There is rapidly expanding interest in application of statistical analysis in the field of integrity management, particularly with respect to use of data from, and for planning of, inspections. Integrity practitioners are increasingly seeing the benefits of the added insights that statistical analysis brings to both efficiency and effectiveness. The language used in integrity management is starting to reflect this, with increasing references to terms such as Data Science and Predictive Analytics. As with many other fields, integrity management is beginning a transformation that is essential to realising the true value of data and analysis driven decision support. Part of this transformation is in the skills and disciplines needed in integrity teams. There is clearly a growing role for Statisticians and Data Scientists. At the same time, existing integrity practitioners, including those in inspection and corrosion disciplines, can benefit by building an understanding of key elements of the new approaches. A challenge to widening uptake lies in making key concepts, which have direct practical relevance, readily understandable. We’re putting together a series of short articles, under the title Analysis Matters, to help with this – the first of these is below.

**Analysis Matters: Errors Amplified**

** **By: Mark Stone BSc Eng (Mech) PhD August 2020

One of the roles of non-destructive testing (NDT) in integrity management of pressure systems is to provide thickness measurements used to assess the condition of equipment against the threat of wall loss. Comparison of repeat measurements, taken at time intervals, is widely used to make estimates of corrosion growth rates. This article highlights that the errors or uncertainties in the differences between measurements are larger than the errors for an individual measurement. Hence corrosion rates can have a proportionately wider spread of uncertainties than the original thickness readings. This has important implications for planning and evaluation of inspection strategies as emphasis is placed on the maximum rather than average corrosion rate, and the maximum corrosion rate is more likely to be associated with the maximum measurement error.

All measurements include some degree of error or uncertainty. In the case of ultrasonic thickness measurement there are many contributors to error; for example, the nature of the coupling, the transducer characteristics, the algorithms used for thickness extraction, the repeatability of the location of measurement. Errors can often be taken as consisting of a systematic component, which remains the same with each measurement, and a random component, which is different each time the measurement is repeated. The nature of these errors is illustrated in Figure 1 below where the error for each point is the distance from the centre of the target. Figure 1 (a) shows a case where the systematic error is small, i.e. the points are generally located around the centre of the target. The random error in Figure 1 (a) is also small, with not much dispersion of the points, most of them being close together. Figure 1 (b) shows small random errors but now with a general displacement of the points away from the centre, i.e. a large systematic error. Figure 1 (c) illustrates the case of large random errors, indicated by the wide dispersion of points. The systematic error is small in this case however as the points remain on average around the centre. Finally, Figure 1 (d) shows a case where both the systematic and random error components are large, with significant dispersion and general offset from the centre.

Figure 1: Illustration of systematic and random errors

The random component often, but not always, shows variability consistent with a normal or Gaussian distribution. In these cases, the nature of the errors can be described reasonably well by just two parameters, i.e. the mean, which reflects the systematic component, and the standard deviation, which reflects the random component.

The systematic error can be minimised with appropriate calibration. Consequently, the standard deviation alone is often taken as a basis for defining the accuracy or measurement tolerances of the technique in a specific application environment. It is possible to quantify the likelihoods for any size of error by simply considering the properties of a normal distribution, e.g. typically approximately 68% of measurements would have random errors with a magnitude of less than one standard deviation and 95% would have random errors with a magnitude of less than two standard deviations. A high standard deviation indicates that the spread of random errors is larger than in the case of a low standard deviation.

Measurement systems and approaches which result in large standard deviations can provide misleading information, driving inappropriate integrity decisions in some cases. For example, in many applications one of the main aims will be to allow demonstration that the current condition remains acceptable, e.g. within defined limits based on fitness for service considerations. This allows follow up action to be triggered in the event the thickness is found to be outside of the limits. Potential errors in thickness measurement are important in these applications because large errors can lead to inappropriate follow up, e.g. excessive spend on premature repair/replacement or, conversely, in some cases, increasing the potential for in-service failure when the thickness is significantly overestimated in the measurements.

Knowledge of the current condition is important but on its own not sufficient for integrity management. It is also necessary to have some view on the future condition so that continued operation, over a certain interval, can be justified. Thickness measurement plays a key role here in allowing estimation of degradation growth rates, this by comparison of repeat measurements made at specified time intervals. The difference in the measurements, as in reported change in thickness, at repeat location is used to estimate the degradation growth rate. Where the inspection system is appropriately calibrated, this difference should not be substantially affected by systematic errors.

Random error still plays a role however. The effect of the random error is in fact amplified, this because of a simple statistical property, namely that the standard deviation of errors for differences is larger than the standard deviation of the errors for individual measurement. In the case of the errors following a normal distribution, the amplification factor is √2, i.e. approx. 1.41. This represents a 41% increase in standard deviation, which means an inherent, substantial, increase in the uncertainty associated with the reported change in thickness compared to the thickness measurements alone.

