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Transcript of 1 CM4110 Unit Operations Lab Measurement Basics Fundamentals of Measurement and Data Analysis D....
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CM4110Unit Operations Lab
Measurement Basics
Fundamentalsof
Measurement and Data Analysis
D. CasparySeptember, 2008
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CM4110Unit Operations Lab
Measurement Basics
Outline: Principles of measurement Error Analysis“Propagation of error”
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CM4110Unit Operations Lab
Measurement Basics
Principles of Measurement
Nothing can be measured exactly
Measurements are approximations of true value of a characteristic or property
Associated with every measurement is “uncertainty” or “error”
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CM4110Unit Operations Lab
Measurement Basics
Principles of Measurement
Uncertainty is introduced thru Instrument Error (or Reading /Measurement Error)
Uncertainty is observed as fluctuations in replicated experimental data called Experimental Error
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CM4110Unit Operations Lab
Measurement Basics
Reporting Measured Values
Engineering and scientific reporting must be ethical and honest – always report appropriate estimate of uncertainty with the results
Learn/ Use appropriate statistical tools
Use common sense
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CM4110Unit Operations Lab
Measurement Basics
Example problem statement :
“Calculate the overall heat transfer coefficient for a shell and tube heat exchanger.”
How will Instrument and Experimental Error affect the calculated results?
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CM4110Unit Operations Lab
Measurement Basics
Planning your experimental strategy:
What is known? from mfg. data, tables, etc. What do I need to measure?
What instruments are available?What is the precision of each instrument?And, what about accuracy in measurements?How will precision and accuracy of these instruments affect the calculated results?
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CM4110Unit Operations Lab
Measurement Basics
Instrument Error can show up as:
Systematic error – determinate (or fixed) error – defines accuracy
Random error – indeterminate error associated with the instrument
– defines precision
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CM4110Unit Operations Lab
Measurement Basics
Accuracy and Precision are independent
Accurate measurement – small systematic error
Precise measurement – small random variation (random error)
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CM4110Unit Operations Lab
Measurement Basics
Poor Accuracy
Poor Precision
Poor Accuracy
Good Precision
Good Accuracy
Poor Precision
Good Accuracy
Good Precision
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CM4110Unit Operations Lab
Measurement Basics
Reporting Instrument Error
For analog scalesTypically plus or minus ½ the smallest increment
For digital readoutsReport the value as displayed, then look up
accuracy and precision spec’s in manufacturer’s data
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CM4110Unit Operations Lab
Error Analysis
Estimating Experimental Error – again, the Experimental Strategy
Usually you will perform a set of experiments: How many replicates of each test should you
perform? How will variation in each replicate affect the
result?
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CM4110Unit Operations Lab
Error Analysis
Three Types of Experimental Error
Gross error – mistakes
Systematic error – determinate (or fixed) error. Correct this first!
Random error – indeterminate error. Use statistics to extimate.
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CM4110Unit Operations Lab
Error Analysis
… liars, damned liars, and statisticians…
“Your goal is to present the Location and Dispersion of your results.”
Wheeler and Chambers, Understanding Statistical Process Control, SPC Press, 1992
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CM4110Unit Operations Lab
Error Analysis
Location of Data
With three or more replicates typically report the Average
With a single value (or 2 values), report the value(s).
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CM4110Unit Operations Lab
Error Analysis
Dispersion of Data
RangeLowest value and highest valueOften used for small data setsEasy to report
Not used for our purposes as it hides data – says nothing about the dispersion of the “middle values”
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CM4110Unit Operations Lab
Error Analysis
Dispersion of Data
RMS Deviation (aka Standard Deviation)calculate the average for the sample setcalculate the deviation from the average for each valuesquare the individual deviationssum all the squares of the deviationsfind the average squared deviationtake the square root of the average squared deviation
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CM4110Unit Operations Lab
Error Analysis
Dispersion of Data
Standard Deviation (aka Average Std. Dev.)Calculate like RMS deviation except use (n-1) in the denominator when calculating the average squared deviationAs data set gets large, Std. Dev. approaches the value for RMS Dev.
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CM4110Unit Operations Lab
Error Analysis
Rules of Thumb
Be realistic (honest) in reporting the measurement error or uncertainty.Normally report Average, Error, and sample size for UO Lab measurementsDo not hide data.Do not allow yourself to adjust the results to match some “expected value”.
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CM4110Unit Operations Lab
Error Analysis
Discarding DataBad Data caused by obvious blunders can be discarded if it has “assignable cause”
“Unexplained” Data cannot be discarded because it doesn’t meet our
expectations no assignable cause (is random)
Any data filtering must be consistent and unbiased.
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CM4110Unit Operations Lab
Propagation of Error
Estimating the error in your calculated results:
The Error in measured quantities that are arithmetically combined must also be combined.
Use standard practice for “propagating” error through calculations.
Error can be reported in EU’s or %.
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CM4110Unit Operations Lab
Propagation of Error
Text ReferencesUnderstanding Statistical Process Control, 2nd
edition, D.J. Wheeler, D.S. Chambers, SPC Press, 1992.
Experimental Methods for Engineers, 3rd edition, J.P. Holman, McGraw-Hill, 1978.
Data Reduction and Error Analysis for the Physical Sciences, P.R. Bevington, Mcgraw-Hill, 1969.
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CM4110Unit Operations Lab
Propagation of Error
Web References
http://science.widener.edu/svb/stats/error.html – shows how to arithmetically combine
individual errors to get error in calculated result.
http://www.upscale.utoronto.ca/PVB/Harrison/ErrorAnalysis/Propagation.html – propagation of error and error analysis for all
situationsDr. Pintar’s Error Analysis Handout – link on course web page for definitions and a
worked out example from actual UO Lab data