Transcript Process Measurement & Process Capability Variable Data

Process Measurement &
Process Capability
Variable Data
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Measurement Study Fundamentals
Measurement Study (Tools)
Measurement Capability
Formulas
Gage D&P Study – ANOVA Method
Gage Run Chart
Gage Linearity and Bias Accuracy Study
Measurement Study Fundamentals
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Measurement System can have both
– Bias
– Variation
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Formulas
– Bias: µ observed = µ actual (part) + µ measurement
system
– Variation:  2 observed (total) =  2 o actual (part) +
 2 measurement system
Where µ is the mean
 2 is the variance
Possible Sources of Variation for a
Process and Its Measurement System
Parts
(Example)
• Observations
•Measurements
•Data
Definition of Terms
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Linearity
– A measure of how the size of a part affects the accuracy of the measurement
system. It is the difference in the observed accuracy values through the expected
range of measurements.
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Accuracy
– A measure of the bias in the measurement system. It is the difference between
the observed measurement and a master value.
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Stability (Drift)
– A measure of how accurately a system performs over time. It is the total
variation obtained with a particular measurement instrument, on the same part,
when measuring a single characteristic over time.
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Precision
– Precision or measurement variation is the variation due to a measurement system
and can be broken down into the following two components:
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Repeatability
– The variation observed when the same operatior measures the sam part
repeatedly with the same device.
Reproductibility
– The variation observed when different operators measure the same parts using the
same insturment.
Measurement Issues
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The bottom line is that we really want to answer
the following questions:
– How large is the measurement bias?
– How big is the measurement variation?
– What are the sources of bias and measurement
variation?
– Is the measurement instrument stable over time?
– How capable is the instrument for measuring the part
alignment?
– How can we improve the measurement system?
Measurement Study (Tools)
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Gage Run chart:
– 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, or a value can
be entered from prior knowledge of the process. You can use this chart to quickly
assess differences in measurements between different operators and parts. A
stable process would give you a random horizontal scattering of pointsw; an
operator or part effect would give you some kind of pattern in the plot.
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Gage R&R Study:
– Determines how much of the obgserved process variation is due 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) 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) reproducibility. The ANOVA method
goes one step further and breaks down reproducibility into its operator and
operator by part interaction.
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Gage Lineaity and Accuracy Study:
– Tells how accurate the measurements are through the expected range of 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 study examines
the difference between the observed average measurement and a reference or
master value. It answers the question, "How accurate is the measurement
instrument when compared to a master value?"
Measurement Capability
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Precision-to-Tolerance (P/T) Ratio:
– It is usually 5.15 * total gage R&R standard deviation
(obtained from the ouptut of the Gage R&R Study)
divided by the tolerance, I.e.,
Spring 2006
Process Measurement – Classroom Exercise
Page 5 of 14
where
USL, LSL are the upper and lower specification limits respectively
If the P/T ratio is <10%, the measurement instrument is considered
acceptable; if it is between 10% and 30%, it is marginal; and greater
than 30% it is unacceptable."
Formulas
Gage R&R Study ANOVA Method
F Tests
Gage R&R Table . . . Var Comp for ANOVA
Method
(Operator * Part Not included)
Number of Distinct Categories
(Resolution)
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Represents number of non-overlapping
confidence intervals that will span the range of
product variation. Think of it as the number of
groups within process data that measurement
system can discern:
Rule: Good number should be equal to or greater than 5.
Gage Run Chart
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Shows
– Part-to-Part Variation
– Operator-to-Operator Variation
– Repeatability (Variation within each data
group)
Gage Linearity & Bias (Accuracy)
Study
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Linearity
– Measures how accurate measurements are through
their expected range. It answers the question, "Does
my gage have the same accuracy for all sizes of
objects being measured?"
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% Linearity
– Linearity expressed as a percent of the overall process
variation
Gage Bias
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Bias
– The actual measurment minus the corresponding
reference value
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% Bias
– Bias expressed as a percent of the overall process
variation