Measurement Precision – Repeatability of Measurements – Measurement

Measurement precision is a cornerstone concept in analytical science, quality control, and metrology. Understanding how closely repeated measurements agree—and what factors influence consistency—ensures reliable decision-making in laboratories, manufacturing, research, and regulatory contexts.

Precision

Precision is the closeness of agreement among a set of results obtained from repeated measurements of the same quantity under specified conditions. It is solely concerned with the consistency or repeatability of results, regardless of their closeness to the true value. According to the International Vocabulary of Metrology (VIM 3), precision is the degree to which repeated measurements under unchanged conditions yield the same results.

Precision is typically quantified using statistical tools, most commonly the standard deviation. A smaller standard deviation indicates that repeated measurements are tightly grouped—high precision—whereas a larger spread indicates low precision.

Key points:

• Precision is independent of accuracy.
• High precision means low variability among results.
• The conditions under which measurements are made must be clearly specified (e.g., same operator, equipment, environment, and timeframe).

Precision is crucial in:

• Quality control: Consistency in measurements ensures uniformity of products.
• Scientific research: Reliable data is necessary for valid conclusions.
• Calibration and metrology: Ensures measurement systems perform reliably over time.

Accuracy

Accuracy is the closeness of agreement between a measured value and the true or reference value. It combines both trueness (absence of systematic bias) and precision (random error) as per VIM 3 and ISO 5725-1:1994.

• Trueness: How close the average of multiple measurements is to the actual true value.
• Precision: How consistent those measurements are.

A measurement system can be:

• Precise but not accurate: Consistently yields the wrong value (systematic error).
• Accurate but not precise: Results average out to the true value, but individual measurements vary widely.
• Both accurate and precise: Ideal case; consistent, correct results.

Regular calibration, use of reference materials, and method validation are crucial for maintaining accuracy.

Repeatability

Repeatability is the degree of agreement between consecutive measurements of the same item under identical, strictly controlled conditions. These conditions include:

• Same measurement procedure and operator
• Same instrument and location
• Short time interval
• Same or equivalent samples

Repeatability reflects the minimum inherent variability of a measurement system. The metric used to express it statistically is the repeatability standard deviation (sᵣ).

Example: An analyst measures the concentration of a solution several times using the same instrument and technique within a single session to assess repeatability.

High repeatability is essential for:

• Establishing baseline performance of instruments and methods
• Ensuring that observed process variation is not due to measurement noise
• Validating new procedures and troubleshooting issues

Intermediate Precision

Intermediate precision extends the concept of repeatability to more realistic laboratory conditions. It accounts for routine variations such as:

• Different operators
• Different days or time periods
• Different calibration events
• Different batches of reagents
• (Possibly) different but equivalent instruments

Intermediate precision is critical for method validation. It represents the variability likely to be encountered during normal operation in a single laboratory.

Statistical measure: Standard deviation for intermediate precision (e.g., s_RW or s_ip) is calculated from pooled data across these variable conditions.

Use case: A pharmaceutical laboratory assesses intermediate precision by having different analysts measure a reference standard over several weeks, using the same method but different reagent batches.

Reproducibility

Reproducibility measures the agreement among results obtained under the broadest possible range of conditions:

• Different laboratories or locations
• Different operators
• Different measuring systems or instruments
• Possibly different measurement procedures

Reproducibility is quantified by the reproducibility standard deviation (s_R) and is essential for:

• Inter-laboratory studies
• Establishing the robustness and reliability of methods across organizations or countries
• Regulatory submissions and standardization

Example: Multiple accredited labs worldwide measure the same reference material using a standardized protocol. The spread in their results determines the method’s reproducibility.

Measurement Procedure

A measurement procedure is a detailed, standardized document describing every step in the measurement process—from instrument calibration and sample preparation to data recording and analysis. A robust procedure ensures:

• Consistency among different operators and over time
• Minimization and control of sources of variation
• Reliable transfer of methods between laboratories

Components of a measurement procedure:

• Instrument type, model, and calibration status
• Operator qualifications and responsibilities
• Environmental conditions (controlled or monitored)
• Sample handling and preparation instructions
• Data collection and processing protocols
• Quality control measures (e.g., use of control samples)

Standard Deviation (Repeatability Standard Deviation, sᵣ)

The standard deviation quantifies the spread of a set of results around their mean. The repeatability standard deviation (sᵣ) refers specifically to measurements made under repeatability conditions.

How to calculate sᵣ:

1. Perform n replicate measurements under controlled (repeatability) conditions.
2. Calculate the mean of the measurements.
3. Subtract the mean from each measurement to find deviations.
4. Square each deviation and sum them.
5. Divide the sum by (n-1) to get the variance.
6. Take the square root of the variance to obtain the standard deviation.

A lower sᵣ indicates higher repeatability and less random error in the measurement system.

Repeatability Conditions

Repeatability is defined by strict conditions to isolate the measurement system’s inherent variability:

• Same measurement procedure
• Same operator
• Same measuring instrument/system
• Same location
• Short period of time
• Same or equivalent samples

Purpose: To determine the best-case (minimum) variability of the system.

Intermediate Precision Conditions

Intermediate precision studies relax repeatability conditions to reflect daily laboratory realities:

• Same procedure and location
• Different operators
• Different calibration events or reagent batches
• Measurements over longer periods (days/weeks/months)
• Possibly different but functionally equivalent instruments

Goal: To quantify normal, intra-laboratory variability.

Reproducibility Conditions

Reproducibility conditions are the broadest:

• Different laboratories or locations
• Different operators and instruments
• Possible differences in measurement procedures
• Replicate measurements on standardized samples

Purpose: To determine how comparable results are across organizations and environments.

Measurement Procedure and Sources of Variation

A robust measurement procedure identifies and controls all sources of variation, including:

• Instrumental: Calibration errors, drift, software bugs
• Operator-related: Technique, training, interpretation
• Environmental: Temperature, humidity, pressure, electromagnetic fields
• Sample-related: Inhomogeneity, contamination, degradation

Careful documentation, calibration, training, and environmental control are essential for minimizing these sources and ensuring reliable measurements.

Statistical Assessment and Calculation

Standard deviation is the core statistical metric for precision. Depending on the scope:

• sᵣ: Repeatability standard deviation
• s_RW or s_ip: Intermediate precision standard deviation
• s_R: Reproducibility standard deviation

Example Calculation for sᵣ:

Practical Applications

• Analytical laboratories use precision studies to validate new methods and ensure compliance with standards.
• Pharmaceutical manufacturers require precise and accurate measurements for dosing and regulatory approval.
• Industrial quality control relies on repeatable measurements for process control and product acceptance.
• Metrology institutes strive for reproducibility to maintain uniformity of standards worldwide.

Summary Table: Types of Measurement Precision

Further Reading and Key Standards

• ISO 5725-1:1994: Accuracy (trueness and precision) of measurement methods and results—Part 1: General principles and definitions.
• VIM 3 (International Vocabulary of Metrology): Key definitions for measurement science.
• ASTM E177: Standard Practice for Use of the Terms Precision and Bias in ASTM Test Methods.

Conclusion

Measurement precision is essential for reliable data in science, industry, and quality assurance. By understanding and controlling repeatability, intermediate precision, and reproducibility, organizations can ensure their measurements are not just consistent, but also dependable and fit for their intended purpose.

For more information on implementing robust measurement systems or validating methods for regulatory compliance, contact our experts or schedule a demo today.