Measuerement Uncertainty | Calculation of Measurement Uncertainty

# Measurement Uncertainty and Method of Calculation Uncertainty

## What is Measurement Uncertainty

In implementation of ISO/IEC 17025 for test laboratory or calibration laboratory accreditation Measurement Uncertainty needs to be calculated. The measurement uncertainty is not calculated in the cases of Qualitative or semi-quantitative tests, where the result is numerically rated by judgment or test method itself had calculated measurement uncertainty like ASTM E9, Tension Testing of Metals ASTM E8, Mooney Viscosity ASTM D1646.

Some key points for measurement uncertainties are given below.

• No measurement can be made with 100% confidence
• All measurements have influencing factors which cannot be perfectly quantified.
• Hence all measurements statement shall include measurement uncertainty
• The uncertainty of measurement is a parameter that characterizes the spread of values that could reasonable be attributed to measure and.
• It states the range of values within which the value of the measure and is estimated to lie with a stated level of confidence.

What is not a Measurement Uncertainty?

• Mistakes made by operators are not measurement uncertainties.
• Tolerances are not uncertainties. They are acceptance limits which are chosen for a process or a product.
• Specifications are not uncertainties. A specification tells you what you can expect from a product..
• Errors are not the same as uncertainties
• Statistical analysis is not the same as uncertainty analysis.

### ISO 17025 Requirements for Measurement Uncertainty - Clause 5.4.6 :

• The calibration laboratory or a testing laboratory, which is having ISO 17025 and is performing its own calibrations must have procedure to estimate the uncertainty of measurement for all calibrations and types of calibrations. The Testing laboratories have to apply procedures for estimating uncertainty of measurement.
• In test laboratory has to at least attempt to identify all the components of uncertainty and make a reasonable estimation, and ensure that the form of reporting of the result does not give a wrong impression of the uncertainty measurement. Reasonable estimation is based on knowledge of the performance of the method and on the measurement scope and makes use of, for example, previous experience and validation data.
• When estimating the uncertainty of measurement, all uncertainty components which are of importance in the given situation, is taken into account using appropriate methods of analysis. The predicted long-term behavior of the tested and/or calibrated item is not normally taken into account when estimating the measurement uncertainty.

#### IEC17025: 5.10: Reporting the Result

1. Uncertainty is must to be reported for calibration certificate and not must for testing laboratory.
2. For testing laboratory where applicable, a statement on the estimated uncertainty of measurement; information on uncertainty is needed in test reports,
3.  when a client's instruction so requires to report uncertainty measurement for test laboratory,
4.  when the uncertainty affects compliance to a specification limit;
5. Reporting measurement uncertainty with a statement like this:

“The measured result is 10,000.051 W  ± 0.028 W .  The reported uncertainty is expanded using a coverage factor k=2 for a level of confidence of approximately 95%, assuming a normal distribution.”

### Who and When Measurement Uncertainty Needs to be Calculated?

In below cases Uncertainty of measurement needs to be calculated.

• Testing Labs, performing internal calibration
• Testing labs, when the method, the client or a decision on conformity with narrow limits
• Calibration Labs, whenever they issue certificates need to report uncertainty of measurement.

The uncertainty measurement needs to be calculated for test laboratory in below cases.

• Any changes in the test set up like instrument, calibration, human, primary standard, change of testing area etc.
• Normally instruments are calibrated once in a year, so uncertainty is measured after 1 year.

The measurement uncertainty needs to be calculated for the calibration laboratory normally after each instrument is calibrated..

### Estimating Uncertainty: Summary of Contributors to Measurement Uncertainty

 Environmental conditions Measurement setup Measurement object Measurement process Software & calculations Physical constant & conversion factors Metrologies effects Definition of the measurement characteristic Human factors

#### Where does Measurement Uncertainty come from?

1. The measuring instrument - instruments can suffer from errors including bias, changes due to ageing, wear, or other kinds of drift, poor readability, noise and many other problems.
2. The item being measured - which may not be stable. (concentration of unstable chemical due to light or heat)
3. The measurement process - the measurement itself may be difficult to make. For example measuring the concentration through automated instruments is more accurate than human process.
4. ‘Imported’ uncertainties - calibration of your instrument has an uncertainty which is then built into the uncertainty of the measurements you make.
5. Operator skill - some measurements depend on the skill and judgment of the operator. One person may be better than another at the delicate work of setting up a measurement, or at reading fine detail by eye. The use of an instrument such as a stopwatch depends on the reaction time of the operator.
6. Sampling issues - the measurements you make must be properly representative of the process you are trying to assess. If you want to know the temperature at the work-bench, don’t measure it with a thermometer placed on the wall near an air conditioning outlet.
7. The environment - temperature, air pressure, humidity and many other conditions can affect the measuring instrument or the item being measured.

## Step-by-step Procedure for Calculation of Measurement Uncertainty

Below are the step by step procedure given to calculate the uncertainty of measurement.

1. Define the unit of measure
2. List all sources of uncertainty in the form of an uncertainty analysis for type B calculation
3. Take 5 readings of same sample, and calculate the standard uncertainty for repeatedly measured quantities in accordance with Type A evaluation of Standard uncertainty.
4. Calculate uncertainty for each component of type B and standard uncertainty. For single values, e.g. resultant values of previous measurements, correction values or values from the literature, adopt the standard uncertainty where it is given or can be calculated.
5. Convert type A and type B uncertainty of measurement in same unit
6. Calculate combined uncertainty
7. Calculate coverage factor K from student’s t table
8. Calculate the expanded uncertainty U by multiplying the standard uncertainty u(y) associated with output estimate by a coverage factor k chosen.

Expanded Uncertainty is = k * UC

1. Report the result of the measurement comprising the estimate y of the measured, the associated expanded uncertainty U and the coverage factor k in the certificate

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