In radiography the signal may equally correspond to decreased intensity, for example from a dense inclusion. In this case the integrals must be taken in the opposite direction, and a lower threshold T defined. If defects of either sense may be present then the two probabilities for positive and negative integral limits must be added together. A key unknown in these integrals is the threshold T. It may be estimated from the experimental limit in the differentiation of density changes which the eye can distinguish, about 5%. However it remains a variable parameter in the present model. Its choice depends on the application, for example, on how expensive the repair of false indications compared with the expense of missing a defect. The well-known ROC curves are designed to achieve the optimal threshold giving the best compromise between missing defects and picking up false indications.

3. Human visual perception

When examining a radiograph the human eye identifies the presence of a defect in a complex way very different from any simple threshold. Any radiographic interpretation course is designed to train the future inspector to recognise any given type of defect by example. It is not a quick process, for actual defects are always different in size, density and shape from one another. Of course in practice they might appear at any position over a radiograph, or in any one of a series of radiographs. The brain has to learn to recognise the general features of the object being searched for from a series of different examples. The eye then scans over the radiograph searching for this generalised image. The eye has built into its operation an impressive list of options for image analysis. It is able to work at several levels of resolution simultaneously. Thus even in a situation where the mean noise level means that many pixels exceed the 5% threshold, if the mean signal changes over an area encompassing many pixels, the eye is able to integrate over these and pick up the defect from a single glance at the image. It seems therefore to be able to start work at an extremely coarse resolution and as we search in more detail continuously reduce the search area covered by our eye. Almost all real radiographs have smooth intensity changes across their area caused by the differing X-ray path lengths. The eye hardly sees these, and is able to pick out contrast details much smaller than the actual density changes across the extent of the radiograph. The eye is particularly good at searching for a feature which it has previously seen and remembered. We all recognise how well we can search some text for a particular word. This "template matching" mode can be performed by the eye simultaneously for several different templates.

Neural network receptive field methods are able to work in exactly this mode. They sweep a small field of view over the radiograph, mimicking the human fovea, and present the pixels within the receptive field to a neural network trained to give a large output when a defect of a given type is presented to it. However the eye does not scan in any such systematic way. A defect, obvious to the eye when pointed out afterwards, may often be missed during the original radiographic interpretation. It is not just the human factors of fatigue, boredom or carelessness which cause the error, although these are all important, for even a fresh well-motivated inspector will not perform as an ideal model predicts. It is rather the intrinsic difficulty that humans have in behaving like computers - performing the lengthy, repetitive task of scanning every section of the radiograph and searching for one of any number of possible types, sizes and shapes of defect. A key factor is experience - it is a well known fact that radiographic inspectors see one gauge finer wire in an Image Quality Indicator than do raw recruits.

This paper takes a pragmatic approach of attempting to validate its POD calculations by simulating radiographs together with noise, defects and IQI's, and asking operators to compare their own performance with that of the model. The human factors are thus included at the same time as the model based factors. The model doubles as a training tool in its own right by giving operators a view of the size, contrast and sharpness of typical defects that they need to be able to identify.

Figure 3.The principle factors which need to be taken into account in evaluating a defect Probability of Detection using X-radiography.

Figure 3 shows the key factors which need to be included in any radiographic simulation. It is not practical to build in all the detail which should ideally be included. Appendix 1 shows the parameters which have been included in the present code XPOSE. The parameters are entered in from a series of menus and toggled in (T), entered as variables (V), or measured or interpolated from experimental data (E). A key objective of the code is that the derivation of all data used are clear and referenced to their source, and that the data finally used are, at least optionally, displayed to the user.

Source

There are important differences between X-ray and gamma sources in radiography. An X-ray set usually has a variable electron acceleration voltage which becomes a key factor in determining exposure and contrast. The energy spectrum of the X-rays produced depends on this energy and also on the target material. There is generally a set of monochromatic lines produced by electrons dropping back into an empty deep atomic orbital whose occupant had been ejected by the X-ray. These transitions are superimposed on a continuous distribution, the Bremsstrahlung or slowing down radiation, produced as the electrons are stopped in the target. Tungsten is by far the most commonly used isotope in industrial radiography, and its use is assumed in this study. The intensity of X-rays emitted by a tungsten target being hit by electrons of a given current and voltage is assumed to be the same. The distribution with voltage is presently taken from the PANTEC source data, and is assumed to be independent of current so that exposures are measured in ampere-hours. Filters are widely used in X-ray sources to remove low energy X-rays which, because of high multiple scattering, reduce the effective contrast. The emitted X-ray flux will be assumed to be measured with the filter in place.

