INTRODUCTION TO METROLOGY

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DEFINITIONS

Metrology is the study of measurements

Measurements are quantitative observations; numerical descriptions

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OVERVIEW

This longer lecture explores general principles of metrology

Next 3 shorter lectures apply principles to specific measurements: weight, volume, pH

Later will talk about measuring light transmittance (spectrophotometry)

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WE WANT TO MAKE “GOOD” MEASUREMENTS Making measurements is woven throughout

daily life in a lab.

Often take measurements for granted, but measurements must be “good”.

What is a “good” measurement?

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EXAMPLE

A man weighs himself in the morning on his bathroom scale, 172 pounds.

Later, he weighs himself at the gym,173 pounds.

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QUESTIONS

How much does he really weigh?

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Do you trust one or other scale? Which one? Could both be wrong? Do you think he actually gained a pound?

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Are these “good measurements”?

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NOT SURE

We are not exactly certain of the man’s true weight because: Maybe his weight really did change – always

sample issues Maybe one or both scales are wrong – always

instrument issues

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DO WE REALLY CARE?

Do you care if he really gained a pound?

How many think “give or take” a pound is OK?

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ANOTHER EXAMPLE

Suppose a premature baby is weighed. The weight is recorded as 5 pounds 3 ounces and the baby is sent home.

Do we care if the scale is off by a pound?

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“GOOD” MEASUREMENTS

A “good” measurement is one that can be trusted when making decisions.

We just made judgments about scales.

We make this type of judgment routinely.

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IN THE LAB

Anyone who works in a lab makes judgments about whether measurements are “good enough” – but often the judgments are made subconsciously differently by different people

Want to make decisions Conscious Consistent

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QUALITY SYSTEMS

All laboratory quality systems are concerned with measurements

All want “good” measurements

Some language is quoted in your lab manual

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NEED

Awareness of issues so can make “good” measurements.

Language to discuss measurements.

Tools to evaluate measurements.

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METROLOGY VOCABULARY

Very precise science with imprecise vocabulary (word “precise” has several precise meanings that

are, without uncertainty, different)

Words have multiple meanings, but specific meanings

VOCABULARY

Units of measurement

Standards Calibration Traceability Tolerance

Accuracy Precision Errors Uncertainty

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UNITS OF MEASUREMENT

Units define measurements Example, gram is the unit for mass What is the mass of a gram? How do we

know?

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DEFINITIONS MADE BY AGREEMENT Definitions of units are made by international

agreements, SI system Example, kilogram prototype in France K10 and K20 at NIST

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EXTERNAL AUTHORITY

Measurements are always made in accordance with external authority

Early authority was Pharaoh’s arm length

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A standard is an external authority Also, standard is a physical embodiment

of a unit

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STANDARDS ARE:

Physical objects, the properties of which are known with sufficient accuracy to be used to evaluate other items.

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STANDARDS ARE AFFECTED BY THE ENVIRONMENT Units are unaffected by the environment, but

standards are Example, Pharaoh’s arm length might change Example, a ruler is a physical embodiment of

centimeters Can change with temperature But cm doesn’t change

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STANDARDS ALSO ARE:

In chemical and biological assays, substances or solutions used to establish the response of an instrument or assay method to an analyte

See these in spectrophotometry labs

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STANDARDS ALSO ARE:

Documents established by consensus and approved by a recognized body that establish rules to make a process consistent Example ISO 9000 ASTM standard method calibrating micropipettor

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CALIBRATION IS:

Bringing a measuring system into accordance with external authority, using standards

For example, calibrating a balance Use standards that have known masses Relate response of balance to units of kg Do this in lab

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PERFORMANCE VERIFICATION IS: Check of the performance of an instrument or

method without adjusting it.

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TOLERANCE IS:

Amount of error that is allowed in the calibration of a particular item. National and international standards specify tolerances.

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EXAMPLE

Standards for balance calibration can have slight variation from “true” value Highest quality 100 g standards have a tolerance

of + 2.5 mg 99.99975-100.00025 g Leads to uncertainty in all weight measurements

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TRACEABILITY IS:

The chain of calibrations, genealogy, that establishes the value of a standard or measurement

In the U.S. traceability for most physical and some chemical standards goes back to NIST

TRACEABILITY

Note in this catalog example, “traceable to NIST”

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VOCABULARY

Standards Calibration Traceability Tolerance Play with these ideas in labs

ACCURACY AND PRECISION ARE: Accuracy is how close an individual value is

to the true or accepted value Precision is the consistency of a series of

measurements

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EXPRESS ACCURACY

% error = True value – measured value X 100%

True value

Will calculate this in volume lab

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EXPRESS PRECISION

Standard deviation Expression of variability Take the mean (average) Calculate how much each measurement deviates

from mean Take an average of the deviation, so it is the

average deviation from the mean Try this in the volume lab

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ERROR IS:

Error is responsible for the difference between a measured value and the “true” value

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CATEGORIES OF ERRORS

Three types of error: Gross Random Systematic

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GROSS ERROR

Blunders

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RANDOM ERROR

In U.S., weigh particular 10 g standard every day. They see: 9.999590 g, 9.999601 g, 9.999592 g ….

What do you think about this?

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RANDOM ERROR

Variability No one knows why They correct for humidity, barometric

pressure, temperature Error that cannot be eliminated. Called

“random error”

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RANDOM ERROR

Do you think that repeating the measurement over and over would allow us to be more certain of the “true” weight of this standard?

