Process Measurement & Process Capability Variable Data Measurement Study Fundamentals Measurement Study Fundamentals Measurement Study (Tools) Measurement.

Process Measurement & Process Measurement & Process CapabilityProcess Capability

Variable DataVariable Data

Measurement Study FundamentalsMeasurement Study Fundamentals Measurement Study (Tools)Measurement Study (Tools) Measurement CapabilityMeasurement Capability FormulasFormulas Gage D&P Study – ANOVA MethodGage D&P Study – ANOVA Method Gage Run ChartGage Run Chart Gage Linearity and Bias Accuracy StudyGage Linearity and Bias Accuracy Study

Measurement Study Measurement Study FundamentalsFundamentals Measurement System can have bothMeasurement System can have both

– BiasBias– VariationVariation

FormulasFormulas– Bias: Bias: µµ observed observed = = µµ actual (part) + actual (part) + µµ

measurement systemmeasurement system– Variation: Variation: 22 observed observed (total) = (total) = 22 o actual o actual

(part) + (part) + 22 measurement systemmeasurement system

Where Where µµ is the meanis the mean

22 is the variance is the variance

Possible Sources of Variation for a Possible Sources of Variation for a Process and Its Measurement SystemProcess and Its Measurement System

Parts(Example)

• Observations•Measurements•Data

Definition of TermsDefinition of Terms LinearityLinearity

– A measure of how the size of a part affects the accuracy of the A measure of how the size of a part affects the accuracy of the measurement system. It is the difference in the observed accuracy measurement system. It is the difference in the observed accuracy values through the expected range of measurements.values through the expected range of measurements.

AccuracyAccuracy– A measure of the bias in the measurement system. It is the difference A measure of the bias in the measurement system. It is the difference

between the observed measurement and a master value.between the observed measurement and a master value. Stability (Drift)Stability (Drift)

– A measure of how accurately a system performs over time. It is the A measure of how accurately a system performs over time. It is the total variation obtained with a particular measurement instrument, on total variation obtained with a particular measurement instrument, on the same part, when measuring a single characteristic over time.the same part, when measuring a single characteristic over time.

PrecisionPrecision– Precision or measurement variation is the variation due to a Precision or measurement variation is the variation due to a

measurement system and can be broken down into the following two measurement system and can be broken down into the following two components:components:

RepeatabilityRepeatability– The variation observed when the same operatior measures the sam part The variation observed when the same operatior measures the sam part

repeatedly with the same device.repeatedly with the same device. ReproductibilityReproductibility

– The variation observed when different operators measure the same The variation observed when different operators measure the same parts using the same insturment. parts using the same insturment.

Measurement IssuesMeasurement Issues

The bottom line is that we really want to The bottom line is that we really want to answer the following questions:answer the following questions:– How large is the measurement bias?How large is the measurement bias?– How big is the measurement variation?How big is the measurement variation?– What are the sources of bias and measurement What are the sources of bias and measurement

variation?variation?– Is the measurement instrument stable over Is the measurement instrument stable over

time?time?– How capable is the instrument for measuring How capable is the instrument for measuring

the part alignment?the part alignment?– How can we improve the measurement How can we improve the measurement

system?system?

Measurement Study (Tools)Measurement Study (Tools) Gage Run chart:Gage Run chart:

– A plot of all observations by operator and part number. A horizontal A plot of all observations by operator and part number. A horizontal reference line is drawn at the mean, which can be calculated from the data, reference line is drawn at the mean, which can be calculated from the data, or a value can be entered from prior knowledge of the process. You can or a value can be entered from prior knowledge of the process. You can use this chart to quickly assess differences in measurements between use this chart to quickly assess differences in measurements between different operators and parts. A stable process would give you a random different operators and parts. A stable process would give you a random horizontal scattering of pointsw; an operator or part effect would give you horizontal scattering of pointsw; an operator or part effect would give you some kind of pattern in the plot.some kind of pattern in the plot.

