| Measurement System
Analysis
Measurement systems are
fundamental to data collection. To obtain quantitative
data, some “system” must be used. Examples include a
thermometer to measure temperature, a blood test to
detect disease, and a test instrument to determine
whether a cell phone works properly. Measurement
system analysis (MSA) determines the adequacy of the
system as it is being used. Here a measurement system
refers to the combination of the measuring device
itself, the procedures for taking the measurement, the
people taking the measurement (if any), and the device
(or person) being measured. The objective of an MSA is
to understand the contribution of each of the components
of the measurement system to the total variation in the
observed values. MSA is a prerequisite to conducting
designed experiments or doing control charts to ensure
the data taken can be considered reliable enough to
accomplish the objective.
Measurement systems are often used to discriminate among
products or to determine whether or not a disease is
present. In this context, a test is done and two
different errors are possible. A false failure (false
positive) occurs when the test result is a fail
(positive) and the device (person) under test is truly
good (healthy). The second error that can occur is a
missed fault (false negative). In this case, the test
result is a pass (negative) and the device (person) is
truly bad (sick). Both of these errors are problematic
and the MSA provides estimates of the magnitude.
Further, if costs can be assigned to the errors, test
limits can be determined to minimize the total cost of
error.
Test
results can be based on a single measured variable or
they can be the composite of several variables. Methods
exist to jointly assess the capability to measure two or
more possibly correlated variables. Error rates and
associated costs can be estimated for the multivariate
test situation. In electronics manufacturing, MSA has
been used to identify inadequate tests, estimate and
improve test error rates, and reduce total test time.
MSA
makes use of designed experiments and variance component
analysis to separate and quantify the different sources
of variation in the measured value. Much research has
been done to not only estimate the magnitude of the
variance components but also to quantify the uncertainty
in those estimates. The experiments used in MSA need to
include more factor levels than standard designed
experiments used to estimate means. Recent references
include the following papers.
Larsen, G.A., “Capability
Measures for Measurement Systems Analysis”, in
Encyclopedia of Statistics in Quality and Reliability,
Ruggeri, F., Kenett, R. and Faltin, F.W. (eds). John
Wiley & Sons Ltd, Chichester, UK, pp 1070-1074. 2007.
Larsen, G.A., “Measurement
System Analysis in a Production Environment with
Multiple Test Parameters”, Quality Engineering,
December 2003.
Larsen, G.A., “Measurement System
Analysis – The Usual Metrics Can be Non-Informative”,
Quality Engineering,
December 2002.
Burdick, R.K., Allen, A.E.,
and G.A. Larsen, “Comparing Variability of Two
Measurement Processes Using R&R Studies”, Journal of
Quality Technology, January 2002.
Burdick, R.K., and G.A.
Larsen, "Confidence Intervals on Measures of Variability
in a Repeatability and Reproducibility Study",
Journal of Quality Technology, July 1997.
A good reference book for
MSA is the following.
Design and Analysis
of Gauge R&R Studies: Making Decisions with Confidence
Intervals in Random and Mixed ANOVA Models,
Burdick, R.K., Borror, C.M. and D.C. Montgomery, ASA-SIAM
Series on Statistics and Applied Probability, 2005.
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