Reliability estimation for populations with limited and
heavily censored failure information
Lukasz Chmura, P.H.F. Morshuis, E.Gulski,
J.J. Smit
Delft University of Technology
Delft, The Netherlands
L.a.chmura@tudelft.nl
Anton Janssen
Liander – The Network Operator
Arnhem, The Netherlands
Abstract—Statistical analysis of the life data, is a useful tool
helping to assess the life-time of populations of high-voltage
components. More specific, the results of such analysis give
overview over the failure behavior of the population under
investigation, i.e. number and trend of expected failures. For the
analysis, the detailed information about ages and numbers and
ages of installed units and failed units has to be collected.
Subsequently, the distribution representing the behavior of the
population is fitted to the data. The latter allows deriving the
time-dependent failure rate function, which in turn, directly
indicates the trends of the future failures. However, this method
requires homogeneous and independent data of sufficient
amount. The latter becomes a problem, particularly that for past
periods the failure data is often unavailable. It is important to
estimate the population reliability and number of expected
failures, for the whole population of components being operated.
This is also important in the case when the available failure data
comes only from one part of the area where the components are
installed. In this paper we will show how to deal with populations
where the available failure data is heavily censored, and what will
the influence of the data division according to the regions in
which the transformers are operated, on the failure expectancy.
Keywords-failure analysis, transformers, tap-changers, data
censoring, reliability
I. INTRODUCTION
The reliability of transformers is crucial for the reliability of
the transmission and distribution network. For that reason it is
necessary to assess the life-time of the population of the
transformers, so that the replacement and spare units policies
can be planned in advance. The mentioned policies aim to
assure redundancy of the whole network, if certain component
of the network fails. This situation refers to the N-1 criterion,
which says that if any single component of the power network
fails, the other components should be able to take over the load,
so that no single user is disconnected from the supply.
The statistical analysis is often used as one of the
methodologies for the life-time assessment of the high-voltage
components [2]. Fitting mathematical model to the life-time
data of the population and derivation of the describing
functions, allows to conclude about the actual life-stage of the
population. In addition, the number of upcoming failures can
be estimated with given confidence interval However, for the
proper statistical analysis, the supplied data must display the
following features: homogeneity, independence, randomness
and sufficient amount. Firstly, the data is to be drawn from one
population , where all factors are constant for the whole period
of population operation. Secondly, the data are independent for
different subject, and every outcome (failure of the component)
is equally likely to occur within the population. Finally,
sufficient amount of data has to be provided to enable the
proper and confident distribution fitting.
Figure 1. Schematic showing the data handling for the statistical analysis
For the statistical analysis, the detailed information about
ages and numbers installed and failed transformers has to be
collected. To ensure the robustness of the analysis, the reason
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2013 Electrical Insulation Conference, Ottawa, Ontario, Canada, 2 to 5 June 2013
978-978-1-4673-4744-0/13/$31.00 ©2013 IEEE