A Risk Based Approach to Determine Ultrasonic Inspection
Frequencies in Railway Applications
Jorn Vatn , Hans Svee
The Norwegian National Rail Administration
Pirsentret
7462 Trondheim, Norway
6^{th} Proceedings of the 22^{nd} ESReDA Seminar, Madrid, Spain May 2728, 2002
Abstract
In railway applications the rails are regulary inspected by means of ultrasonic techniques to detect cracks before these develop to rail breakage's. Usually the measurement equipment is mounted on a vehicle operating at a speed of 4050 km per hour. The current inspection intervals in Norway are based on experience from other countries, international recommendation etc, but currently these intervals have not been evaluated based on cost benefit analysis. The yearly cost of inspecting the Norwegian network comprises several hundred thousands of Euro. On the other hand there are significant costs if cracks are overlooked leading to rail breakage and a possible derailment. In a pilot study JBV (the Norwegian National Rail Administration) has developeda probabilistic model wich has been used for optimising the intervals for one of the major line in Norway. The results show that yearly cost savings of the order of 35 000 Euro could be achieved for that line by changing inspection intervals from 24 months to 12 months. The most important factors in the model are. i) number of cracks initiated per year, ii) expectation and variation of the PF intervals, iii) measurement precision, iv) cost of inspection, v) cost of derailment and vi) cost of replacing rails.
1.Introduction
To ensure safe railway operation it is important that the rails are free from defects such as cracks, geometry failures etc. In modern railway operation there exist two types of monitoring cars for the rails:
 Ordinary measurement cars measuring rail geometry and surface deterioration;
 Ultrasonic inspection cars measuring rail breakage's and internal cracks.
In this paper we will discuss the use of ultrasonic inspection cars. The main objective of this inspection method is to reveal latent failures such as cracks in the rail before they develop to rail breakage's wich is a severe threat to safe railway operation. A conceptual risk model is shown in Figure 1 where the different barriers are visualised. The main set of barriers are:
Rail quality  The rails are primarily constructed to have a strength that ensures an
approximately infinite life length. However, high axle loads, wheel failures and substructure failures can compromise this barrier significantly.
 Ultrasonic inspection  Due to fatigue and other failure mechanisms cracks might be initiated in
the rails. In order to detect such cracks ultrasonic monitoring cars have been
developed. The objektive of this study is to investigate the optimal frequency
for running these cars. The concept of " PF intervals" is important in this
context, and will be discussed later.
 Track circuit detection  For some networks track circuits have been implemented as a part of the
signaling system. A convenient "extra effect" of this system is that it is
possible to detect rail breakage's. The track circuit is a part of the centralized
Traffic control system ( CTC ). Only breakage's that result in a complete
breakage of the rail may be detected by this system.
 Physical barriers  If a breakage is not detected this may lead to a derailment. However,
there are some physical barriers such as "guide rails" used on bridges, in
in curves and tunnels etc.


Fig 1: Barrier model

2. Model
In order to optimise the "Ultrasonic inspection" in Figure 1 it is necessary to establish a more comprehensive model. A basis for such modelling is the use of socalled influence diagrams. In the JBV study the influence diagram proved very efficient as a communication tool between the analyst, the experts and the safety department.
Influence diagram
An influence diagram ( see e.g. Vatn et al 1996) is an excellent tool to visualize the qualitative effects of a measure. The influence diagram shows the relation between decisions ( e.g. maintenance actions), random quantities ( e.g. number of broken rails), and values ( e.g. cost of derailments). The influence diagram comprises nodes and arrows. There are three types of nodes:
 Decision nodes represent states where the decision maker is able to choose an action, typically type and frequency of maintenance.

 Change nodes represent random quantities and are influenced by the decision nodes.

 Value nodes represent costs, e.g. for maintenance or damages.

The arrows represent the relations ( influences) between the nodes in the diagram, i.e. cause and effects. The arrows only indicate that there is a relationship, but do not say anything about how strong this relationship is.
The diagram is a basis for setting up the mathemetical model that is used in the final optimisation.
Influence diagram for ultrasonic inspection
The influence diagram is shown in Figure 2. The only decision node in the diagram is the "inspection interval" of the USI measuring car. The node influences directly the costs for USI and the probability of crack detection. The probability of crack detection is influenced by the PF interval and the detection probability of the ultrasonic technique as well.