The nature of errors for measurement and the differences are illustrated in Figure 2 below. The y-axis shows the probabilities, which can be considered as a proportion of locations, according to error which is expressed as a function of the standard deviation of the error for individual measurements (σ_{ε}). The y-axis value indicates a probability of shortfall for the left-hand part of the graph (negative errors where the measurement or difference in measurements is smaller than the true value) and a probability of exceedance for the right-hand side of the graph (positive errors where the measurement or difference in measurements is greater than the true value). It is evident that the errors in the differences are significantly larger, e.g. approximately 2% of locations would have a thickness error exceeding 2σ_{ε} but this same proportion would have errors in the differences, or change in thickness, exceeding 2.8σ_{ε}_{. }

Figure 2: Probabilities according to error level

Another way to look at this is to consider the probability levels for the same error value, e.g. in the figure above the error will exceed +2σ_{ε} for approximately 2% of individual measurements and 8% of differences in measurements. Hence, for example in the case of 100 measurement locations, one would expect 2 locations in the current measurements to have an error of greater than +2σ_{ε} but 8 locations to have errors in the change in thickness exceeding +2σ_{ε}. This represents a significant increase in probability (by a factor much larger than √2) and the relative increase in probability actually grows with larger error values.

The measured change in thickness feeds directly into corrosion growth calculations for individual measurement locations. The outcome is that, in many situations in practice, the calculated corrosion growth is dominated by errors in the measured change, even where measurements that have been determined as “spurious” are removed. This impacts directly on remaining life estimates which are often taken as the basis for defining subsequent inspection intervals. Remaining life estimates are themselves often extremely sensitive to error in the corrosion growth value used (the impact of thickness measurement error on the statistical characteristics of remaining life estimates will be the subject of a future article as it’s also currently not widely appreciated by integrity practitioners).

Even relatively small inspection errors can drive large variability in the remaining life estimates. One consequence of this variability is a large number of cases where the remaining life, to some limiting condition, is severely underestimated. This is frequently observed in practice and is a major contributor to pipework integrity and inspection becoming an exercise in tail chasing, with massive arising inefficiency.

The amplification of error when taking differences between measurements, or more correctly an insufficient understanding of its effects, is a key factor that sets the dynamic dog in motion. Then, together with other factors, it adds momentum to the cycle, which often grows increasingly inefficient. This is observed even when risk based inspection (RBI) systems, which aim to use feedback to improve efficiency, are in place for pipework integrity management. Fortunately, putting the brakes on the cycle of inefficiency is easily done and there is a range of good industry guidance available to help you do this. Some key points for consideration are provided below.

- Avoid reliance on location or feature based comparison, particularly for estimation of short-term corrosion growth rates as a basis for remaining life estimates, even where that may be the expectation of the RBI system in place. Consider implementation of analysis approaches that remove sensitivity to measurement error. HOIS-G-010: Guidance on Effective Pipework Inspection [1] provides in-depth information on methods of analysis that acknowledge and minimise sensitivity to measurement variability

- Recognise the potential for measurement errors and aim to understand the primary drivers for errors as well as their influence on each stage of the analysis and decision-making process. Note that thickness error is affected by a range of application specific parameters, including for example the nature of the corrosion present and how that evolves over time. It is not sufficient to consider the performance of the thickness measurement system in isolation as this will often underestimate the errors affecting real data collected. HOIS-G-010 [1] provides information on practical factors affecting measurements. The HOIS Recommended Practice for Statistical Analysis of Inspection Data, HOIS(12)R8, [2] includes data on measurement capability. It also provides information on how to analyse the effects of measurement variability as well as giving examples of its impact on results used in the integrity process.

- Consider improvements to the inspection methods used. These may include:
- Reducing the sensitivity of measurement accuracy to corrosion morphology by following, for example, the guidance in the HOIS Recommended Practice for Precision Thickness Measurements for Corrosion, HOIS-RP-003, [3].
- Changes to the techniques used, e.g. advances in inspection technology mean it’s increasingly feasible to replace manual ultrasonic measurements with high density corrosion mapping. That also affords enhanced analysis using the methods specifically for corrosion mapping outlined in [2]. Note that some technique changes may also be driven by a change in strategy, e.g. where screening methods, providing categorical output, may be preferable.

ESR Technology can help you make better use of data and enhance the value of NDT to optimise your inspection and integrity programmes. We do this via training and independent consultancy covering data analytics, NDT, corrosion and mechanical integrity. If you would like more information or have any questions please get in touch via This email address is being protected from spambots. You need JavaScript enabled to view it..

**References**

- HOIS Guidance for More Effective Pipework Inspection, HOIS-G-010, 2018.
- HOIS Recommended Practice for Statistical Analysis of Inspection Data, HOIS(12)R8, 2013.
- HOIS Recommended Practice for Precision Thickness Measurements for Corrosion, HOIS-RP-003, 2017.