Isotope sources are used for thicker specimens when electromagnetic quanta of higher energy, gamma rays are needed to give adequate penetration. These sources emit one or more gamma rays which together are assumed to have some characteristic mean energy. This energy remains fixed with time, although its intensity will decay with an exponential fall-off with a time constant depending on the half-life of the source. Since there is no way of varying the gamma ray energy, there is no analogue of the X-ray voltage, nor of the X-ray current. The intensity of gamma ray sources is defined simply from the number of disintegrations per second.

Betatron sources are relatively portable accelerators than can produce very hard gamma rays of several MeV energies capable of penetrating many inches of steel or metres of concrete. Again the voltage is effectively fixed.

Sample

The sample material effects an X-radiograph in several respects. The absorption of X-rays is material dependent, and this in turn effects the recommended voltage, the exposure curve, and the number of X-rays reaching the film. Table 6.9 from Halmshaw's book gives recommended X-ray voltages as a function of thickness for iron and aluminium. Figure 4 shows the graph of this function as used. A warning is given if the sample thicknesses lies outside the recommended range of suitability, either for X-rays or for any chosen gamma source.

Figure 4. The linear relationship used by Halmshaw[1] to evaluate an appropriate X-ray voltage for a given sample thickness of iron. The circle shows the operating position.

An iron plate scatters X-rays strongly enough that the change of an X-ray being scattered rather than absorbed is by no means negligible. This means that the geometric image of any defect can be degraded by X-rays which enter its shadow. This "build up factor" is defined as the ratio of the total X-ray intensity at the film divided by the intensity arising from X-rays which arrive at the film directly. The factor is therefore greater than unity, and can rise to large values so that the majority of the observed X-ray intensity comes not from the image forming direct radiation, but from the diffuse scattered intensity. The effect increases with material thickness, and with its atomic number which effects its scattering cross section. Since low energy radiation is more readily scattered build up increases with decreasing X-ray energy. Figure 5 shows the measured data used in the program from Halmshaw. The lines through the data are quadratic fits to the data at each thickness, whose coefficients have been fitted as a function of energy so that the build up may be interpolated at any voltage or energy. Similar data exists for aluminium plates, and for iron plates under gamma radiation. These data are only relevant for the simple slab geometry. However a cylindrical geometry may be approximated by that of two flat plates each equal to the wall thickness and separated by the diameter of the cylinder. The scattering from the upper plate may be considered an isotropic scatterer on to the lower plate. There exists good data on these effects for iron and aluminium. For this reason, a given thickness of most other materials is expressed in terms of an equivalent thickness of one of these two standard materials. The conversion factors are derived from the table originating from Kodak quoted in the Welding Institute Handbook [6].

Figure 5. The measured build up factor (BUF) as a function of thickness for various X-ray voltages from Halmshaw [1]. The lines shows the double variable interpolation to his data. The circle shows the current operating position.

The absorption cross section has several components and needs to be considered as a function of both X-ray energy, or gamma ray source, and thickness. These have been tabulated by Halmshaw and figure 6 shows the interpolated fit to these data for iron.

Figure 6. The measured material absorption as a function of thickness for various X-ray voltages from Halmshaw [1]. Again the lines shows the double variable interpolation to his data and the circle shows the current operating position.

Figure 7. The sample geometries detailed in the model.

Figure 8. The definition of a single angled cuboid defect, with respect to conventional axes in a weld.

Defects

The modelling of defects near the limit of visibility need not be taken to the same degree of detail as would be possible for more clearly seen defects. For this reason only assemblies of cuboidal defects are presently considered. With these shapes the necessary convolution of the Gaussian unsharpness over the defect volume may be performed analytically. Different types of defect are then defined in terms of length and depth aspect ratios, orientation and number of components. A single defect component is defined as in figure 8 by its length along the weld x, its depth or "gape" y, its width across the weld z, and the angle q defining the orientation of the defect x axis in the plane along and perpendicular to the weld. In order to compare and visualise defects of different type the effective diameter of the sphere of equivalent volume is taken as the size standard. The two further definable parameters are the aspect ratio along the weld ax=x/y and its aspect ratio across the weld a_x=z/y. The volume and effective diameter of a cluster of n such defects is therefore

V = nxyz = na_xa_zy³ = (1/6)np d_eff³.

Figure 9. Defect sizes are defined in terms of the diameter of the sphere deff having the same volume as the composite defect.