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RANDOM ERROR

Yes, because in the presence of only random error, the mean is more likely to be correct if repeat the measurement many times

Standard is probably really a bit light

Average of all the values is a good estimate of its true weight

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RANDOM ERROR AND ACCURACY In presence of only random error, average

value will tend to be correct

With only one or a few measurements, may or may not be accurate

MeanMedianMode

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THERE IS ALWAYS RANDOM ERROR If can’t see it, system isn’t sensitive enough

Less sensitive balance: 10.00 g,

10.00 g, 10.00 g

Versus 9.999600 g…

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SO…

Can we ever be positive of true weight of that standard?

No There is uncertainty in every weight

measurement

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RELATIONSHIP RANDOM ERROR AND PRECISION Random error –

Leads to a loss of precision

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SYSTEMATIC ERROR

Defined as measurements that are consistently too high or too low, bias

Many causes, contaminated solutions, malfunctioning instruments, temperature fluctuations, etc., etc.

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SYSTEMATIC ERROR

Technician controls sources of systematic error and should try to eliminate them, if possible Temperature effects Humidity effects Calibration of instruments Etc.

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In the presence of systematic error, does it help to repeat measurements?

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SYSTEMATIC ERROR

Systematic error – Does impact accuracy

Repeating measurements with systematic error does not improve the accuracy of the measurements

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ANOTHER DEFINTION OF ERROR IS: Error = is the difference between the measured

value and the “true” value due to any cause

Absolute error = “True” value - measured value

Percent error is:“True” value - measured value (100 %)

“True” value

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ERRORS AND UNCERTAINTY

Errors lead to uncertainty in measurements Can never know the exact, “true” value for

any measurement. Idea of a “true” value is abstract – never

knowable. In practice, get close enough

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UNCERTAINTY IS:

Estimate of the inaccuracy of a measurement that includes both the random and systematic components.

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UNCERTAINTY ALSO IS:

An estimate of the range within which the true value for a measurement lies, with a given probability level.

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UNCERTAINTY

Not surprisingly, it is difficult to state, with certainty, how much uncertainty there is in a measurement value.

But that doesn’t keep metrologists from trying …

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METROLOGISTS

Metrologists try to figure out all the possible sources of uncertainty and estimate their magnitude

One or another factor may be more significant. For example, when measuring very short lengths with micrometers, care a lot about repeatability. But, with measurements of longer lengths, temperature effects are far more important

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REPORT VALUES

Metrologists come up with a value for uncertainty

You may see this in catalogues or specifications Example:

measured value + an estimate of uncertainty

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UNCERTAINTY ESTIMATES

Details are not important to us now

But principle is: any measurement, need to know where the important sources of error might be

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SIGNIFICANT FIGURES

One cause of uncertainty in all measurements is that the value for the measurement can only read to a certain number of places

This type of uncertainty. It is called “resolution error”. (It is often evaluated using Type B methods.)

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SIIGNIFICANT FIGURE CONVENTIONS Significant figure conventions are used to

record the values from measurements Expression of uncertainty Also apply to very large counted values

Do not apply to “exact” values Counts where are certain of value Conversion factors

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ROUNDING CONVENTIONS

Combine numbers in calculations Confusing Look up rules when they need them

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RECORDING MEASURED VALUES Record measured values (or large counts) with

correct number of significant figures Don’t add extra zeros; don’t drop ones that are

significant With digital reading, record exactly what it says;

assume the last value is estimated With analog values, record all measured values plus

one that is estimated Discussed in Laboratory Exercise 1

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ROUNDING

A Biotechnology company specifies that the level of RNA impurities in a certain product must be less than or equal to 0.02%. If the level of RNA in a particular lot is 0.024%, does that lot meet the specifications?

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The specification is set at the hundredth decimal place. Therefore, the result is rounded to that place when it is reported. The result rounded is therefore 0.02%, and it meets the specification.

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Look at all the problems for chapter 13.

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GOOD WEB SITE FOR SIGNIFICANT FIGURES http://antoine.frostburg.edu/cgi-bin/senese/

tutorials/sigfig/index.cgi

Match these descriptions with the 4 distributions in the figure:

Good precision, poor accuracy

Good accuracy, poor precision

Good accuracy, good precision

Poor accuracy, poor precision

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THERMOMETERS

Look at the values for the thermometers on the board.

Significant figure conventions can guide us in how to record the value that we read off any measuring instrument.

With these thermometers, correct number of sig figs is _______.

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THERMOMETERS

Were they accurate? How could we figure out the “true” value for

the temperature?

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REPEATING MEASUREMENTS

Would repeating measurements with these thermometers, assuming we did not calibrate them, improve our ability to trust them?

Is their error an example of random or systematic error?

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CALIBRATION

Calibration of the thermometers could lead to increased accuracy

This is a type of systematic error In the presence of systematic error, repeating

the measurement will not improve its accuracy

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TOLERANCE

Here is a catalog description of mercury thermometers.

Are these thermometers out of the range for which their tolerance is specified?

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PRECISION

Were they precise? How could precision be measured?

Would calibration help to make them more precise?

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CALIBRATION

Calibration would probably not improve their precision

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RETURN TO OUR ORIGINAL TYPE OF QUESTION Are our temperature measurements “good”

measurements? How do you make that judgment? Can we trust them?

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THERMOMETERS – GOOD ENOUGH? Are times that we need to be very close in

temperature measurements. For example PCR is fairly picky.

Other times we can be pretty far off and process will still work.

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EXPLORE SOME OF THESE IDEAS In lab:

Calibrate instruments Use standards Check performance of micropipettes Record measurement values Calculate per cent errors Calculate repeatability