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Dielectric breakdown statistics of polyethylene for progressively-
censored data
M. Carmo Lana and J. Marat-Mendes
*
Departamento de CiŒncia dos Materiais, Secªo de Materiais Electroactivos (CENIMAT),
Faculdade de CiŒncias e Tecnologia, Universidade Nova de Lisboa,
2825-114 Caparica, Portugal
Keywords : power cables, dielectric breakdown, Weibull function, polyethylene.
Abstract. The dielectric breakdown of thin films of low-density polyethylene (LDPE) electrically
aged in an aqueous solution of NaCl under an AC electric field was investigated. A two-parameter
Weibull function was used for the dielectric breakdown time to failure. The probability of failure
for a sample was obtained by the White method for progressively censored data. Samples aged at
different temperatures were compared. The results show that initially the samples aged at lower
temperature (25
o
C) are more prone to fail, while those aged at higher temperature (50
o
C) fail at
longer times. This was attributed to a competition between oxidation and diffusion.
Introduction
Polyethylene is widely used as the polymeric insulation for medium and high voltage power cables.
The combined effect of the electrical field and environmental conditions originate electrical aging
of the polyethylene [1]. In the long run aging reduces the useful lifetime of cable when dielectric
breakdown occurs. Many parameters influence breakdown (temperature, electric field amplitude
and frequency, mechanical stress and the type and concentration of ionic species present). The
published studies include cables aged under service conditions but it is often more convenient to
accelerate aging in the laboratory [1].
Dielectric breakdown is a localized and stochastic process and a statistical approach is often
applied. The most common is to fit the data (failure times) using a two-parameter Weibull function
[1,2]. Laboratory accelerated electrical aging experiments do not necessarily end in the failure of all
samples (some experiments are aimed for studying other aspects of aging prior to failure and quite
often samples are aged for specific time periods). However it is unavoidable that some of the
samples will breakdown before the predicted aging time is reached. In this situation the set of
samples aged are composed of a group of samples that failed prematurely and another group that
has been aged for different aging times without failing. If a statistical approach is used in such a set,
the data is called progressively-censored (meaning that from a total of n samples only r have
suffered breakdown while n r were aged for a given time). The two parameters in the Weibull
function are the shape parameter (a) and the characteristic time (
W
) and the probability to failure
(
F
P ), at a given time t, is given by:
()
=
a
W
F
t
t P exp 1 (1)
Information about the dielectric breakdown mechanism can be obtained from these two
parameters. Both parameters can give some information on the breakdown mechanisms.
The methods used for the estimation of parameters are the least squares linear regression method
and the maximum likelihood estimator [3]. Several techniques were compared for estimation
accuracy, especially bias in the estimated parameters [4,5]. For progressively censored data the
White method [6] was recommended and simplified by Montanari et al. for electrical aging [5]. The
White method is a weighted version of the least squares linear regression method.
*
corresponding author, jnm@fct.unl.pt
Materials Science Forum Vols. 455-456 (2004) pp. 602-605
online at http://www.scientific.net
© (2004) Trans Tech Publications, Switzerland
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the
written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net . (ID: 193.136.121.72-03/11/06,18:08:31)