Measurement System Uncertainty: Part 2 – How?

Measurement System Uncertainty: Part 1 – Why? (Process Industry Informer April 2024 issue) explored the concept of measurement system uncertainty. The key points being:

1. Every measurement has an associated uncertainty.
2. When considering at measurement uncertainty examine the entire measurement system and not just the instrument.
3. If measurement system uncertainty is bigger than processing limits, while the displayed value might be within the limits, the actual value may be outside the limits.

This continuation of the theme will address how to evaluate measurement system uncertainty.

Harmonised Approach

According to the Joint Committee for Guides in Metrology (JCGM) there are two acceptable methods of evaluating measurement uncertainty: Type A Evaluation and Type B Evaluation. The JCGM are an organisation that stives to harmonise meteorological standards by maintaining and promoting the two key documents:

1. Guide to the Expression of Uncertainty in Measurement (known as the GUM).
2. International Vocabulary of Metrology – Basic and General Concepts and Associated Terms (known as the VIM).

It is made up of the following member organisations all of which promote the JCGM’s approach:

• International Bureau of Weights & Measures (BIPM).
• International Electrotechnical Commission (IEC).
• International Federation of Clinical Chemistry and Laboratory Medicine (IFCC).
• International Laboratory Accreditation Cooperation (ILAC).
• International Organisation for Standardisation (ISO).
• International Organisation of Legal Metrology (OMIL).
• International Union of Pure and Applied Chemistry (IUPAC).
• International Union of Pure and Applied Physics (IUPAP).

It’s safe to say evaluating measurement system uncertainty via the Type A Evaluation or Type B Evaluation is widely acceptable and will stand up to an audit.

Type A Evaluation

The Type A Evaluation is a statistical approach based on physical measurements of the measurement system being evaluated. There are two approaches to gathering data:

1. Single Occurrence: Record multiple measurements performed in short succession of each other as part of the same data gathering session.
2. Multiple Occurrences: Record multiple measurements performed periodically over a period of time. This approach can be applied to taking previous calibration data over a number of years. Depending on the time between calibrations there may be some drift combined with measurement uncertainty which could end up in measurement uncertainty being over estimated.

Which ever approach is used to gathering data, the same measurement value should be repeated (i.e. single point of measurement). There is no set rule for this but best practice would be to use the largest measurement that represents normal usage or in the case of reviewing calibration histories the highest calibration point.

When it comes to the number of measurements, like all statistical techniques more is better! Ideally no less than 10 measurements (or 10 historic calibrations). In the case of using a single occurrence approach 20 is feasible and more ideal.

To perform the Type A calculation, calculate the standard deviation of the dataset. If using MS Excel to record the measurements this can easily be calculated via the STDEV function. The standard deviation represents the uncertainty with a statistical confidence of 68.3%, it is normal to express uncertainty to either 95.4% or 99.7% when using this method by multiplying the standard deviation by a coverage factor of 2 or 3 respectively.

The advantages to using this approach are:

• Evaluates the measurement system in its unique application & environment.
• Accurately models complex systems.
• No manufacturers data is needed, this is particularly useful if you can’t easily identify the instrument due to physical condition or location.
• Can be more accurate than manufacturers data (some manufacturers are more conservative than others with their published specifications).

Type B Evaluation

The B Type evaluation involves taking specifications from manufacturers data sheets for each measurement system component and combining them (typically) via a root mean square equation. In the case of a typical process instrument loop, it would look like the following:

The equation can be tailored for the application, for example sometimes manufacturers combine sensor and transmitter uncertainty data in which case it would look like this:

The advantages to using this approach are:

• No physical data required.
• Simple, quick calculation.
• Ideal for new equipment with no history.

Combined Approach

Whilst Type A and Type B Evaluations are usually used alone, they can be used together. One or more Type A Evaluations of an individual components of a measurement system could be combined with manufactures specifications the remaining measurement system components in a Type B Evaluation (i.e. root mean square equation).

Application Flexibility

Whilst the JCGM specify two approaches, they do not specify when each approach should be used, that is down to the user. If all the measurement system components are identifiable and their respective manufacturers specifications are readily available, it makes sense in most cases to use a Type B Evaluation.

However, if this approach does not lead to the desired measurement system capability, its worth trying a Type A Evaluation or even a combination of the two before looking to invest in new equipment. As mentioned already some manufacturers publish more conservatively than others depending on what statistical confidence they are applying to their data. For more complicated measurement systems or where details of all components are not easily identifiable the Type A Evaluation can be a better fit.

Summary

In summary, when evaluating measurement system uncertainty there are a couple of key points to remember:

1. Make sure it’s a recognised method (i.e. Type A or Type B Evaluation), that way it will stand up to audit scrutiny should the situation arise.
2. Neither Type A nor Type B Evaluations are a better method than the other, they each have their advantages and disadvantages and its up to the user to decide which to apply.
3. Type A and Type B Evaluations are not mutually exclusive, in some instances a combined approach can be the most appropriate.