In addition to classical analytical methods, we have several instruments that are helpful in our routine laboratory analysis. Examples are aplenty, such as pH meter, dissolved oxygen meter, turbidity meter, Conductivity meter, UV-visible spectrometer, FT-IR spectrophotometer, etc. Some are being used for in-situ measurements in the field. Hence, it is important to estimate their respective measurement uncertainty.
Most measuring instruments are generally characterized by:
To evaluate the uncertainty of readings from a measuring instrument, we look for two basic uncertainty contributors, namely:
By VIM definition, MPE is an extreme value of measurement error, with respect to a known reference quantity value, permitted by specifications or regulations for a given measurement, measuring instrument, or measuring system. It is the ‘best’ accuracy confirmed by a calibration and specified by the manufacturer of the instrument during the warranty period.
MPE data can always be found in the manufacturer’s manual under the instrument specification. It is usually expressed in one of the following manners:
MPE = +/-a
where a is a given value for its unit.
For example, a glass thermometer with a measuring range of 0 – 50oC with sub-divided units of 0.1oC, MPE = +/-0.2oC
MPE = +/-(a + bx)
where x is a measured value.
When the measuring instrument uses a constant relative standard deviation RSD, its MPE can be expressed as:
When the measuring instrument uses a constant relative standard deviation RSD, its MPE can be expressed as:
Repeatability is the closeness of the agreement between the results of successive measurements of the same measure carried out under the same conditions of measurement, being taken by a single person or instrument on the same item, under the same conditions, and in a short period of time. Indeed, repeatability is a measure of instrument indicator’s variation under successive measurement exercise. It is expressed as sr, the standard deviation of a series of repeated measurements.
A breathalyzer is a device for estimating blood alcohol content (BAC) from a breath sample. A given brand breathalyzer has the following performance data:
BAC < 0.20 g/100ml MPE = +/- 0.025 g/100ml
BAC 0.20 – 0.40 g/100ml MPE = +/- 0.04 g/100ml
sr = +/- 0.006 g/100ml
Evaluating measurement uncertainty of the breathalyzer
BAC < 0.20 g/100ml u(E) = +/- 0.014(4) g/100ml
BAC 0.20 – 0.40 g/100ml u(E) = +/- 0.023(1) g/100ml
sr = +/- 0.006 g/100ml
The combined standard uncertainty u (Comb) = SQRT(u(E)2 + sr2) and the expanded uncertainties which are 2 x u(Comb) with 95% confidence for the two ranges are as follows:
The method traditionally practiced by most test laboratories in the estimation of measurement uncertainty is by the ISO GUM (ISO/IEC Guide 98-3) approach, which is quite tedious and time consuming to study and gather uncertainty contributions from each and every step of the test method. An alternative way of looking at uncertainty is to attempt to study the overall performance of the analytical procedure by involving replication of the whole procedure to give a direct estimate of the uncertainty for the final test result. This is the so-called ‘top-down’ approach.
We may use the data from inter-laboratory study, in-house validation or ongoing quality control. This approach is particularly appropriate where individual effects are poorly understood in terms of their quantitative theoretical models which are capable of predicting the behavior of analytical results for particular sample types. By this approach, it is suffice to consider reproducibility from inter-laboratory data or long-term within-laboratory precision as recommended by ISO 21748, ISO 11352 and ASTM D 6299.
However, one must be aware of that by repeatedly analyzing a given sample over several times will not be a good estimate of the uncertainty unless the following conditions are fulfilled:
The conclusion is that replicated data by a single analyst on same equipment over a short period of time are not sufficient for uncertainty estimation. If the top-down approach is to be followed, we must obtain a good estimate of the long-term precision of the analytical method. This can be done for example, by studying the precision for a typical test method used as a QC material over a reasonable period of time. We may also use a published reproducibility standard deviation for the method in use, provided we document proof that we are able to follow the procedure closely and competently.
When we evaluate the validity of a test result, we are mostly concern if the performance of the test method used is precise and reproducible enough to fit for a particular purpose or to meet the customer’s requirements. That concern also includes in some cases whether the method detection limit is low enough to meet the regulatory or specification limits required. Read on …. .Types of precision estimates