Developing AI Prompts for Determining Measurement Uncertainty

In an era where artificial intelligence (AI) is rapidly transforming scientific workflows, the field of metrology—long regarded as a cornerstone of precision and standardization—stands to benefit significantly from this technological advancement. One critical application is in the domain of measurement uncertainty, a foundational concept governed by the Guide to the Expression of Uncertainty in Measurement (GUM). The ability to quantify uncertainty with accuracy and consistency is essential for ensuring the validity, comparability, and traceability of measurement results across industries and disciplines.

As AI systems become increasingly integrated into metrological processes, the development of precise, context-aware prompts becomes essential for guiding these tools in complex analytical tasks. This article examines the methodology for creating effective AI prompts specifically designed to aid in determining and calculating measurement uncertainty following the GUM framework. By aligning natural language inputs with metrological standards, AI can be leveraged to automate uncertainty budgets, interpret measurement models, and enhance compliance with ISO/IEC 17025 requirements. Through this lens, we present a structured approach to prompt engineering that bridges domain expertise with intelligent automation.

AI Prompt example to develop a comprehensive prompt for calculating measurement uncertainty in accordance with the Guide to the Expression of Uncertainty in Measurement (GUM):

PROMPT:

“Develop a detailed procedure for determining measurement uncertainty in accordance with the Guide to the Expression of Uncertainty in Measurement (GUM). The procedure should include the following sections:

Scope – Define the measurement process and the objective of the uncertainty evaluation.
Normative References – List standards, including GUM and any relevant ISO documents.
Terms and Definitions – Provide GUM-aligned definitions of key terms (e.g., standard uncertainty, expanded uncertainty, coverage factor).
Identification of the Measurand – Clearly define the quantity being measured.
Uncertainty Sources – Identify all significant sources of uncertainty (e.g., instrument calibration, environmental conditions, operator variability).
Uncertainty Components – Classify components as Type A (statistical) or Type B (non-statistical) and describe the rationale.
Mathematical Model – Construct the equation that relates input quantities to the measurand.
Uncertainty Propagation – Apply the law of propagation of uncertainty to determine the combined standard uncertainty.
Expanded Uncertainty – Determine the expanded uncertainty using an appropriate coverage factor for a specified confidence level (e.g., 95%).
Reporting Results – Outline how uncertainty should be expressed in reports, including numerical format and units.
Worked Example – Include a numerical example to illustrate the step-by-step application of the procedure.
Annexes (Optional) – Provide templates or forms for uncertainty budgets and data recording.

Ensure that the procedure is suitable for use in an ISO/IEC 17025-accredited laboratory environment and reflects traceability and transparency principles.”

AI Prompt example for calculating measurement uncertainty in accordance with the Guide to the Expression of Uncertainty in Measurement (GUM):

PROMPT:

“Calculate the measurement uncertainty of a specified measurement process in accordance with the Guide to the Expression of Uncertainty in Measurement (GUM). The calculation should include the following steps:

Define the Measurand – Clearly state the quantity intended to be measured, including units.
Identify the Input Quantities – List all input quantities that affect the measurand. Provide their estimated values, standard uncertainties, probability distributions (e.g., normal, rectangular), and sources of data.
Develop a Mathematical Model – Create an equation or function that relates the input quantities to the output (measurand).
Classify Uncertainty Components – Distinguish between:
- Type A (evaluated by statistical methods, e.g., standard deviation of repeated measurements)
- Type B (evaluated by other means, e.g., calibration certificates, manufacturer’s specifications)
Evaluate Standard Uncertainties – For each input quantity, determine the standard uncertainty (u), using appropriate statistical or analytical methods.
Propagate Uncertainty – Use the law of propagation of uncertainty or numerical methods (e.g., Monte Carlo method) to combine the input uncertainties and calculate the combined standard uncertainty (uc).
Calculate Expanded Uncertainty – Determine the expanded uncertainty (U) by multiplying the combined standard uncertainty by a coverage factor (k) appropriate for a given confidence level (typically k = 2 for approximately 95% confidence).
Present the Result – Express the final result in the format:
- Y = y ± U (units), at a confidence level of approximately 95%, where:
  - y is the measured value,
  - U is the expanded uncertainty.
Include an Uncertainty Budget Table – Summarize all components, values, standard uncertainties, sensitivity coefficients, and contributions to combined uncertainty.

Use consistent units throughout and provide clear documentation for all assumptions, sources, and numerical values used in the uncertainty calculation. Ensure traceability and conformance with ISO/IEC 17025 requirements.”