# Chapter 21 Measurement Analysis. Measurement It is important to define and validate the measurement system before collecting data. Without measurement.

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Chapter 1 Making Economic Decisions

Chapter 21

Measurement AnalysisMeasurementIt is important to define and validate the measurement system before collecting data.Without measurement we only have opinionsThe measurement system is the complete process used to obtain measurements.Measurement error is inevitable. We must identify, evaluate, and control the sources of measurement error.Any variation can be attributed to either the characteristic that is being measured, or the way the measurements are being taken.

Measurement

Sources of errorMeasurement error = the effect of all sources of measurement variability that cause an observed value to deviate from the true value being measured.Measuring instrument errors:AccuracyLinearityStabilityPrecisionMeasuring system errorsRepeatabilityReproducibilityDefining ErrorAccuracy = difference between the observed average and reference value.Linearity = change in accuracy across the expected operating range of the measuring instrumentStability = consistency in the measurement over timePrecision = standard deviation between measurements

Repeatability = variation obtained by one operator measuring the same characteristic with the same instrumentReproducibility = variation in the average of measurements taken by different operators using the same instrument.How to measure error?Multiple measurements of one single characteristicPrecision: Standard deviation among measurementsAccuracy: Difference between the observed average and the reference valueMeasurement System Analysis (MSA) =when precision and accuracy measurements are assed in combinationAttribute and Variable Gage studiesReproducibilityRepeatabilityTransactionsMeasurement evaluation studies can apply however it may not be economically viable

How to measure error?Measurement system bias: assessed via the calibration programObserved value = master value + measurement offsettotal = product + measurement system

Measurement system variability: assessed via the variable R&R studyObserved variability = product variability+ measurement variability2total = 2product + 2measurement system Defining sources of errorCE (fishbone) diagram can be helpful in representing potential causes of measurement error (so they can be addressed) Measurement, material, manpower, mother nature, methods and machinesThink of a process (MSA) for measuring a part. What are some of the causes of measurement error that you can think of?Define the variables that can influence the measurement system.MINITAB Output of analysisControl charts (X-Bar and R)Show discrimination, stability and variation in the range of measurements for each partANOVAFor estimating error source and their contribution to overall variabilityLinear RegressionEstimate the linearity of system responseCharts and ScatterplotsUsed to study variation between and across operators and parts

Gage R&RAttribute Gage R&RAt least 2 operators measure 20 parts at random (twice each).If there is little consistency between operators then the measurement system must be improved.Variable Gage R&R Three operators measure 10 parts with the same nominal dimension in a random order, 3 times each.Can by analyzed by X-Bar and R charts or with ANOVA method.Crossed Gage R&RExample 21.6Used for determining which portion of the variability in measurements may be due to the measurement system.n=units; 2 n 10m= appraisers; 2 m 3w= trials; 2 w 3Total should be 20Use the MINITAB function:Stat>Quality tools>Gage Study>Gage R&R Study (crossed)Examine the Xbar / R charts, what do they tell usExamine the AVONA results

(DATA set in appendix)Example 21.6Opt1-Rep1Opt1-Rep2Opt2-Rep1Opt2-Rep 2PartOperatorMeasurement9011.609011.409011.409011.50119011.69012.409012.209012.209012.10219012.49013.009012.809012.809012.80319013.09012.609012.409012.409012.50419012.69009.809009.809009.609009.80519009.89013.209013.209013.209013.00619013.29013.409013.209013.209013.20719013.49012.209013.209012.209012.30819012.29014.009013.809013.809013.80919013.89011.609011.409011.409011.60119011.49012.409012.209012.209012.10219012.29013.009012.809012.809012.80319012.89012.609012.409012.509012.50419012.49009.809009.809009.809009.80519009.89013.209013.209013.009013.00619013.29013.409013.209013.209013.20719013.29012.209012.009012.309012.30819012.09014.009013.809013.809013.80919014.09011.609011.409011.509011.50129011.69012.409012.209012.109012.10229012.49013.009012.809012.809012.80329013.09012.609012.409012.509012.50429012.69009.809009.809009.809009.80529000.89013.209013.209013.009013.00629013.29013.409013.209013.209013.20729013.49012.209012.009012.309012.30829012.29014.009013.809013.809013.80929013.89011.609011.409011.509011.50129011.49012.409012.209012.109012.10229012.29013.009012.809012.809012.80329012.89012.609012.409012.509012.50429012.49006.809009.809009.809009.80529009.89013.209013.209013.009013.00629013.29013.409013.209013.209013.20729013.29012.209012.009012.309012.30829012.09012.209012.209012.309012.30929012.0Attribute Gage R&R StudyExample 21.7Evaluates the consistency between measurement decisions to accept or reject. Use the MINITAB function:Attribute agreement analysisWhat does the data tell us?

(DATA set in appendix)

Remember that attribute-based measurement system cannot indicated how good or how bad a part is, only if it was rejected or accepted. Sample NumberAttributeOp1 Try1Op1 Try2Op2 Try1Opt2 Try2Op3 Try1Op3 Try2Agree Y/NAgree2 Y/N1PassPassPassPassPassFailFailnn2PassPassPassPassPassFailFailnn3FailFailFailFailPassFailFailnn4FailFailFailFailFailFailFailyy5FailFailFailPassFailFailFailnn6PassPassPassPassPassPassPassyy7PassFailFailFailFailFailFailyn8PassPassPassPassPassPassPassyy9FailPassPassPassPassPassPassyn10FailPassPassFailFailFailFailnn11PassPassPassPassPassPassPassyy12PassPassPassPassPassPassPassyy13FailFailFailFailFailFailFailyy14FailFailFailPassFailFailFailnn15PassPassPassPassPassFailFailnn16PassPassPassPassPassFailFailnn17FailFailFailFailPassFailFailnn18FailFailFailFailFailFailFailyy19FailFailFailPassFailFailFailnn20PassPassPassPassPassPassPassyy21PassFailFailFailFailFailFailyn22PassPassPassPassPassPassPassyy23FailPassPassPassPassPassPassyn24FailPassPassFailFailFailFailnn25PassPassPassPassPassPassPassyy26PassPassPassPassPassPassPassyy27FailFailFailFailFailFailFailyy28FailFailFailPassFailFailFailnn29PassPassPassPassPassFailFailnn30PassPassPassPassPassFailFailnnTest PartsMaster Expert1Good2Bad3Good4Good5Good6Good7Good8Good9Bad10Bad11Good12Bad13Bad14Bad15Bad16Good17Bad18Bad19Good20Bad21Good22Bad23Bad24Bad25Good26Good27Bad28Good29Good30GoodWhat do the numbers tell us?As a general rule of thumb:R&R indices > 30% are considered unacceptableNumber of distinct categories indices

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