INTRODUCTION TO METROLOGY DEFINITIONS n Metrology is the

INTRODUCTION TO METROLOGY

DEFINITIONS n Metrology is the study of measurements n Measurements are quantitative observations; numerical descriptions lseidman@matcmadison. edu

OVERVIEW n This longer lecture explores general principles of metrology n Next 3 shorter lectures apply principles to specific measurements: weight, volume, p. H n Later will talk about measuring light transmittance (spectrophotometry) lseidman@matcmadison. edu

WE WANT TO MAKE “GOOD” MEASUREMENTS n Making measurements is woven throughout daily life in a lab. n Often take measurements for granted, but measurements must be “good”. n What is a “good” measurement? lseidman@matcmadison. edu

EXAMPLE n n A man weighs himself in the morning on his bathroom scale, 172 pounds. Later, he weighs himself at the gym, 173 pounds. lseidman@matcmadison. edu

QUESTIONS n How much does he really weigh? lseidman@matcmadison. edu

n Do you trust one or other scale? Which one? Could both be wrong? Do you think he actually gained a pound? lseidman@matcmadison. edu

n Are these “good measurements”? lseidman@matcmadison. edu

NOT SURE n We are not exactly certain of the man’s true weight because: q q Maybe his weight really did change – always sample issues Maybe one or both scales are wrong – always instrument issues lseidman@matcmadison. edu

DO WE REALLY CARE? n Do you care if he really gained a pound? n How many think “give or take” a pound is OK? lseidman@matcmadison. edu

ANOTHER EXAMPLE n Suppose a premature baby is weighed. The weight is recorded as 5 pounds 3 ounces and the baby is sent home. n Do we care if the scale is off by a pound? lseidman@matcmadison. edu

“GOOD” MEASUREMENTS n A “good” measurement is one that can be trusted when making decisions. n We just made judgments about scales. n We make this type of judgment routinely. lseidman@matcmadison. edu

IN THE LAB n n Anyone who works in a lab makes judgments about whether measurements are “good enough” – q but often the judgments are made subconsciously q differently by different people Want to make decisions q Conscious q Consistent lseidman@matcmadison. edu

QUALITY SYSTEMS n All laboratory quality systems are concerned with measurements n All want “good” measurements n Some language is quoted in your lab manual lseidman@matcmadison. edu

NEED n Awareness of issues so can make “good” measurements. n Language to discuss measurements. n Tools to evaluate measurements. lseidman@matcmadison. edu

METROLOGY VOCABULARY n Very precise science with imprecise vocabulary q n (word “precise” has several precise meanings that are, without uncertainty, different) Words have multiple meanings, but specific meanings lseidman@matcmadison. edu

VOCABULARY n Units of measurement n Standards Calibration Traceability Tolerance n n n n Accuracy Precision Errors Uncertainty

UNITS OF MEASUREMENT n n n Units define measurements Example, gram is the unit for mass What is the mass of a gram? How do we know? lseidman@matcmadison. edu

DEFINITIONS MADE BY AGREEMENT n Definitions of units are made by international agreements, SI system q q Example, kilogram prototype in France K 10 and K 20 at NIST lseidman@matcmadison. edu

EXTERNAL AUTHORITY n n Measurements are always made in accordance with external authority Early authority was Pharaoh’s arm length lseidman@matcmadison. edu

n n A standard is an external authority Also, standard is a physical embodiment of a unit lseidman@matcmadison. edu

STANDARDS ARE: n Physical objects, the properties of which are known with sufficient accuracy to be used to evaluate other items. lseidman@matcmadison. edu

STANDARDS ARE AFFECTED BY THE ENVIRONMENT n Units are unaffected by the environment, but standards are q q Example, Pharaoh’s arm length might change Example, a ruler is a physical embodiment of centimeters n n Can change with temperature But cm doesn’t change lseidman@matcmadison. edu

