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@PHDTHESIS{Lu:1022767,
author = {Lu, Yao},
othercontributors = {Kateri, Maria and Kamps, Udo},
title = {{H}eterogeneous step-stress accelerated life testing},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2025-10244},
pages = {1 Online-Ressource : Illustrationen},
year = {2025},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University 2026; Dissertation, RWTH Aachen University, 2025},
abstract = {Accelerated life testing (ALT) evaluates the lifetime
performance of testing units within a limited period of time
by imposing stress levels higher than those encountered
under normal operating conditions. Step-stress ALT (SSALT)
is a special type of ALT where stress is incrementally
adjusted at predefined time points during the experiment.
Statistical models for SSALT experiments, assuming a
homogeneous population and various lifetime distributions,
have been extensively discussed in the literature, also
taking different censoring schemes into account. However,
SSALT for a heterogeneous population, consisting of two or
more groups, has received little attention so far,
especially in cases where the group membership is unknown
and the testing units form disjoint groups. Therefore, this
thesis introduces a heterogeneous SSALT (hSSALT) model with
two stress levels, and develops associated inferential
procedures for both Type-I and Type-II censoring. Procedures
are developed for continuously monitored experimental data,
as well as, in case of Type-I censoring, for interval
monitored data. Assuming the cumulative exposure model and
exponentially distributed lifetimes, the hSSALT model
accounts for unobserved heterogeneity at the second stress
level by employing a two-component exponential mixture. The
parameter estimates are obtained via the adapted
Expectation-Maximization algorithm, with closed-form update
rules derived for handling censored mixture data. Both
asymptotic and bootstrap confidence intervals are
constructed for interval estimation. In the presence of
heterogeneity, the advantage of the hSSALT model over its
homogeneous counterpart is demonstrated through theoretical
analysis and simulation studies, particularly in yielding
more accurate parameter estimates. A segmented log-link
function is introduced to adjust lifetime extrapolation at
normal operating condition, demonstrating that the
homogeneous SSALT model tends to overestimate product
lifetimes when heterogeneity is present. Furthermore, to
determine the necessity of applying the hSSALT model, a
likelihood ratio type test is developed for assessing
homogeneity in mixture models under censoring, focusing on
two-component exponential distributions. The test evaluates
homogeneity against a two-subpopulation alternative and
accommodates for both Type-I and Type-II censoring. The
proposed test modifies the test statistic in a data-driven
manner, offering a practial solution for homogeneity testing
in censored mixture models. The associated critical values
are obtained through simulation studies. In addition, power
analyses under various scenarios demonstrate the
effectiveness of the proposed test and confirm its practical
applicability using real-world datasets from the
literature.},
cin = {116510 / 110000},
ddc = {510},
cid = {$I:(DE-82)116510_20140620$ / $I:(DE-82)110000_20140620$},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2025-10244},
url = {https://publications.rwth-aachen.de/record/1022767},
}
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