Fig 2: Influence diagram for ultrasonic inspection 
Table 1: Abbreviations used in the influence diagramm

The starting point of the diagram used in the present study is the number of rail cracks
(# det. Cracks us. ) The number of rail cracks are influenced on many factors, and only the main factors are shown in the diagam: traffic load, temperature/season, and quality of the material. These factors influence the PF interval as well.
Some cracks are deteced by USI (# det. Crack USI) some others are not (#undet. Crack USI). However, a couple of cracks that are undetected by ultrasonic measuring, can be detected in other ways ( # det. cracks by visual obs. etc. ), e.g. visual inspection. They implicate together with the detected cracks by USI  planned rail renewals. A couple of cracks always remain undetected in the rail ( # det. undet. cracks). The others lead to rail breakage ( # rail breakages). A large portion of the rail breakage's can be detected by Centralized Train Control ( # det. breakages by CTC) and other detection methods such as visual inspection, by train personnel, etc. ( # det. breakages by visual observ. etc.). The repair of the detected breakage's results in nonplanned rail renewal. The remaining rail breakages lead to derailments or other damages. Table 1 explains the content of the nodes used in the influence diagram in Figure 2.
PF interval
The concept of "PF intervals" is very important in maintenance analysis. Please see e.g. Moubray (1991) and Vatn ( 1998) for further discussion of the PF interval is the time interval from a potential failure could be detected until a failure occurs as illustrated in Figure 3.

Fig 3: Illustration of the PF interval

The point "P" is the first point in time where we are able to reveal the outset of a failure. When the progression is above some value a breakage/failure will occur (point "F" ). The length from a potential failure is detectable until a failure occurs is denotes the PF interval T_{PF}. The legth of the PF interval is assumed to vary from time to time because cracks can be initialized in diffrent places of the rail and the crack propagation depends on several diffrent facors etc. The length of the PF interval should therefore be treated as a random quantity as illustrated in Figure 4.

Fig 4: Variation in the PF interval

Periodic ultrasonic inspection is conducted at intervals of length t to detect potential failures. The length of the inspection intervals should not be longer than the average PF interval. However, since the PF interval varies from time to time, and because there is also probability that a potential failure is not revealed during and inspection, the inspection interval should be shorter than the average PF interval. In Appendix A a model to calculate the failure probability in this situation is presented.
3. Parameter values and cost figures
In order to optimise the inspection intervals for ultrasonic inspection we need to assess the parameter values and cost figures used in the influence diagram. We differentiate between two types of figures:
 Parameter values describing the physical barrier model, e.g. number of cracks, PF interval distribution, track circuit detection probability etc.;
 Cost figures related to cost of maintenance, cost of a derailment etc.
There are mainly three data sources for assessing: the parameter values used in the influence diagram
 Norwegian railway statistic;
 Experts from JBV (the Norwegian National Rail Administration);
 Others, e.g. literature, magazines etc.
Number of cracks and PF interval lengths
It's obvious that the age of the rail, traffic load, and quality of the material have a significant influence on the initiation of cracks, the velocity of crack propagation, and consequentially the length of the P F interval. All these factors appear simultaneously and therefore it is very difficult to describe the influence of the factors quantitatively.
Palese and Zarembski (2001) published that as rail accumulates tonnage, it tends to develop more internal fatigue defects, based on various factors such as metallurgy of the rail, traffic (to include such factors as axle loading and speed), track support conditions, etc.
Influence of temperature/season
It is a fact that much more rail breakage's occur under low temperature conditions than under warm conditions. The temperature values in the Norwegian statistics are the temperature at the time of detection. However. they can act as a clue for the temperature when the breakage occurred. The distribution of the temperature of 676 rail breakage's on the Norwegian rail routes Bergensbanen, Dovrebanen, Nordlandsbanen. and Rorosbanen is shown in Figure 5. It is evident that most of the rail breakage's occurs at low temperatures. The majority of the breakage's occur in the temperature interval from 9°C to 0°C and more than two thirds of the breakage's are in the temperature region below zero degrees Celsius.
Figure 5 shows the number of rail breakage's found in the railway statistic versus month number. The values for Bergensbanen, Dovrebanen and Sorlandsbanen are shown in the diagram and in addition the total summation of the breakage's on the three track sections. If we summarize the total values for winter, spring, summer, and autumn the seasonal influence on the number of rail breakage's can be seen. Much more rail breakage's occur under cold conditions (winter) than under warm conditions (summer).
It is assumed that the factors traffic load, material quality and temperature have a significant influence on the crack and breakage problem. However, these influences couldn't be quantified during this work. Therefore these nodes are omitted in the influence diagram and the following optimisation.
However, it is an important future work to include these nodes in the diagram and find a mathematical description of these influences. This will lead to an improvement of the modelling.

