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SAE AIR5925 Document Information:
Title
Measurement Uncertainty Applied to Cost-Effective Testing
SAE International
Publication Date:
Feb 1, 2007
Scope:
The report shows how the methodology of measurement uncertainty
can usefully be applied to test programs in order to optimize
resources and save money. In doing so, it stresses the importance
of integrating the generation of the Defined Measurement Process
into more conventional project management techniques to create a
Test Plan that allows accurate estimation of resources and
trouble-free execution of the actual test. Finally, the report
describes the need for post-test review and the importance of
recycling lessons learned for the next project.
Introduction
Uncertainty analysis is a practical, scientific tool that is
used to estimate the uncertainty of test measurements and of test
results determined from the measurements. Prior to actually running
a test, the methodology of uncertainty analysis allows the
experimenter to learn much about the potential accuracy of a test
result and to assess the relative effects of various error sources
on the total test uncertainty. After data is obtained in the test,
uncertainty analysis is used to quantify the goodness of the
experimental results. There has been an increase in the awareness
of uncertainty analysis over the past several years, and some of
the key sources of information on it are given in References
2.1.1.1, 2.1.2.1, 2.2.1, and 2.2.2.
Unfortunately, the planning, design, and execution of testing
programs is still too frequently carried out without reference at
the planning stage to the detailed needs of the recipient/end-user
of the test results and consequently without proper regard to the
required uncertainty of the test measurements. A common scenario is
that a test is planned within budgeted costs and timescales,
utilizing facilities which are not optimal to the testing program
but which are either already available or are readily accessible at
reasonable cost. If the assessment of the uncertainty of the
results takes place after the testing has been completed, then
there is a risk that the accuracies actually obtained fail to meet
the desired, sometimes contractual, requirements.
Obviously, cost-effectiveness in the use of testing resources is
vitally important within both industrial and academic environments,
and the scenario described above is based upon this necessity for
economy. Finding that test results are too uncertain to be used
effectively is not cost effective. However, the application of
measurement uncertainty methodologies to the planning of the test
program can benefit not only the final accuracy of the test but
also the cost effectiveness of its execution. The action of
defining the measurement processes, including the detailed
breakdown of calibration hierarchies and elemental error sources,
ensures that the test that is performed actually provides the
required level of measurement uncertainty. It is not cost-effective
to obtain a greater accuracy than is required. In this way, the use
of expensive laboratory or industrial scale testing facilities may
be optimized and real savings made.
It is the purpose of this report to present a clearly defined
approach to the application of uncertainty methodology to the
planning and cost effective conduct of test programs. The report is
written in the aero engine-testing environment, in particular the
determination of in-flight thrust. However, the approach described
in the report can be applied to almost any experimental setting and
is recommended to all who undertake testing programs for commercial
gain.
The report begins by defining the basic requirements for a
preliminary test plan from which estimates of resources,
timescales, etc. may be drawn. It emphasizes the need to address
the actual needs of the "customer" (whoever that may be) at the
initial stages of planning. The required uncertainty of the test
results must be established through expert dialogue between the
supplier/test engineer and the customer/user. At this stage in the
test program, an initial uncertainty analysis is performed using
knowledge of the probable instrumentation uncertainties and
experience of similar testing work. This initial uncertainty
analysis helps to identify potential problems and to verify that
the test has some reasonable probability of meeting the required
uncertainty for the test results.
Potential problems with both human and material resources,
schedules, and other major test issues are identified in this
initial phase of the test program. The preliminary test plan
section of the report stipulates the need to recognize the
limitations, risks, and the importance of a clear definition of
program accuracy requirements.
The report continues with the description of the development of
the Defined Measurement Process (DMP) in detail. The DMP is
comprised of three parts:
• Definition of the measurement chain, including details of the
type and number of instruments to be used and their calibration
requirements.
• An elemental uncertainty analysis, in which all possible
sources of both systematic and random error are defined and
estimates are made of the uncertainties associated with each error
source.
• A results uncertainty analysis, where the effects of
propagation of the elemental uncertainties into the results are
assessed.
Using this procedure, an estimate of the uncertainty of the
final results is obtained and can therefore be compared to the
original requirement. Where there is a discrepancy, in the sense
that the uncertainty is either greater or smaller than what is
demanded, the test plan can be modified, the DMP revised, and a new
uncertainty estimate made. The uncertainty analysis gives
significant guidance on where the problems are and what needs to be
corrected. By iteration of these processes, the test plan can be
optimized prior to or during the initiation of any actual testing
work. This optimized plan may then be reviewed and agreed upon by
the customer, if necessary, before a final Test Plan is
published.
Once the test plan is finalized, the next stage is to perform a
preliminary test and to review the results obtained. The quality of
the data can be checked against the expectations from the DMP, and
the discrepancies can be investigated. Comparisons are made between
the current test results and expected results obtained from similar
tests or model simulations. These comparisons provide checks of the
uncertainty estimates and help to identify problems with the test
program. The report emphasizes the importance of planning this
preliminary test into the program since it offers the last, but
most effective, opportunity for revisions to the test plan before
serious testing proceeds.
Following the execution of the tests, the actual results must be
analyzed and their uncertainties estimated. Since much of the
groundwork for this exercise will have been carried out already in
an earlier stage, the effort required here is reduced.
Finally, a post-test review is recommended, where the results
obtained and the uncertainties associated with them are compared
with predictions and discrepancies are investigated. Such
investigations should be reported openly and may be used to assist
in planning the next similar testing program.
Concluding Remarks
Measurement uncertainty is a tool that can be applied to test
programs in order to optimize resources and save money. Sections 3
through 8 of this document describe how this tool is used, with an
example. Figure 1 gives a roadmap of the report.
About IHS
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