·Home ·Table of Contents ·Workshop  Reliability  Metric for Reliability Measurement with Special Focus on Application Parameters
Christina Nockemann, GerdRüdiger Tillack, Carsten Bellon, Martina Scharmach BAM Berlin, Germany Unter den Eichen 87 12205 Berlin
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1. SUMMARY
A metric for the application factor, g(AP), is discussed. The factor g(AP)functionally captures the degradation in NDE reliability due to operational constraints related to materials being inspected and the NDE equipment being used. It was first suggested as part of the reliability formula, R = f(IC)  g(AP)  h(HF), coined during the 1997 EuropeanAmerican Reliability Workshop held in Berlin. The intrinsic capability of the method, f(IC), establishes a reliability upper bound while the factor h(HF) captures reductions in NDE reliability attributable to human factors.
The issue of NDE reliability is considered both as it applies to flaw detection and dimensional measurements. Examples discussed include (1) radiographic crack detection in welded ferritic tubes, (2) ultrasonic detection of pores in electronbeam welds, and (3) radiographicprojection wall thickness measurement of isolated tubes found in petrochemical plants.
Considerations will be given to the different types and categories of application parameters suitable to the experimental examples. Methods for combining g(AP) with f(IC) and h(HF) will also be discussed, thus addressing the issue of how overall NDE reliability might become quantified and modeled.
2. INTRODUCTION
The metric for the application factor will be treated as for the whole reliability and considered in chapter 3. Chapter 4 will investigate how to combine the application factor with the other factors to form the whole reliability R, which means to consider what is the right mathematical shape of the formula. Chapter 5 contains the consideration how to distinguish between different application factors according to type and categories. The final chapter describes above mentioned examples for the proposed approaches.
3. METRIC FOR THE RELIABILITY MEASUREMENT IN GENERAL
We propose to treat the application factor using the same metric as for the whole reliability R. This metric depends on the nature of the nondestructive test concerning its quantitative (measurement) or qualitative (detection task) character and should consider to be able to include the requirements of the client as well.
I. Quantitative Test (Measurement)
Fig 1: illustrates a set up for a test in terms of a measurement 
The task of the test is here to measure a physical magnitude like a wall thickness. The new ISO Guide 17025 about accreditation of testing laboratories in general proposes here to use the uncertainty in measurement (ISO Guide about the Expression of Uncertainty in Measurement) for the characterization of the reliability which is in its simplest form a standard deviation determined from a series of experiments if possible or from a judgement of experts.
formula 1:
II. Qualitative Test (Detection)
The formulation of the task is here more difficult and often a combination of two parts (a and b):
 Detect present flaws or
Detect present flaws of a certain size or
Detect present flaws of a certain type
 Confirm flaw free parts of a component to be free of flaws actually or
Confirm flaws greater or equal to that certain size are not present
Confirm flaws of that certain type are not present.
The formulation of this task should be done according to the requirements of the client which should be in connection with the allowed risk for the component.
Fig 2: shows the typical constellation for a detection task 
The proposed characterization:
 POD Probability of detection based on hit/miss results of experiments.
POD("â versus a") Probability of detection based on a quantitative signal distribution.
A POD combined with the success in correct defect type indication.
 PFA Probability of false alarms based on false indications in experiments
PFA based on the quantitative noise distribution of the NDE system.
These magnitudes for characterization might depend on the flaw size.
The full scale characterization of the NDE system should be done by ROCcurves where POD versus PFA is indicated for different threshold or sensitivity levels.
4. HOW TO COMBINE THE DIFFERENT FACTORS WITHIN A MODULAR APPROACH
The alternative formulation for the headline would be what is the right mathematical shape for the formula when I want to combine the different contributions to the reliability. Again we have to distinguish between quantitative and qualitative detection tasks.
 Measurement with a Standard Deviation as Reliability Characteristics (Quantitative Test)
The total uncertainty d is a combined standard deviation composed according to the
ERROR PROPAGATION LAW to be determined with reference to the ISO Guide about the Expression of Uncertainty in Measurement.
 Detection with a Probability as Reliability Characteristics (Qualitative Test)
In case the NDE system can be described by a linear chain of modules of IC, AP and HF with no correlation in between then
formula 2:
P_{tot} = P_{IC}*P_{AP}*P_{HF}
the combination consists in a simple multiplication of probabilities.
For more complicated cases of interrelationship between the factors
formula 3:
P_{tot} = Á[ P_{IC} ,P_{AP} ,P_{HF}]
where F is a mathematical functional to be determined according to the RELIABILITY THEORY OF SYSTEMS which works similar to a fault tree analysis.
