Abstract—Asset failures, that needs to be managed, has an uncertain characteristic and analysis of uncertainty is essential to Asset Management (AM). Forecasting the technical performance of assets forms an integral part of strategic and operational activities within AM. To establish the failure behaviour of assets requires a significant degree of reliable asset information, which, in many practical cases, is not sufficiently rich or available to provide a basis for straightforward decision-making. In this paper a practical and systematic statistical methodology is used for dealing with incomplete asset lifetime data. The method described in this paper is based on a statistical parametric method and is applied with the aim of obtaining an indicator of the future failure expectancy with a certain confidence interval. On the whole, the paper concludes that, even though input data was either missing or incomplete, it is in certain cases possible to develop sensible probability models. These models take into account uncertainty and ultimately can be applied to facilitate the asset manager in AM decision-making. In addition to applying statistical methods, this contribution highlights the vital role of engineering and expert knowledge in interpreting the statistical results.

1. J-6 2012 IEEE International Conference on Condition Monitoring and Diagnosis
23-27 September 2012, Bali, Indonesia
Statistical Approach to Establish Failure Behaviour
on Incomplete Asset Lifetime Data
Ravish P.Y. Mehairjan, Arjan M. van Voorden
Dhiradj Djairam, Qikai Zhuang, Johan J. Smit Asset Management
High Voltage Technology & Asset Management Stedin B.V.
Delft University of Technology Rotterdam, the Netherlands
Delft, the Netherlands
r.p.y.mehairjan@tudelft.nl/ ravish.mehairjan@stedin.net
Abstract—Asset failures, that needs to be managed, has an due to many mergers and acquisitions of smaller regional
uncertain characteristic and analysis of uncertainty is essential to utilities into larger consolidated utilities, intellectual properties
Asset Management (AM). Forecasting the technical performance often was lost. Correspondingly, AM is a fairly new concept
of assets forms an integral part of strategic and operational for the electric power sector. Hence, in the earlier days, many
activities within AM. To establish the failure behaviour of assets utilities did not see reasons for collecting detailed information
requires a significant degree of reliable asset information, which, to track equipment lifetimes [3]. Nevertheless, with the AM
in many practical cases, is not sufficiently rich or available to framework heavily relying on asset level data to support sound
provide a basis for straightforward decision-making. In this AM decisions [4], a strong demand for methods and tools was
paper a practical and systematic statistical methodology is used
brought forth. These methods and tools should be able to
for dealing with incomplete asset lifetime data. The method
described in this paper is based on a statistical parametric
analyse equipment lifetime data even in the often occurring
method and is applied with the aim of obtaining an indicator of case of incomplete or inconsistent data. In section II , a
the future failure expectancy with a certain confidence interval. systematic statistical approach is described, followed by the
On the whole, the paper concludes that, even though input data application of this approach to a practical case of incomplete
was either missing or incomplete, it is in certain cases possible to asset data for distribution cable assets. In section III, two case
develop sensible probability models. These models take into studies are presented. The former discusses a sensitivity
account uncertainty and ultimately can be applied to facilitate analysis used for the presence of a suspect asset group in a
the asset manager in AM decision-making. In addition to certain failure dataset. The latter delves into a case of dealing
applying statistical methods, this contribution highlights the vital with incomplete data, in which expert judgements played a
role of engineering and expert knowledge in interpreting the crucial role.
statistical results.
II. STATISTICAL LIFE DATA ANALYSIS
Keywords-asset management; failure rate; statistical life data
analysis. A. Parametric Distribution Fitting Method
Reference [5] described the application of statistical
I. INTRODUCTION analysis in AM decision processes. Likewise, the parametric
Supported by the publicly available specification method [6], [7], which uses mathematical assumptions to fit
,BSI:PAS55, and the forthcoming ISO55000/1/2 Standards, hypothesized probability of failure distributions to the data, is
the discipline of AM is progressively emerging as a framework used. This method comprises a number of steps and this
for competent asset intensive organizations [1]. In this context, straightforward procedure is depicted in figure 1.
forecasting asset failure behaviour, based on reliability
engineering, is connected to aging asset strategies and is
guiding operations and maintenance decision-making. The key
to making good AM decisions is acquiring appropriate asset
knowledge. Consequently, in the past years, electric utilities
and industries have progressively created databases to record
asset or business data, such as failure, maintenance, operation
and cost [2]. However, throughout electric utilities, and
probably in other industries as well, it is commonly
encountered that asset managers raise the matter of lack of
sufficient information for making good decisions. There are
many reasons for this shortcoming. The majority of assets in Figure 1: Evaluation flowchart for life data analysis, with emphasis on the
power systems are aged and at that specific time in history parametric method, which is applied in this study.
there were no information recording systems available to
B. Data Types
record asset information. In cases where such information
systems were gradually becoming available, it occurred that Statistical failure distribution models rely extensively on
due to system modifications, information was lost. Moreover, the data, life data or time-to-failure of a component, to make
This research has been performed in close collaboration with Stedin (a
Dutch Distribution Network Operator, DNO).
978-1-4673-1018-5/12/$31.00 ©2012 IEEE 517