Fig 5: Influence of temperature: Number of breakages versus month number

Assessing parameter values
Number of cracks per year
Even though the number of rail cracks per year is the bottom line in the cost model derived from the influence diagram this number is unknown and must be estimated. Analysis of the railway statistics for several railway routes in Norway gave the average number of cracks and breakage's per year as shown in Table 2.
Track section, from  to, km  Detected rail cracks  Detected rail breakages

Dovrebanen,
Lillehammer  Trondheim, 368 km  30,14  9,17

Bergensbanen,
Honefoss  Bergen, 381 km  36,00  9,00

Nordlandsbanen,
TrondheimGrong, 220 km  20,41  4,50

Table 2: Number of detected cracks and breakage's per annum

Estimation of the P F interval and the standard deviation
JBV uses a classification system for rail failures. The system is based on four failure classes. For each class it is defined a maintenance procedure:
Failure class 2b:  Keep rail under observation
 Failure class 2a:  Repair failure
 Failure class 1:  Repair failure quickly
 Failure class 0:  Repair failure immediately and initiate traffic restrictions until failure is fixed

One possibility to get information about the length of the P F interval is, to check the railway statistic if there is any crack reported twice; but classified into different failure classes. In the statistics this information was found for a couple of rail cracks that first had been classified as failure class 2b and later on as class 1. The survey of the time interval between these reported events leads to an average value of 1.68 years. This value can be claimed to be the time for the average P F interval between failure class 2b and failure class 1. However, there is a significant variance in the values. The standard deviation is 1.71 years. The length of the P F interval T_{PF}= 1.68 years is the mean time that a crack needs for the propagation from class 2b to class 1. The value for the searched P F interval will in all circumstances be longer. This applies for the standard deviation of the P F interval as well. However, the values can be used for the estimation of the P F interval.

Fig 6: Basis for estimation of average PF interval and standard deviation 
Palese and Zarembski (2001) has further found that the interval between the time when the defect grows to detectable size to the time when the actual failure is imminent is of the order of 10 to 50 mgt (megaton), depending on a number of track, traffic and environmental factors. On Dovrebanen there is an annual traffic load of about 4 mgt. This indicates that the average P F interval should be between 2.5 and 12.5 years.
Experts from JBV were also interviewed to assess the P F interval length. They estimated the P F interval to be 5 years in average.
Based on this a length of the average P F interval (µ) of 5 years (60 months) was used. The standard deviation (d) was assumed to be 3 years (36 months).
Failure probability ultrasonic measuring: q
Even if there is a potential failure (crack) at the point of time when the ultrasonic inspection car is run, there is a probability that this crack will not be detected. As discussed in Appendix A the probability that a given inspection fails to detect a potential failure should be divided into a "common cause" part and an "independent" part. However, in the present study only one parameter q was used as an approximation to represent the failure probability of the measuring car. In the study q was estimated to 50%. This estimate is partly based on dicussions with experts within JBV, but also based on a "calibration" of the influence diagram in Figure 2.
Parameter  Value

Number of cracks per year  30

Average PF interval length  5 years

Standard deviation,PF interval  3 years

Failure probability, one USI  50%

Table 3: Summarising parameter values

Number of derailments
In the last 10 years there were 2 derailments due to rail breakage's in Norway. This means that on the average there are about 0.2 derailments per year on the Norwegian railway system. The length of a track section like, e.g. Dovrebanen, represents approx. 9 % of the Norwegian railway system (4180 km). The average value for the traffic load in Norway is about three megaton. The traffic load on Dovrebanen is somewhat higher than the average value, hence it can be expected about 0.025 derailments per year on Dovrebanen. The values for 3 other track sections of the Norwegian railway system were also estimated as shown in Table 3.
Track section  Length  Traffic load  Expected number of derailments per year 
Dovrebanen,
Lillehammer  Trondheim  368 km  4,3 mgt/year  0,025