STANDARDS ALSO ARE: n In chemical and biological assays, substances or solutions used to establish the response of an instrument or assay method to an analyte n See these in spectrophotometry labs lseidman@matcmadison. edu

STANDARDS ALSO ARE: n Documents established by consensus and approved by a recognized body that establish rules to make a process consistent q q Example ISO 9000 ASTM standard method calibrating micropipettor lseidman@matcmadison. edu

CALIBRATION IS: n n Bringing a measuring system into accordance with external authority, using standards For example, calibrating a balance q q q Use standards that have known masses Relate response of balance to units of kg Do this in lab lseidman@matcmadison. edu

PERFORMANCE VERIFICATION IS: n Check of the performance of an instrument or method without adjusting it. lseidman@matcmadison. edu

TOLERANCE IS: n Amount of error that is allowed in the calibration of a particular item. National and international standards specify tolerances. lseidman@matcmadison. edu

EXAMPLE n Standards for balance calibration can have slight variation from “true” value q q q Highest quality 100 g standards have a tolerance of + 2. 5 mg 99. 99975 -100. 00025 g Leads to uncertainty in all weight measurements lseidman@matcmadison. edu

TRACEABILITY IS: n The chain of calibrations, genealogy, that establishes the value of a standard or measurement n In the U. S. traceability for most physical and some chemical standards goes back to NIST lseidman@matcmadison. edu

TRACEABILITY n Note in this catalog example, “traceable to NIST”

VOCABULARY n n n Standards Calibration Traceability Tolerance Play with these ideas in labs lseidman@matcmadison. edu

ACCURACY AND PRECISION ARE: n n Accuracy is how close an individual value is to the true or accepted value Precision is the consistency of a series of measurements

EXPRESS ACCURACY % error = True value – measured value X 100% True value Will calculate this in volume lab lseidman@matcmadison. edu

EXPRESS PRECISION n Standard deviation q q n 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 lseidman@matcmadison. edu

ERROR IS: n Error is responsible for the difference between a measured value and the “true” value lseidman@matcmadison. edu

CATEGORIES OF ERRORS n Three types of error: q q q Gross Random Systematic lseidman@matcmadison. edu

GROSS ERROR n Blunders lseidman@matcmadison. edu

RANDOM ERROR n In U. S. , weigh particular 10 g standard every day. They see: q n 9. 999590 g, 9. 999601 g, 9. 999592 g …. What do you think about this? lseidman@matcmadison. edu

RANDOM ERROR n n Variability No one knows why They correct for humidity, barometric pressure, temperature Error that cannot be eliminated. Called “random error” lseidman@matcmadison. edu

RANDOM ERROR n Do you think that repeating the measurement over and over would allow us to be more certain of the “true” weight of this standard? lseidman@matcmadison. edu

RANDOM ERROR n Yes, because in the presence of only random error, the mean is more likely to be correct if repeat the measurement many times n Standard is probably really a bit light n Average of all the values is a good estimate of its true weight lseidman@matcmadison. edu

RANDOM ERROR AND ACCURACY n In presence of only random error, average value will tend to be correct n With only one or a few measurements, may or may not be accurate lseidman@matcmadison. edu

Mean Median Mode

THERE IS ALWAYS RANDOM ERROR n If can’t see it, system isn’t sensitive enough Less sensitive balance: 10. 00 g, 10. 00 g Versus 9. 999600 g… n lseidman@matcmadison. edu

SO… n n n Can we ever be positive of true weight of that standard? No There is uncertainty in every weight measurement lseidman@matcmadison. edu

RELATIONSHIP RANDOM ERROR AND PRECISION n Random error – q Leads to a loss of precision lseidman@matcmadison. edu

SYSTEMATIC ERROR n Defined as measurements that are consistently too high or too low, bias n Many causes, contaminated solutions, malfunctioning instruments, temperature fluctuations, etc. lseidman@matcmadison. edu