The X-ray transmission through a single oriented cuboidal void is only dependent on the path length along the beam, and not on the material distribution along the beam. It is therefore to make an approximation that cuboids of area 2a.2b orientated at the angle q to the X-ray beam may be transformed into cuboids of area 2a_effx2b_eff as illustrated in figure 10. A sensible definition for the transformed volume is

a_eff = nxyz = 1/(cos q/a + sin q/b ) b_eff = b cos q +a sin q

This definition keeps the area precisely correct and has the correct limits for the extreme angles of q9 =0 and 90^o when the X-ray beam is perpendicular or along to the defect length. The approximation is good for high aspect ratio b/a, as for example the case b/a=20 in the figure. For moderate aspect ratios it works less well as it fails to describe the true trapesoidal form of the transmission. However the differences are likely to be unimportant in the practical case of defects at the limit of visibility when geometric unsharpness broadens the tapesoidal edges of the profile.

Figure 10. Cuboid defects whose normal lies at an angle q9 =0 to the X-ray beam axis are transformed into cuboids in the plane perpendicular to the beam with effective length 2b_eff and gape 2a_eff. The true trapesoidal path length variation is turned into a rectangular one. The figure shows the variation of these as a function of angle for b/a=20.

The present study is limited to just four generic types of flaw, whose parameters are collected together in table 1.

i) Slag inclusions are a common type of flaw, and being volumetric are much less likely to initiate failure than the various types of crack. They are typically rectangular in section elongated along the axis of the weld. Our model will assume a single cuboid n= 1 with a square section of variable gape and width y, az=l, elongated along the weld by a length aspect ratio ax=4. These parameters may of course be changed within the definition file.

ii) Porosity is common in the centre of welds and being volumetric is again relatively benign in its ability to initiate failure. The key parameter is the mean width y of the cuboid individual pores making up the volume of porosity. The area of porosity is assumed to be 5 times the pore width along, across and down the weld b_x=5,b_y=5,b_z=5 and to have a 12.5% volume fraction so that n=12.

iii) Lack of Fusion cracks occur along the boundaries between the weld material and the workpiece when fusion has been incomplete. They are serious flaws as their edges contain stress concentrations which may initiate crack growth leading to failure. They are usually flat in cross section in the plane of the weld face. Our model assumes a gape width y with factor 10 aspect ratio both along and transverse to the weld a_x=10,a_z=10. They are usually orientated at a known angle to the X-ray beam, so their visibility depends crucially on the angle of the normal to the crack to that of the X-ray beam. An angle of 70° is typical for conventional "double V" welds.

iv) Rough cracks occur when excessive thermal stresses cause metal within the weld or the heat affected zone to fracture. They are at once most serious, and difficult to model, since their shape and orientation are highly variable. However they share a general feature of having many facets at different angles, and the present model assumes 10 facets with a specified mean angle, and spread of angles around this mean. It assumes a variable gape width y, an aspect ratio along the weld a_x=10, an aspect ratio across the weld a_zz=10, a mean facet angle q of 70°, and 10 individual facets with a angular spread dq, of 20°. Figure 11 shows a Lack of Fusion crack some 50x1O mm. in area with a gape of 1 mm, compared with its model.

Table 1. The definitions of the assumed defect types

Film

X-ray photographic film responds to a given flux of X-ray quanta in a complicated way defined by film density, or logarithm to the base 10 of the light transmission after development, as a function of the logarithm of the exposure. This "characteristic curve" is strictly unique to a particular make and speed of film. However the main parameter is the speed, which mainly affects the position of the curve along the exposure axis, and only to a lesser extent effects the shape of the curve. The speeds are obtained from Halmshaw Table 5.1 page 98 [1]. Figure 13 shows the very precise fits achieved to the Kodak MX and CX films which are most commonly used. The function used is a quadratic polynomial divided into two regions, together with a constant "fog" term. These are fitted to actual data from the manufacturers data sheets as the program is run.

Figure 13. The exposure curves for Kodak MX and CX X-ray films. The points are from the manufacturers product sheets, while the lines show the fitted function. The circle shows the chosen working position. The contrast factor, needed in the POD calculation is evaluated by numerical differentiation of the fitted curve at the working position

The evaluation of the unsharpness, or spatial resolution, in the radiograph is a prerequisite to both the simulation of the radiograph and the defect probability of detection. The total unsharpness is derived by convoluting the unsharpness terms originating from the film, from the X-ray source size, and from the geometry as defined by the source to sample and sample to film distances. The present model assumes that all these contributions may be approximated by Gaussian distributions.

u_I = (2ps_i²)^-0.5 exp(-2x²/s_i²

where x is any linear dimension. This enables them to be described by a single number, the full width at half height of the Gaussian distribution, FWHH_j =(21og_e2) ^1/2s_i , and to convolute the various contributions by summing squares and taking the square root. As we shall see later it also allows the convolution with a rectangular defect to be performed analytically.