Gage R&R Study:Gage R&R Study:– Determines how much of the obgserved process variation is due to Determines how much of the obgserved process variation is due to

measurement system variation. Either of two methods can be used to measurement system variation. Either of two methods can be used to perform this analysis, the latter being more informative: (a) X and R, or (b) perform this analysis, the latter being more informative: (a) X and R, or (b) ANOVA (Analysis of Variance). The X and R method breaks down the overall ANOVA (Analysis of Variance). The X and R method breaks down the overall variation into three categories: (1)part-to-part, (2) repeatability, and (3) variation into three categories: (1)part-to-part, (2) repeatability, and (3) reproducibility. The ANOVA method goes one step further and breaks down reproducibility. The ANOVA method goes one step further and breaks down reproducibility into its operator and operator by part interaction.reproducibility into its operator and operator by part interaction.

Gage Lineaity and Accuracy Study:Gage Lineaity and Accuracy Study:– Tells how accurate the measurements are through the expected range of Tells how accurate the measurements are through the expected range of

the measurements. It answers the question, "Does the gage have the same the measurements. It answers the question, "Does the gage have the same accuracy for all sizes of parts or objects being measured?" A gage accuracy accuracy for all sizes of parts or objects being measured?" A gage accuracy study examines the difference between the observed average study examines the difference between the observed average measurement and a reference or master value. It answers the question, measurement and a reference or master value. It answers the question, "How accurate is the measurement instrument when compared to a master "How accurate is the measurement instrument when compared to a master value?"value?"

Measurement CapabilityMeasurement Capability

Precision-to-Tolerance (P/T) Ratio:Precision-to-Tolerance (P/T) Ratio:– It is usually 5.15 * total gage R&R standard It is usually 5.15 * total gage R&R standard

deviation (obtained from the ouptut of the Gage deviation (obtained from the ouptut of the Gage R&R Study) divided by the tolerance, I.e.,R&R Study) divided by the tolerance, I.e.,

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Process Measurement – Classroom ExerciseProcess Measurement – Classroom Exercise

wherewhere

USL, LSL are the upper and lower specification limits USL, LSL are the upper and lower specification limits respectivelyrespectively

If the P/T ratio is <10%, the measurement instrument is If the P/T ratio is <10%, the measurement instrument is considered acceptable; if it is between 10% and 30%, it is considered acceptable; if it is between 10% and 30%, it is marginal; and greater than 30% it is unacceptable."marginal; and greater than 30% it is unacceptable."

FormulasFormulasGage R&R Study ANOVA MethodGage R&R Study ANOVA Method

F TestsF Tests

Gage R&R Table . . . Var Comp for Gage R&R Table . . . Var Comp for ANOVA MethodANOVA Method

(Operator * Part Not included)(Operator * Part Not included)

Number of Distinct Categories Number of Distinct Categories (Resolution)(Resolution) Represents number of non-overlapping Represents number of non-overlapping

confidence intervals that will span the confidence intervals that will span the range of product variation. Think of it as range of product variation. Think of it as the number of groups within process data the number of groups within process data that measurement system can discern:that measurement system can discern:

Rule: Good number should be equal to or greater than 5.

Gage Run ChartGage Run Chart

ShowsShows– Part-to-Part VariationPart-to-Part Variation– Operator-to-Operator VariationOperator-to-Operator Variation– Repeatability (Variation within each Repeatability (Variation within each

data group)data group)

Gage Linearity & Bias Gage Linearity & Bias (Accuracy) Study(Accuracy) Study LinearityLinearity

– Measures how accurate measurements are Measures how accurate measurements are through their expected range. It answers the through their expected range. It answers the question, "Does my gage have the same question, "Does my gage have the same accuracy for all sizes of objects being measured?"accuracy for all sizes of objects being measured?"

% Linearity% Linearity– Linearity expressed as a percent of the overall Linearity expressed as a percent of the overall

process variationprocess variation

Gage BiasGage Bias

BiasBias– The actual measurment minus the The actual measurment minus the

corresponding reference valuecorresponding reference value % Bias% Bias

– Bias expressed as a percent of the overall Bias expressed as a percent of the overall process variationprocess variation