SYSTEMATIC ERROR n Technician controls sources of systematic error and should try to eliminate them, if possible q q Temperature effects Humidity effects Calibration of instruments Etc. lseidman@matcmadison. edu

n In the presence of systematic error, does it help to repeat measurements? lseidman@matcmadison. edu

SYSTEMATIC ERROR n Systematic error – q n Does impact accuracy Repeating measurements with systematic error does not improve the accuracy of the measurements lseidman@matcmadison. edu

ANOTHER DEFINTION OF ERROR IS: n Error = is the difference between the measured value and the “true” value due to any cause Absolute error = “True” value - measured value n Percent error is: “True” value - measured value (100 %) “True” value lseidman@matcmadison. edu

ERRORS AND UNCERTAINTY n n 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 lseidman@matcmadison. edu

UNCERTAINTY IS: n Estimate of the inaccuracy of a measurement that includes both the random and systematic components. lseidman@matcmadison. edu

UNCERTAINTY ALSO IS: n An estimate of the range within which the true value for a measurement lies, with a given probability level. lseidman@matcmadison. edu

UNCERTAINTY n Not surprisingly, it is difficult to state, with certainty, how much uncertainty there is in a measurement value. n But that doesn’t keep metrologists from trying … lseidman@matcmadison. edu

METROLOGISTS n n 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 lseidman@matcmadison. edu

REPORT VALUES n n Metrologists come up with a value for uncertainty You may see this in catalogues or specifications q Example: measured value + an estimate of uncertainty lseidman@matcmadison. edu

UNCERTAINTY ESTIMATES n Details are not important to us now n But principle is: any measurement, need to know where the important sources of error might be lseidman@matcmadison. edu

SIGNIFICANT FIGURES n One cause of uncertainty in all measurements is that the value for the measurement can only read to a certain number of places n This type of uncertainty. It is called “resolution error”. (It is often evaluated using Type B methods. ) lseidman@matcmadison. edu

SIIGNIFICANT FIGURE CONVENTIONS n n n Significant figure conventions are used to record the values from measurements Expression of uncertainty Also apply to very large counted values q Do not apply to “exact” values n n Counts where are certain of value Conversion factors lseidman@matcmadison. edu

ROUNDING CONVENTIONS n n n Combine numbers in calculations Confusing Look up rules when they need them lseidman@matcmadison. edu

RECORDING MEASURED VALUES n n n 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 lseidman@matcmadison. edu

ROUNDING n 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? lseidman@matcmadison. edu

n 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. lseidman@matcmadison. edu

n Look at all the problems for chapter 13. lseidman@matcmadison. edu

GOOD WEB SITE FOR SIGNIFICANT FIGURES n http: //antoine. frostburg. edu/cgibin/senese/tutorials/sigfig/index. cgi lseidman@matcmadison. edu

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

THERMOMETERS n n n Look at the values for 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 _______. lseidman@matcmadison. edu

THERMOMETERS n n Were they accurate? How could we figure out the “true” value for the temperature? lseidman@matcmadison. edu

REPEATING MEASUREMENTS n n 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? lseidman@matcmadison. edu

CALIBRATION n n n Calibration of 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 lseidman@matcmadison. edu

TOLERANCE n n Here is a catalog description of mercury thermometers. Are these thermometers out of the range for which their tolerance is specified? lseidman@matcmadison. edu

PRECISION n n Were they precise? How could precision be measured? Would calibration help to make them more precise? lseidman@matcmadison. edu

CALIBRATION n Calibration would probably not improve their precision lseidman@matcmadison. edu

RETURN TO OUR ORIGINAL TYPE OF QUESTION n n n Are our temperature measurements “good” measurements? How do you make that judgment? Can we trust them? lseidman@matcmadison. edu

THERMOMETERS – GOOD ENOUGH? n n 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. lseidman@matcmadison. edu

EXPLORE SOME OF THESE IDEAS n In lab: q q q Calibrate instruments Use standards Check performance of micropipettes Record measurement values Calculate per cent errors Calculate repeatability lseidman@matcmadison. edu