Film

The film unsharpness U_f is a function of the voltage of the X or gamma rays, and figure 14 shows the film unsharpness measured by Halmshaw[l].

Figure 14. The film unsharpness U_f as measured by Halmshaw[1] and fitted in the model. The circle shows the currentlfcuboidefy assumed value.

Source

A second important contribution is the source size unsharpness U_s. This is usually evaluated according to the most pessimistic case from the diagonal length of the X-ray target or gamma source dimensions

u_s = [ U_{source_length}² + U_{source_width}² ]^1/2

A better approximation can be derived experimentally by measuring the source function by using a pinhole geometry and evaluating the best fitting u_s.

Geometric

It is conventional to assume that the defect or IQI lies close to the upper surface of the sample, where the geometric unsharpness is largest. The overall geometric unsharpness is then calculated for a given source to film distance sfd with the defect to film distance equal to the sample thickness t

u_g = [ U_s/)sfd/t-1)

Alternatively if the geometric unsharpness is to be specified then a minimum source to film distance sfd may be calculated from

sfd = t.[1+ U_s/U_g]

The program gives a visual demonstration of the three unsharpness distances U_s, U_g , and U_f, as illustrated in figure 15. The total unsharpness may be simply evaluated by quadrature within the Gaussian approximation.

In order to speed up the simulation the full random noise pattern is calculated only over a limited area of the screen, say just a 32x32 area from the 640x340 pixels available. This area may then be copied over the rest of the area of the simulation with little loss in the perception of randomness.

The 32x32 pixel area is also used to demonstrate the geometric unsharpness. An absorption in the form of a Gaussian distribution with a full width at half height equal to the calculated geometric unsharpness is superimposed on the small area of noise. The image is thus that of a fully absorbing pinhead. This gives a visual impression of the resolution broadening expected around any feature in the radiograph.

The image of a defect as seen on the simulated radiograph takes the form of an array of exponential absorption factors appropriate to the path length though the specimen at each point, convoluted with this Gaussian resolution function. The defects in the present version are assumed to be void cuboids with axes along the plane of the sample. It is then possible to perform the resolution convolution analytically. Suppose the cuboid has depth dx and lies in a medium with an absorption constant m and a thickness t. The intensity I will be attenuated in the material as a function of depth x according to

I = I_oexp(-mx)

change in intensity DI/ caused by the defect of path length DI/ will be

DI/I = -mDx

The relative change in intensity DI/ is converted in the film to a density change DD/ depending on the gradient of the characteristic curve for the particular film and exposure G_d according to

DI/I = -DD/ (log₁₀G_d

Having evaluated this change in absorption it is necessary to perform a convolution with the Gaussian unsharpness function discussed above. For cuboid defects this integral becomes analytic being, at each point, the integral of a Gaussian between the two limits formed by the edges of the defect which takes the form of the error function. The final intensity at pixel i,j is given for a defect of width w and length l by

C= 0.5{erf[w-i.U_f/s] -i.U_f/s -erf[-w - i.U_f/s]} .0.5{erf[1-j.U_f/s] -erf[-1 -j.U_f/s]}

The differential change in film density caused by the defect will then be according to Halmshaw's equation 2.17, and including the build up factor B

Dd = -0.4344.C.m.G_dm dx/B

This represents the basic equation for the density change expected from a given defect.

The optional simulation of an Image Quality Indicator (IQI) is an important aspect of the radiographic simulation as it is an important option in any real radiograph. The two most suitable IQIs are chosen from the list of the most commonly available types as shown in table 2. Only conventional multi-wire gauges composed of 6 or 8 wires about 80 mm long encased in a plastic case are considered at present. These indicators are composed of wires of iron, aluminium or copper, and the optimum wire diameter is either specified or evaluated from the specified thickness sensitivity. The actual wire thickness must be adjusted according to the material if it is not one of the standard materials, iron, aluminium or copper. The next lowest diameter wire gauge available is selected from this list, and the two most suitable IQIs chosen from the list of those available by choosing that which has the desired wire gauge most nearly in the middle of the IQI. The image of each wire is evaluated by choosing a width across the image of the wire that will be sufficient to include the geometric unsharpness, with pixels equal to the film unsharpness. The convolution of the Gaussian geometric unsharpness with the arc length distribution across the cylindrical wire is then evaluated and stored in an array. This convolution is unchanged down the length of the wire so that it is possible to evaluate new random pixels at each pixel along the length of the wire from the same stored array of mean intensities. A typical simulation is shown in figure 16.

