Metrology and measurements basics of investing

In addition to the GUM itself, a number of supplements have been proposed which will assist with interpretation and enhance the scope and applicability of the GUM. The suggested approach is rule-based and is defined by the functional relationship equation which specifies the input variables for calculating the particular measurand.

The GUM equation may be applied to any mathematical form or functional relationship the starting point for laboratory calculations and describes the propagation of uncertainty from the input variable s to the measurand the end point or outcome of the laboratory calculation. The mathematical procedures used for evaluating the propagation of uncertainty in any particular situation will depend on the form of the functional relationship describing the input and output variables.

Measurand Measurand is the term that denotes the quantity being measured. It replaces previous terms such as analyte or the name of the substance being measured which was often provided without further definition. These conditions are required to fully define the measurand, as different measurement procedures may determine different properties or attribute of a substance.

For example, the measurement of serum sodium by a direct ion-selective electrode procedure provides a measurand which should be described as serum sodium activity, while serum sodium measured by flame photometry or an indirect ion-selective electrode procedure provides a measurand which should be described as serum sodium concentration. Further examples and discussion of the term measurand are available in several articles 1 , 7 , 12 , 13 and recent text books on clinical biochemistry.

Uncertainty of Measurement and Measurement Error The result of any quantitative measurement has two essential components: A numerical value expressed in SI units as required by ISO which gives the best estimate of the quantity being measured the measurand.

This estimate may well be a single measurement or the mean value of a series of measurements. A measure of the uncertainty associated with this estimated value. In clinical biochemistry this may well be the variability or dispersion of a series of similar measurements for example, a series of quality control specimens expressed as a standard uncertainty standard deviation or combined standard uncertainty see below.

By definition, the term error or measurement error is the difference between the true value and the measured value. As the measured value and its uncertainty component are at best only estimates, it follows that the true value is indeterminate VIM, GUM. Uncertainty is caused by the interplay of errors which create dispersion around the estimated value of the measurand; the smaller the dispersion, the smaller the uncertainty.

Even if the terms error and uncertainty are used somewhat interchangeably in everyday descriptions, they actually have different meanings according to the definitions provided by VIM and GUM. They should not be used as synonyms. If repeated measurements are made of the same quantity, statistical procedures can be used to determine the uncertainties in the measurement process. This type of statistical analysis provides uncertainties which are determined from the data themselves without requiring further estimates.

The important variables in such analyses are the mean, the standard deviation and the standard uncertainty of the mean also referred to as the standard deviation of the mean or the standard error of the mean. Systematic and Random Errors Uncertainties Experimental errors may be divided into two classes: systematic errors and random errors.

Three terms which are often used in association with laboratory errors are accuracy inaccuracy , bias, and precision imprecision. Both VIM and GUM define accuracy as a qualitative concept which describes the closeness of agreement between a measured quantity value and a true quantity value of a measurand. As such, accuracy includes the effects of systematic error even though it does not have a numerical value. The main distinctions with regard to systematic and random errors are that: Systematic error bias can, at least theoretically, be eliminated from the result by an appropriate correction.

Random errors arise from unpredictable variations which influence the measurement procedure, are associated with the actual measurement for example, failure to properly account for temperature fluctuations or measurement pipette variability , or possible imprecision in the definition of the measurand itself. Random errors may be analysed statistically while systematic errors are resistant to statistical analysis.

Systematic errors are generally evaluated by non-statistical procedures. In clinical laboratories, random error uncertainty is usually evaluated through internal quality control procedures. The GUM procedures are based on the assumption that all systematic errors have been corrected and the only uncertainty relating to systematic error is the uncertainty of the correction itself.

This correction uncertainty and its contribution to the uncertainty of the measurand may be either Type A or Type B depending on the evaluation procedure used see Type A and Type B uncertainties below. The uncertainty in the reported value of the measurand comprises the uncertainty due to random errors and the uncertainty of any corrections for systematic errors.

Systematic error, often referred to as bias, can be identified as a fixed value for a discrepancy and should be corrected at the earliest practical opportunity in the measurement process. Alternatively, random error indicates that the error fluctuates over the period of measurement, or from one set of measurements to the next. This variation may be caused by small continuous fluctuations in the environment, in the measuring instrument or at any point in the measurement process.

For this reason, it is more appropriate to refer to random error in the plural, as random errors. For example, when an instrument provides a digital reading, random errors may manifest themselves by a fluctuation in the least or least two or even more significant digit s in the output display. The range of the fluctuations is a measure of the uncertainty created by the random errors.

Today, many clinical laboratories have more than one instrument or analytical module which can perform the same group of tests. Laboratories with automated systems which incorporate several analytical modules providing the same test capability may provide uncertainty estimates for each of the measurands on a system basis irrespective of which module actually produced the result.

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How do we evaluate and state the full uncertainty in measurement and what does that statement mean to you as a customer of 3D Engineering Solutions? Let us first explain the factors commonly used to evaluate this. The first item we look at is the resolution of the gage. We find the resolution of the gage stated by the manufacturer as. Note that Mitutoyo uses a linear equation formula, similar to what we will use for our uncertainty, so it depends on the measured dimension Mitutoyo.

Since 3DES has a third party calibrate our metrology tools on regular intervals, we also need to review the measurement uncertainty of the calibration and include this number. At that point we look at the deviation between multiple measurements for single or multiple users. For the height gage we would use a registered standard such as a calibrated gage block, and then have one or more users take a single measurement multiple times.

From this data we glean the repeatability of personnel. With all of this data we can then come up with the Expanded Measurement Uncertainty for our height gage. There is quite a bit more going on here, but for brevity we have only covered the basic ideas. In metrology we must always consider this uncertainty when making a measurement.

Confidence in Measurements Related to uncertainty is the concept of confidence. This is assigning limits to our uncertainty. We would be more confident in saying that the bolt is mm plus or minus 10 mm than we would be in saying it is within 5 mm.

In metrology we must be very clear about the level of our uncertainty at a given confidence level. We can carry out an uncertainty evaluation which includes analysis and experiments to determine the uncertainty of a measurement.

Most uncertainties follow the normal distribution. Standard deviations and the normal distribution are explained in detail in Part 2: Uncertainty of Measurement. Many Variable Quantities are Distributed Normally: with Calibration and Traceability in Metrology It is very important that we are all using the same standards of measurement around the world.

When parts are manufactured the machines are set and the finished parts are checked using measurements. By using the same standards of measurement we know that a nut made in China will fit to a bolt made in the USA. Calibration is the way that the standards are transferred from one country to another, and from one instrument to another. The primary reference standards for the SI units of measurement are held in France and each country compares their national standards against these.

Calibration simply means comparing one measurement with another. For example when a ruler is made it might be compared with a reference ruler to determine where the markings are positioned. This is a simple calibration. The markings will not be at exactly the same positions as the ones on the reference ruler; there will be some uncertainty in the calibration process. The reference ruler itself will also not have markings at exactly the right positions since there was some uncertainty when it was calibrated.