5. CONSIDERATION OF THE APPLICATION FACTOR ACCORDING TO CATEGORIES AND TYPES
According to Matthew J. Gohlis ("What is an Application Parameter?" [1]) we should define four categories of application parameters:
 Category involves bulk material characteristics which alter the expected behavior of the waves/rays in the material with respect to the forecast for the intrinsic capability (IC).
 Involves limitations of the source/probe and sensor/detector  the items to create and detect the waves/rays.
 Involves the differences between the naturally occurring flaw (discontinuity) characteristics and the characteristics of the idealized flaws used in defining the technique's intrinsic capability.
 Involves constraints arising from the geometrical shape of the component under test including surface conditions.
These categories cover the different practical mechanical location of the application parameter. The following differentiation according to types shall concern the recognition point of view:
Types
 Application factors are known and well defined physically and mathematically. They could be treated also as part of the intrinsic capability and might be investigated by computer modeling e.g. known flaw shapes, known geometrical magnitudes etc..
 Application factors are empirically known but not well defined in a physical or mathematical way. These application factors e.g. irregular surface shapes, irregular Xray intensity distribution  must be determined by experimental tests with completely controlled conditions (open trials).
 Unknown application factors. Factors not yet recognized. Can be treated only in integral approaches like in the field experiments (blind trials).
For a reliable assessment of an NDEsystem it is important to be aware of these three types. The metric of the application factor (see chapter 2) and the combination with other factors (see chapter 3) are without problems for type 1 and 2. Treatment of type 3 is open.
6. EXAMPLES
First Example
The NDE task consists in the detection of thermal induced cracks in welds of ferritic tubes (nuclear power plants). As metric we use the POD as a function of crack depth. In the IC part we consider the influence of the physics of the Xray penetration and the creation of the crack image with a minimum contrast of 0.01 O. D. for notch like idealized cracks. The probability for IC is determined by a modeling calculation and shown in the left part of Fig.4 As AP+HF we investigated the capability of human inspectors to detect the images of naturally shaped cracks on the radiographic film. Figure 3 shows again the picture of the sharing of this task with the corresponding probability factors. The probability belonging to AP+HF was determined by experiments in counting the hit/miss rates. Because all the experimental cracks had a hight greater than 4 % wall thickness and the POD(IC) reaches 1 before that 4 % the whole POD is represented by POD(AP + HF).
Fig 4: 
The category of this example corresponds to 3 (natural defect shape) the metric is a POD and the type is 2 (known but not well defined).
Second Example
The task is here the detection of pore holes in electron beam welds of Tialloy aircraft engine parts using automated ultrasonic testing with focussed probes. The application factor consists in the "naturally occurring flaw shape" of the pore holes according to category 3 from the above definitions. The type is: known but not well defined. The detailed approach is described in [2]. Fig. 5 shows the scheme of the investigation.
Fig 5: 
As ideal flaws sphere bottom bore holes were taken. The POD in dependence from the sphere diameters is presented in Fig. 6: We see a quickly jumping POD whereas the POD for the naturally occurring pores (Fig. 7) is much slower raising. The shape of the pores seems very much to diminish the POD  which is up to now physically not clear. We can now formally define the application factor influence by dividing the latter POD by the former  which is shown in Fig. 8. This factor could be used to scale other sphere bottom hole values to realistic ones  as a concept.
Third Example
The NDE task consists in the wall thickness determination of insulated tubes using radiographic shadow technique and automated evaluation of the digitized radiographic image.
Fig 9: 
The application factor considered here is the variation in the insulation radius and corresponds to category 4  geometrical shape of the component. The metric is an uncertainty in wall thickness measurement and the type is 1 (known and well defined).Fig.9 illustrates the different parameters. Fig. 10 shows the geometrical set up and the used mathematical formula for the wall thickness determination. The error propagation law was applied to that formula to investigate the influence of the application factor "insulation radius error" on the uncertainty in wall thickness measurement. Fig. 11 shows the combination of parameters investigated and Fig. 12 the results for the uncertainty in wall thickness measurement as a 2 dimensional function of the tube radius and the wall thickness for selected examples of parameter combinations, especially with a different radius of insulation.
REFERENCES
 Matthew J. Golis, "What is an Application Parameter?", ASNT Topical Conference Paper Summaries Book of the AmericanEuropean Workshop on Nondestructive Inspection Reliability, September 2124, 1999, NIST, Boulder, CO, USA, pp 4550
 W. D. Feist, G. R. Tillack, "Ultrasonic Inspection of Pores in Electron Beam Welds  Evaluation of Detectability", Proceedings of the EuropeanAmerican Workshop Determination of Reliability and validation Methods on NDE, June 1820, 1997, BAM, Berlin, Germany, pp 291298