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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.
1.1 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.
1.2 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.
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