Bergensbanen,
Honefoss  Bergen  381 km  3,3 mgt/year  0,02

Nordlandsbanen,
TrondheimGrong  220 km  3,3 mgt/year  0,01

Table 4: Expected number of derailments per annum

Other values for the optimisation model
For the estimation of all other nodes a 'weighting of the arrows' between the nodes is needed. This is done by the use of "percentages". The estimated values are shown in Table 5.
# undet. cracks by us. > # det. cracks by visual obs. etc.  10%
 # undet. cracks by us. > # undet. cracks  10%
 # undet. cracks by us. > # rail breakages  80%
 Sum:  100%
 # rail breakages > # det. breakages by track sirc.  40%
 # rail breakages > # det. breakages by visual obs. etc.  55%
 # rail breakages > # undet. breakages  5%
 Sum:  100%
 # undet. breakages > # derailments  5%
 # undet. breakages > # other derailments  95%
 Sum:  100%

Table 5: Additional values used in the optimisation model

Unfortunately there is almost no information about the required figures in Table 5 in the Norwegian statistics. The only indication from the statistics is the "method of detection" of cracks and breakage's.
Assessing costs figures
For the optimisation analysis it is very important to find realistic basic costs. The real costs can vary considerably from time to time. Therefore the estimation of these values are very difficult.
For the ultrasonic inspection JBV hires the measuring car from an American company that operates in the Nordic countries. The cost for one shift is 60,000 NOK. In addition with costs for personnel, an amount of 100,000 NOK was used in the optimisation analysis. At least two shifts are required for a typical line in Norway.
For the costs of derailments Palese and Zarembski (2001) refer to the Federal
Railroad Administration (FRA) statistics. The entire range of rail defects varies from
1.6 million NOK to 11.2 million NOK depending on defect type, with an overall
average on the order of 3.2 million NOK. But this is FRA reportable cost only. The
actual cost of the derailment, which could include loss of lading, train delays or train
rerouting, can double that amount. In addition to these economic values we may also
have cost of killed and injured persons. In Norway statistics shows an average of 0.2
fatalities per derailment. With a "value of one statistical life" of 20 million NOK as
used in Norwegian in tranportation analyses, the "total" cost of a derailment is set to 15
million NOK.
The costs for renewal and other damages were estimated together with experts from JBV. The figures are summarized in Table 6.
Value node
 Basic Costs
 Cost of ultrasonic inspection
 100,000 NOK
 Scheduled rail renewal
 15,000 NOK
 Unscheduled rail renewal, train delays, and rerouting
 40,000 NOK
 Derailment
 15,000,000 NOK
 Other damages
 40,000 NOK

Table 6: Basic costs for ultrasonic inspection, rail renewal, and damages ( 1€ = 8 NOK )

4. Optimisation results
The influence diagram in Figure 2 is quantitatively modelled in an EXCEL spread sheet. This enables easy optimisation of the inspection intervals, as well as sensitivity analyses. Figure 7 shows the total cost for diferent inspection intervals for Doyrebanen. The current inspection interval is 24 months. From Figure 7 we see that the total costs decreases as the interval become shorter. The minimum cost is reached at approirnately ten months i.e. a duplication of the inspection frequency up to one measuring per year could be recommended. In this case a saying of approx. 300,000 NOK (35,000 Euro) can be expected. Similar optimisation was carried out also for Bergensbanen and Nordlandsbanen.