2. predictions. The combination of sufficient data and appropriate III. ESTABLISHING FAILURE FORECASTS WITH INCOMPLETE
statistical model choice, will usually result in acceptable ASSET LIFE TIME DATA
predictions. In life data analysis a distinction can be made
between failure data (failed unit) and suspended data (un- A. Medium Voltage (MV) Distribution Network [8]
failed unit). Furthermore, the collected life data for statistical At Stedin, the third largest Dutch Distribution Network
analysis purpose should have the following properties [7]: Operator (DNO), MV cable joints contribute to a vast majority
of distribution grid outage times (45%). With the goal to
- Randomness predict the technical performance of this asset group, an
- Independency investigation for the application of statistical life data analysis
- Homogeneity was carried out for a particular region of 10 kV distribution
- Sufficient amount of data network of the utility [8].
In the analysis of life data, it is deemed advisable to use all
available data. In practise, however, it is challenging, B. Available Data
expensive and sometimes impossible to collect all required life Paper-based outage data recording started, partly, around
data. Consequently, the available life data, at utilities, is 1976 in the Netherlands, followed by a database collection tool
incomplete or include uncertainties (censored data), as to when in 1991 named “KEMA Nestor”. This failure reporting
exactly a component failed or was installed. database has developed throughout the years and has been
improved continuously. At the time that this case study was
C. Failure Distribution Fitting/ Parameter Estimation
performed, the available MV failure data for the period 2004
Failure probability distributions are mathematical Time Window
equations allowing a large amount of information, Introduction of Kema Failure Data Available
Nestor database
characteristics and behaviours to be described by a small
number of parameters. In general, a certain failure distribution
for an asset population is chosen based on one or more of the ~ 1976 ~ 1991 2004 2009
Failure Data Unavailable
following considerations: Paper matter
data collection New network components
New voltage levels
- The dominant failure mechanism satisfies most or all New way of data collection
Many utility merges
assumptions which underlie a certain statistical New data definition
distribution until 2009 had been consistent and could be used in a viable
- The choice is limited to the failure distribution that way. The development of failure data recording is shown in
best fits the life time data figure 2.
- A simple distribution, which is well suitable for Figure 2: Timeline showing the availability of failure data in distribution
analytical computations. network for this study. This time window reflects the period where failure data
Often used statistical functions, which describe the failure is available. In between, failure data is often missing or incomplete.
distribution, are the probability density function (pdf), the The analysis takes into account 556 cable joint failures, within
cumulative distribution function (cdf), the reliability function the last 6 years.
(R) and the failure rate functions (λ). These functions contain
all information about the failure process of the assets under Number of reported 10 kV cable joint failures
consideration. Frequently used failure distributions for Synthetic Joint Mass-Insulated Joint Oil-Insulated Joint
250
(continuous) life data analysis are normal, Weibull,
# of joint failures
200
exponential and Gumbel distribution. After a certain failure
distribution is selected to fit the data, the next step is to 150
estimate the parameters of this distribution. Three, often 100
applied, methods are; Probability Plotting (PP), Least Squares 50
Estimation (LSE) and Maximum Likelihood Estimation 0
(MLE). <1 [1-5] [5-10] [10-20] [20-40] > 40
Age Bins (years)
D. Maximum Likelihood Estimation (MLE)
In this contribution, the MLE method is applied, as this Figure 3: 10 kV joint failure records for the period 2004-2009 for three
categories of cable joints. As result of unknown exact age at the moment of
method has the ability to take into account large data sets and failure of a component, age intervals are used to estimate the age of the failed
large quantities of suspended data points, which is common components.
for electric network components. By maximising the value of
the likelihood function (L), which is a statistical expression of Most of the time, the exact age of the cable joints at the
moment of failure is unknown to the utility. To circumvent this
the probability of the parameter, the most likely parameter for
problem, estimated age intervals for the reported failures are
the given data set is estimated.
used, as shown in figure 3, for three categories of cable joints
namely; synthetic insulated, mass-insulated and oil-insulated
cable joints.
518

3. Besides failure data, additional data regarding the un-failed reached ages higher than 20 years. Two scenarios were
assets are also considered. The total recorded population of all analysed, in which failure data points were removed as follows:
three types of cable joints is roughly 31700 pieces. Firstly, for
large portions of the joint population the exact age (year of - All failures from age bin [>40] year and 10 failures
installation) is not specified or unknown. Such records are from age bin [20-40] year
often missing for assets that were installed more than 20 to 30 - All failures from age bin [>40] year and 20 failures
years ago. Secondly, for some parts of the cable joint from age bin [20-40] year.
population the corresponding joint type is unknown. The first The calculated failure rates, according to the best fit failure
shortcoming is dealt with by dividing the number of joints distribution (Weibull), are shown in figure 5.
without age, proportionally, and adding these joints to the
joints installed in particular years (conceptually shown in
figure 4a). A formula related to this procedure is:

( )
The second shortcoming is dealt with by using information,
based on expert knowledge, regarding the historic application
of certain joint types. These experts still have knowledge
regarding the history of when a certain type of joint was taken
into operation (conceptually illustrated in figure 4b).
(a) (b)
[25 - 50]
Number of components
Number of components
Figure 5: This figure shows the failure rate plots for three subsets of life data
for synthetic insulated cable joints. The blue failure rate plot represents the
original data record, while the black and green failure plot represent scenario 1
Population Age Population Age and 2, respectively.
Figure 4: Simplified impression for the estimation methods which are applied
to incorporate the missing data (missing asset installation year). From figure 5, it can be found that the failure rates are
As a result, it was possible to make rough estimations of the considerably lower for the synthetic joints when the suspect
missing records and incorporate these in the statistical analysis. “Nekaldiet” failure records are excluded from the statistical
The systematic approach, which is depicted in figure 1, is used analysis. Therefore, we may reasonably conclude that the
for modelling the life data of the three different 10 kV cable suspect “Nekaldiet” failure records negatively impact the
joints populations. overall failure behaviour of the synthetic insulated joint
population. More specifically, the asset manager can justify,
C. Statistical Analysis: Example 1[8] based on these results, that replacing aged “Nekaldiet” cable
For the case of synthetic insulated cable joints, experts at the joints, or applying condition monitoring to cable feeders with
DNO indicated that the cable joint failures, which are reported these types of joints, can be a feasible strategy to mitigate
in the age intervals [20-40] and [>40] years (see figure 3) are future failures.
probably failures of 10 kV resin joints that were installed in the D. Statistical Analysis: Example 2[8]
1970’s. These resin joints, often referred as “Nekaldiet” joints,
have resulted significantly to outages in the past years, With the developed failure rate models and the number of
however, are not applied anymore and replaced as much as components still in operation, the asset manager can obtain an
possible. Consequently, a sensitivity analysis was performed, indication of the future failure expectancy. To assess whether
using the calculated failure rates, to assess the failure behaviour the predicted number of failures reasonably describe the
of synthetic cable joints without the suspect “Nekaldiet” failure behaviour, it was decided to perform a validation test.
failures. For this purpose, it was required to exclude certain By comparing the actual recorded number of failures for the
failure as well as appropriate in-service data records. After period 2004-2009 with the predicted number of failures for the
consulting experts at the utility, it was agreed to exclude all same period, it is assessed whether the developed failure rate
failures which were recorded in the age bin [>40] years and a models reasonably describe the failure behaviour of the
number of failures from the age bin [20-40] years. Likewise, considered population (validation test). For two joint
the in-service data was adjusted. These considerations were populations (synthetic and oil) the validation test suggests to
based on the viewpoint that “Nekaldiet” joints were installed a be in accordance with the actual occurred failures. However,
few decades ago and ,therefore it was very likely that this for the mass-insulation cable joint population this was not the
group of synthetic joints had operated sufficiently to have case. It is worth noting, that for almost 60% of the mass joint
519

4. population no exact installation year was specified in the pin-pointed condition monitoring is necessary in the coming
database. These incomplete datasets were taken into account years, as part of the AM strategic and operational policies.
as described in section B (figure 4a). In order to assess
whether this first estimation, regarding the 60%, might be an IV. CONCLUSIONS
improper estimation, a number of new estimations were Inherently, asset failure is a source of uncertainty in AM [9],
examined. In a second attempt, the 60% of data was not while asset managers seek to manage this uncertain behaviour,
divided proportionally, but according to a certain age interval, the quest for tools and methods to analyse these are required.
as shown in figure 4b. The main reason behind this second This paper describes a rigorous statistical life data analysis
attempt was based on experts’ opinions, who indicated that methodology, which can be used for assessing and predicting
mass-insulated joints were mostly used a few decades ago. the technical performance of assets. From the first example, we
Thus, it was likely that the missing 60% data should be of a found that with the failure probability models, technical
population which is older than roughly 20 years. Therefore, reliability assessments can be carried out for suspect group of
this 60% was proportionally divided in various age intervals, assets within a population. On top of this, forecasting the
technical performance of assets is one of the main
satisfying this assumption. Different scenarios were used
responsibilities of the asset manager. With the developed
namely; age intervals of [20-30], [20-40], [25-50], etc. The
failure rate models for each population and the number of
expected future failure outcomes for the interval [25-50] years components in operation, the asset manager can anticipate the
were most in accordance with the actual occurred failures in development of future cable joint failures. On that account, the
the period 2004-2009. In figure 6, two scenarios (black and management of the utility has applied the results from this
blue plot) are illustrated together with the actual recorded investigation to justify the need for increased capital
number of failures (red plot). expenditures (CAPEX) towards MV distribution cable assets.
From the second presented example, it is found that by
choosing appropriate statistical models and in-depth
engineering and expert reasoning it is possible to create
valuable information on the failure behaviour of asset
populations, even in case of uncertain or missing data.
Altogether, we can conclude that, even though data was either
missing or incomplete, it is still possible to develop sensible
probability methods in order to provide the asset manager with
useful information to understanding the (uncertain) failure
behaviour of assets and support AM decision making.
ACKNOWLEDGMENT
The authors would like to thank Stedin B.V. for their
support, knowledge and access to data.
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