Defect Detection in Nondestructive Evaluation: Probability & Signal Threshold, Exercises of Materials science

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MM 212

Materials Evaluation Techniques

Fall Semester 2018, FMCE, GIKI

Instructor: Muzammil Irshad Research Associate

Lecture 44 : Defect Detection

Introduction :

 Defect detection is one of the main objectives of nondestructive evaluation.

 Signals from defects exhibit a statistical distribution and therefore, in practice, not all defects will be detected.

 Furthermore, inspections can also suggest the presence of flaws where there are none. This condition is known as a false alarm.

 This chapter discusses both the probability of detection and the probability of false alarms and how the choice of accept–reject criteria can affect these probabilities.

Terminology for nondestructive evaluation

Indication:

 An indication is the response or evidence from a nondestructive examination.

False indication:

 This is an indication that turns out not to be related to a discontinuity or imperfection.

Nonrelevant indication:

 This is an indication that is caused by a condition or discontinuity that does not affect the performance or serviceability of the part.

Relevant indication:

 This is an indication that is caused by a condition or discontinuity that could affect the performance or serviceability of the part.

Interpretation and evaluation:

 Interpretation is the process of determining whether an indication is false, nonrelevant, or relevant.

 Evaluation refers to the whole process of assessment of an indication to determine whether it corresponds to a flaw or not, whether this adversely affects performance or serviceability.

Probability of detection:

 Decisions are made based on measurements of signals, rather than the actual flaw sizes,  Because flaw sizes are not measured directly, only inferred from indications obtained from inspections.

 No matter which inspection techniques are used, there will still be statistical limitations on the detection of defects  Caused by the fact that every measurement procedure has a distribution of signal levels to flaw size

 The probability of detection (POD) is usually determined from empirical studies on standard reference specimens.

 Analysis of the resulting data can proceed by different methods but usually involves a statistical plot of signal amplitudes vs. flaw sizes.  The value of the POD depends on flaw size, and on the measurement technique and its ability to detect signals from flaws of different sizes.

 Another approach to probability of detection is via model-based simulations, whereby predictions are made of expected signal levels for flaws of different sizes and orientations.

Threshold Signal Level:

 At some point in the process of interpretation and evaluation, a decision has to be made about the amplitude of an indication above which the part is deemed flawed.

 A threshold signal level, Vth , is chosen so that any parts giving flaw signals above this level are rejected, and any that give signal levels below this are accepted.

Worked Example

For a certain type of flaw suppose α = 0.7 when V is measured in volts and x is in meters and ε = 10%. If we are looking for a critical flaw of size 1mm, what is the expected signal voltage and what is the range of possible voltages? What is the range of flaw sizes that will give the expected signal voltage?

Solution: log10( V ) = 0.7 * log10(0.001) +/− 10% = −2.1 +/− 10%.

The expected signal voltage is Vex = 0.008 V.

The range is Δ(log10( V )) = −1.9 to −2.3.

With a band of uncertainty ε = 10%, the range of signals for a 1 mm flaw will be from 0.0126 to 0.005 V.

Threshold Signal Level:

 For flaw sizes between 0.51 mm and 1. mm there will be, in addition to some correct accepts, also some false rejects caused by samples that give signal levels above the set threshold of 8 mV. Similarly, for flaw sizes between 1.00 and 1.94 mm there will be, in addition to some correct rejects, also some false accepts caused by samples that give signals below the set threshold of 8 mV.

Probability of Detection: Ideal Conditions:

 It is reasonable to assume that as the flaw size increases, the POD of the flaw also increases toward the value 1.

Under ideal circumstances there is:

1.No uncertainty about the relationship between flaw size and flaw signal, so the value of ε in the above equation would be zero

2.The variation of POD with flaw size is a step function in which the probability of detection suddenly increases from 0 to 1 at the flaw size x 50

 The value of x 50 depends on the choice of the threshold Vth.

 There is one value of this threshold that can be chosen such that x 50 = xc , where xc is the critical flaw size. Then the probability of a false reject is zero (because POD is zero) for flaws less than the critical size. Likewise, the probability of a correct reject is 100% (because POD = 1) for flaws greater than the critical size.

 In reality, the probability of detection usually increases smoothly from 0% for small flaws up to 100% for large flaws

 The dependence of POD on flaw size can be differentiated to give a distribution d(POD) / dx vs. x which often looks like an error function or a normal (Gaussian) statistical distribution

 Real POD for flaws in metal

Probability of Detection: Real Conditions:

Mathematical formalism using a normal distribution:

 If the probability of detection POD increases as the flaw size x increases according to a normal or Gaussian distribution,

 The normal distribution curve, the familiar bell curve that is often associated with random distribution of quantities grouped around a mean, is the derivative of this function, and has the form

Other statistical distributions:

 Normal, Lognormal, Exponential, and Weibull distributions.