Reliability and Lifetime Extension in Materials Evaluation Techniques, Essays (university) of Materials science

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MM 212

Materials Evaluation Techniques

Fall Semester 2018, FMCE, GIKI

Instructor: Muzammil Irshad Research Associate

Lecture 45 : Reliability and Lifetime Extension

Introduction :

 This chapter discusses the decisions that may be made as a result of inspections for materials evaluation and non-destructive testing.

 These include the selection of a threshold level for acceptance/rejection of parts, the concept of false accepts and false rejects.

 How these vary with the chosen threshold

 Use of NDE can lead to economic benefits, such as lower running costs due to less frequent replacement of parts, or timely replacement of parts, thereby avoiding costly failures.

False accept:

 This means acceptance of a part on the basis of no indication, or an indication below a predetermined signal level, which ultimately is found to have a flaw present.

False reject:

 This means rejection of a part on the basis of an indication above a predetermined signal level, which ultimately is found to have no flaw or a noncritical flaw.

Threshold signal level:

 Threshold signal level is set so that above this level the part is rejected and below this level the part is accepted.

 It can be seen that, because of the range of signals between the lower and upper bounds it is possible that for a particular flaw size, there will be false accepts and false rejects based on the chosen accept/reject threshold.

Threshold signal level:

 The combination of conditions of the physical presence of flaw/no flaw in the material, together with the measurement parameter of indication/no indication, can be represented in a decision matrix

WORKED EXAMPLE

In a batch of bolts, 75% give no indications of a flaw. If the percentage of correct accepts was 50%, what was the percentage of false accepts? In addition, if 15% of the bolts were correctly identified as flawed, what is the percentage of false rejects? From this information determine the percentage of bolts that were actually flawed?

Solution

From the above information, the percentage of false accepts was 25%, and the percentage of false rejects is 10%. The percentage of flawed bolts must have been 40%.

 From the above examples it can be seen that for a series of flawed parts, the probability of false accepts (PFA) is related to the probability of detection (POD) by the equation PFA = 1 − POD. Likewise, for a series of unflawed samples, the probability of false rejects (PFR) is related to the probability of correct accepts (PCA) by the equation PFR = 1 − PCA.

False accepts and false rejects:

 From the previous examples we deduce, however, that the PFA and PFR are not identical and are not even directly related. To know both, we need to have three pieces of information from among the following:

• Number of parts with flaws
• Number of parts with no flaws
• Number of parts giving indications
• Number of parts giving no indications
• Number of correct accepts
• Number of correct rejects

Decision Matrix:

WORKED EXAMPLE

In the previous example, more information became available and it was found that 75 parts were found to be acceptable and 25 were rejected. How many false rejects were there? How many correct accepts were there?

Solution:

The additional information can be added into the decision matrix

 From this, it is very easy to see that the number of unflawed components that were incorrectly rejected was 10, and the number of correct accepts was 70.

Dependence of probability of false accepts On threshold signal level

 The PFA is determined by a combination of the chosen threshold signal level and the probability of detection of flaws.

 For any given size of critical flaw, the higher the chosen threshold signal level, the more parts with critical flaws will be accepted.

 As the threshold signal level is decreased, the probability that the part will be accepted decreases towards 0%. On the other hand, as the threshold signal level is increased, the probability that the part will be accepted approaches 100%.

 Variation of the probability of false acceptance (PFA) with signal size, which shows that if the accept/reject threshold is set too high, many bad components will be falsely accepted.

DEPENDENCE OF PROBABILITY OF FALSE REJECTS

ON THRESHOLD SIGNAL LEVEL

 we would need to know either the probability of correct accepts or the probability of correct rejects for a relationship between PFA and PFR.

 If a given signal size is observed to be at or above the threshold signal level, we must ask what is the probability that the indication is noncritical and that the part is, in fact, still serviceable.

 It is clear that the number of false rejects increases as the threshold signal level Vth is decreased, because fewer flaws are being ignored, and the parts containing these flaws are being rejected.

 To minimize the number of false rejects, the threshold signal level Vth has to be set as high as possible, but this will also have the unwanted effect of increasing the number of false accepts.

Reliability and Life time Extension Relative Operating Characteristics: The ROC Curve

 Ideally, one would like to have a high probability of correct rejects (PCR, which of course, is POD) and a low PFR. The plot of these quantities against each other is known as the relative operating characteristic or ROC.

 For a high threshold, there is a low POD but also a low PFR. This condition is represented by the curve in the bottom left-hand corner of the plot.

 For a low threshold, there is a high POD but also a high PFR. This condition is represented by the curve in the upper right-hand corner of the plot.

 If it can give high probabilities of detection with low probabilities of false rejections, then the curve will tend towards the top left-hand corner of the plot, and operating under these conditions provides the best NDE capability.

Economic considerations:

 In plant life extension if the cost of failure is D$, the probability of failure over a given time period is p, the cost of the inspection is C$, and the cost of replacement parts is E$, then we can calculate a probable cost associated with this which is C$ + pD$ + E$.

 An important question is what happens if inspections are not carried out ( C$ = 0). In this case, the frequency of replacement of the parts will have to be increased, which means an increased cost E$.

 Allowing the part to fail means absorbing the cost of failure, pD$, in which p without inspection is greater than p with inspection.

 The economic role of nondestructive testing and evaluation should therefore be to minimize the sum of all the expenditures, E$ + C$ + pD$, associated with operating a plant.

RETIREMENT FOR CAUSE

 An obvious economic benefit of non-destructive testing and evaluation is that it can be used to determine when a part needs to be replaced because of degradation, rather than just by setting up a predetermined retirement schedule for components.

 Retirement of parts on predetermined schedule for large number of low-cost parts, or even for just a few high-cost parts, there is an unnecessary cost resulting from too frequent replacement of parts.

 Retirement for cause is a concept that has grown from a specific research program in which the replacement of parts for reasons arising from non-destructive inspection is seen to be more cost-effective, because parts are only removed from service when there are identifiable problems.