Fig 7: Optimisation for Dovrebanen 
5. Conclusions and suggestions
The present study has provided a simplified model for o~sation of ultrasonic inspection. The elaborated influence diagram was a suitable tool fbr the work and can be a basis for the future work. The mathematical optin iisation model was established with the basis from the influence diagram The ultimate result of the optimisation is the inspection interval should be reduced from the current practice of 24 months to 12 months for the lines being analysed. Yearly savings of 30 40 thousand Euro could be expected per line due to the new maintenance strategy. For the entire Norwegian network this could give savings of more than hundred thousand Euro.
For JBV such models are very helpful because:
 The results can be used directly,
 The influence diagram visualises which parameters that influence the optimisation result. This will be the basis for further improvement in data collection exercises, as well as in the modelling area.
There are many directions for improving both the model, and also the inspection strategies. First of all, sensitivity analyses have shown that many parameters have a large impact on the results. Among these are the mean value and standard deviation of the P F intervals. Currently the quality of the statistics to estimate these values are rather bad. A Norwegian project is now running to improve data quality, and the collection of information that could be used to assess the P F intervals are explicitly addressed. There is also a European initiative under the ProM@in project (http:\\pronkiim.server.de) which addresses the challenge to establish a common European RAMS database that would be very beneficial in such studies. In addition to get better estimates of the P F intervals, it is also important to increase the length of the P F interval. This requires to eliminate or reduce the effect of important influencing factors. One such factor is the damage incurred by the rolling stock, e.g. due to extremely high axle loads or load wheels". There exist detector system that could be used to "detect' wagons with "bad wheels". Such systetris are installed in e.g. Spain and Norway. If these wagons are detected they could be removed, and hence a reduce damage to the rails could be expiated which would increase the P F interval and reduce the frequency of crack initiation. This area is also addressed by ProM@in.
Another important factor is the ultrasonic inspection failure probability, q. This parameter has large impact on the cost figures. In addition to get better estimates for this parameter it is also important to reduce the failure probability. There are several means that could be considered:
 Running the monitoring car slower at sections where a large number of cracks
are expected;
 Running the measuring car back and forth at sections with a high expected rate
of cracks;
 Using manually operated ultrasonic inspection systems (carrier operated by foot)
at sections where a large number of cracks are expected. Manually operated
systems have proved to have a better coverage than cars driving at a high speed.
Acknowledgment
Part of this work has been supported by the European Commission under the EUproject ProM@in (http://promain.server.de). Thanks also to Thomas Welte who has carried out much of the modeling and analyses during his project work at the Norwegian University of Technology and Science (NTNU).
References
 Moubray, J.. Reliability centered Maintenance, Butterworth Heinemann, Oxford,
(1991).
 Palese. LW and Zarembsk A.M., BNSF test risk based ultrasonic detection. Railway Track & Structures. February 2001.
 Vatri, J., Hokstad, P. and Bodsberg, L., An Overall Model for Maintenance Optimisation, published in Reliability Engineering and System Safety, 51:241 257, (1996).
 J. Vatn, Strategic Maintenance Planning in Railway Systems. SINTEF Report STF38 A98425, SINTEF Industrial Management, N7465 Trondheim Norway, 1998.
APPENDEK A:
Calculation of probability that a potential failure is not detected by USI
In the following we will describe the method used for calculating., the probability that a potential failure is not detected by ultrasonic inspection. There are two main sources for not detecting a potential failure in due tinie; i) the inspection interval is to long compared to the P F interval, and ii) the quality of the inspection is to low to detect a potential failure. The following quantities are defled:
T_{PF}  PF interval (random variable).
 x_{PF}  Probability distribution function of T_{PF}
 q  Failure probability of one inspection, i.e. the probability that a given run fails to
detect a potential failure
 q_{C}  Common cause part of q
 q_{l}  Independent part of q
 t  Inspection interval

The probability that the inspection strategy fails to reveal a potential failure before a critical failure occurs could be found by the low of total probability:
 (1)

where Q_{t}(t,q,t) is the probability of not detecting a potential failure given that the P F interval, T_{PF}, equals t. In order to calculate Q_{t}(t,q,t) we observe that when T_{PF} = t, then number of possibilities to detect a failure equals n or n + 1 where n = int(t/t,) where int(.) is the integer function. The probability that we will have n + 1 possibilities equals t/t  n and thus the probability that we will have n possibilities to detect a potential failure equals n +1  t/t. Since the probability that a given inspection fails to detect a potential failure equals q, Q_{t}(t,q,t) could easily be obtained by:
 (2)

if the inspections could be considered statistically independent. However, the
assumption that inspections are independent does not seem realistic. A more realistic
assumption would be to assume that the failure probability of one inspection is given
by:
whcre q_{c} represents common cause failures duo to hystematic failures such as low
coverage, and q_{l} represents the failure probability due to specific conditions for one
run, e.g. inadequate velocity of the measuring wagon, human errors etc.
Assuming that the failure probability of one inspection could be divided into a common and an independent part as shown in eq. (3) we calculate the total failure probability of the inspection strategy as:
 (4)

where Q_{0}(t,q_{l},x_{PF}) is found by eq.(1)
Q_{0}(t,q_{l},x_{PF}) could easily be approximated by an EXCEL spreadsheet function. In the present study x_{PF}) is assumed to be a gamma distribution with mean µ and standard deviation s.
there is also probability that a potential failure is not revealed during an inspection, the inspection interval should be shorter than the average P F interval. In Appendix A a model to calculate the failure probability in this situation is presented.
A prerequisite for using the P F intervals in maintenance planning is that a failure is alerted by some degradation in performance, or some indicator variable is alerting about the failure. Such a variable could be vibration, cracks, increased temperature etc. In this special study this indicator is "cracks".
