEASUREMENT_UNITS
    - DISTINGUISH_UNCERTAINTY_FROM_ERROR
    - DISTINGUISH_TYPE_A_TYPE_B_FROM_RANDOM_SYSTEMATIC
    - MODEL_CORRELATION_WHEN_PRESENT
    - DISTINGUISH_CALIBRATION_FROM_ADJUSTMENT
    - REPORT_COVERAGE_FACTOR_WHEN_USED
    - PRESERVE_DATA_PROVENANCE

FLOW_HASH:
  canonical_entity: "measurement-uncertainty-ontology-2"
  namespace: "probability-statistics/scientific-statistical-methods"
  version: "4.0"
  identity_basis:
    - PAGE_URL
    - CANONICAL_ENTITY
    - ENTITY_TYPE
    - MEASURAND
    - MEASUREMENT_MODEL
    - UNCERTAINTY_PROPAGATION
    - TRACEABILITY

END_FLOW