Figure 15. A radiographic simulation of a typical series of slag-like cuboid defects with increasing size in a 25 mm steel plate. The marker lines are centred on the defect and indicate its size. The smaller defects are not visible in the simulation but the larger ones can just be seen. The inset in the top left corner illustrates the total unsharpness. The numbers indicate the 7 wires of the IQI DIN54.109, only some of which can be seen.

The single pixel probability of detection equations were given earlier. Once again the necessary function is the integral of a Gaussian between fixed limits and may be expressed analytically as an error function. The area of the Gaussian centred on the mean brightness from the threshold to infinity gives the single pixel POD_o and probability of false indication PFI_o per pixel with area equal to the film unsharpness which were given in equations 3 and 4. The threshold value thres needs to be specified. It represents the density change which can be perceived as distinct to the eye, when presented in a series of isolated pixels with a noise distribution characterised by the deviation s. Halmshaw (p237) [1] mentions that a 5% luminance difference, corresponding to a 0.02 film density difference is the sort of performance within the capabilities of the human eye under good film viewing conditions. We follow him in adopting 0.02 as the default threshold. However it must be admitted that this crucial factor is somewhat subjective.

It is well known that the eye is sensitive to much smaller density variations if there are many adjacent pixels with the same mean density difference. The eye is able to integrate over those areas of the image having the same mean density - say inside and outside the image of an extended defect. The effect is the same as if the pixel size had been increased by appropriate averaging to give a higher mean number of quanta per pixels and consequently a lower standard deviation s. However averaging pixels numerically over some area is no solution since the resolution will be degraded and a group of pixels may or may not appear above the threshold depending on whether the averaging length spans the defect edge or not. This problem does not arise with the method used, which is based on that used in the corresponding ultrasonic code by Ogilvy[2]. An odd number n.m of adjacent pixels is considered, and the POD and PFI is evaluated for every possible choice of central pixel. The defect is accepted if all n.m adjacent single pixel probabilities P_i,j individually exceed the threshold. Similarly a false indication is declared if all the n.m adjacent probabilities exceed the pure noise distribution threshold. Thus

PFI_mxmy= 1 - { 1 - [1 - (1-f)^M-m] }ⁿ }^N-n

POD_mxmy= 1 - { 1 - P_{k=0 to n-1} [1 - P_{i=1 to M-m} (1 - P_{l=1 to m-1} ) ] }

Choosing the best values to choose for the averaging distances n,m is a matter for some discussion. The eye tends to choose that distance corresponding to the smallest object for which it is searching, whatever the size of the defect actually seen. The conclusion is that the distances n,m should be fixed to correspond with the smallest defect detectable. However it would be reasonable to enlarge the averaging dimensions as the size of the defect being searched for increases. Thus a human might be imagined to search over an image several times, each time looking for a different size of defect and performing a mental averaging corresponding to this size. The problem with the second approach is that it leads to a much more rapid increase in the probability of detection with defect size than is actually observed. The method presently uses a fixed averaging size of three times the film unsharpness.

The POD curve for the cuboid defects in 25 mm steel illustrated in figure 17 is shown by the points in figure 18. It is seen be close to zero for effective diameters below 0.4 mm then to rise quite sharply at around 0.6 mm rising to essentially 100% by 1 mm.

Figure 17. The points show the calculated probability of detection as a function of defect size for cuboid defects in 25 mm thick steel. The full line shows the experimental results for radiography by Forli [9]. The crosses and dashed line show experimental POD measurements from human trials using radiographic simulations.

There exists a considerable literature of experimental test data on Probability of Detection of defects using X-radiography. This has been gathered into a computerised database by M Wall [8]. As an example of the type of comparison which may be made, the feint line in figure 17 shows a portion of the results of Forli [9]. Although this work covers a range of samples, the results are not inappropriate for radiography of 25 mm plates. There is quite a serious discrepancy between this curve and the calculated results for 25 mm plate shown by the points. In fact the defect size where the defect may first be observed in favourable cases is seen in both cases to be around 4 mm. However while the calculated POD rises rapidly to close to 100%, the experimental curve saturates much more slowly. It is believed that the differences between the two curves are largely accounted for by the human factors.

