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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Measurement Basics

Outline: Principles of measurement Error Analysis“Propagation of error”

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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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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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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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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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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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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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Measurement Basics

Accuracy and Precision are independent

Accurate measurement – small systematic error

Precise measurement – small random variation (random error)

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Measurement Basics

Poor Accuracy

Poor Precision

Poor Accuracy

Good Precision

Good Accuracy

Poor Precision

Good Accuracy

Good Precision

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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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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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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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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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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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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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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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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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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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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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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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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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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

1 cm4110 unit operations lab measurement basics fundamentals of measurement and data analysis d....

Documents

measurement error uncertainty

experimental error slide

fixed error

manufacturers data slide

common sense slide

precision specs

data analysis

experimental strategy