9. The quantitative analysis of a scanned experimental radiograph

An experimental test of the method has been provided by a radiograph of a test specimen containing four drilled holes covering the limit of expected visibility which had been developed to establish a test procedure for an important inspection application. The procedure was as follows:

X-ray set:	Philips PANTEC
Source size:	0.4 mm
Exposure:	8.8 mA.min
SFD:	600 mm
Film:	Kodac MX

The specimen was of steel 9.6 mm thick with cylindrical holes drilled:

Label	Size	Human	XPOD
A:	0.4 mm diameter: 0.4 mm depth	90%	95%
B:	0.3 mm diameter: 0.3 mm depth	60%	45%
C:	0.25 mm diameter: 0.25 mm depth	25%	19%

A radiograph covering these holes was taken. The percentages on the right were a human assessment of the probability of detection of these holes from a careful viewing of the original radiograph under ideal conditions. The radiograph was then scanned through a video camera and captured on an image analysis system. It is not possible to display here the original radiograph with anything like the required quality, but figure 1 showed the direct scans of the image intensity. The heavily sloping background illustrates the problems of naive methods such as taking a simple threshold at the lower limit of the noise and looking for dips below this. The POD values obtained by the program are shown above. They are seen follow the human estimates reasonably well. We would not claim any higher degree of accuracy in POD than the 10 to 20 % precision obtained here.

Figure 18. The screen display from the experimental trial including human factors. The dark square to the upper left shows a clear defect detected by moving the cursor as shown by the parallel dashed lines. The defect in the lower right hand corner was just missed by the cursors .

The radiographic simulation can easily be adapted to provide an experimental tool for the measurement of the human POD (and PFI) for particular defects under any specified circumstances. An average number of defects per display is specified and a random number of defects within a defined effective diameter range is simulated and presented onto the screen for examination by the inspector. Inspectors can move a cursor around the screen as shown in figure 18. They may press ENTER at any time they choose and if the cursor lies within a specified distance of the defect a HIT will be scored. If no defect exists there, a MISS indication will be scored. The inspectors are not told how many defects they are searching for, and they must themselves decide when to press END to indicated the completed inspection of the screen. After a specified number, say 10 screens, the HIT and MISS totals are recorded and plotted as a function of the actual defect effective diameter. The crosses in figure 17 shows such an experimental POD plot obtained from several inspectors. Some were trained X-radiographers, but most were physicists working in an NDT department. There was no significant difference between the two sets of people. Most people obtained a similar performance, but they were all significally below the calculated POD curve, and fall closer to the experimental curve.

11. Conclusions

The XPOD model described here provides a path from a given radiographic procedure, to the simulated radiograph of an assumed defect, and to its POD and PFI. Validation through IQIs give confidence that the method gives a good indication of POD, although there are uncertain factors in the calculation such as the assumed film density threshold, and the averaging distance in the Ogilvy correlation. Ultimately these need to be settle by more extensive validation. Without doubt, these calculated POD curves do not correspond well with experimental trials. We believe much of the difference can be accounted for by human factors. This is especially true for larger defects whose existance is obvious when pointed out but which are nevertheless sometimes missed in practice. A experimental method of measuring human POD from simulated radiographs has been developed.

References

[1]R Halmshaw, "Industrial Radiology, Theory and Practice", Applied Science Publishers Ltd 1982

[2]J A Ogilvy AEA APS 0365, Feb 1993, NDT International, 1994

[3]O Forli,"Reliability of radiography and ultrasonic testing", Procs.5th NDT Symposium, Esbo, Finland, 1990

[4]T A Gray and R B Thompson, "Use of models to predict ultrasonic NDT reliability", Rev.Proc.QNDE, 7B, 1737-1744, Plenum New York, 1988.

[5]Metals Handbook, 9th Edition, Vol 17, "nondestructive Evaluation and Quality Control", "Models of Predicting NDE Reliability", p 702 - 716

[6]The Welding Institute Course Handbook "Practical Radiography NDT20 1996

[7]Murgatroyd R L et al: Human Reliability in Inspection: Results of Action 7 of PISC III programme, 1994

[8]M Wall, APS POD Database, April 1992, Unpublished

[9]O Forli, NDT SYMPOSffiT ESBO, Finland 1990-08-26...28, Nordest, Finlands, Svetstekniska Forening NDT-KOMMITEEN.