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Abstract:
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Early papers dealing with so-called stress-strength problems were
published in the middle of the 20th century. This topic, which belongs to the
reliability theory, is still very active nowadays, which can be seen through
the number of published papers dealing with it - around ten each year. In
this dissertation, some methods for estimation of the reliability parameter
for a system with independent stress and strength are presented. Also, two
new models are introduced and some estimators of the reliability parameter
for each of them are derived. The dissertation is divided into four chapters.
In the rst chapter, some basic terms are introduced and some examples
from real life, illustrating big possibilities for application of the results from
this scienti c eld, are described. Sorted based on the stress and strength
distributions, a chronological overview of all research activities dealing with
these topics, to the author's best knowledge, is presented. Some special func-
tions, which are later used for calculations, along with their main properties
are shown. The expressions for the reliability parameter for some stress and
strength distributions are either derived or listed.
The second chapter is devoted to different methods used for point esti-
mation, as well as for interval estimation of the reliability parameter of a
system. For each methods estimators of the reliability parameter for some
stress and strength distributions are either derived or listed.
In the third chapter, a new model is introduced. In this model, the stress
has geometric, while the strength has Poisson distribution. This is one of
the rst, if not the rst, appearances in the literature, where the stress and
strength distributions do not belong to the same family of distributions. For
this model, the reliability parameter is estimated using different methods
and decision on optimal estimators for usage in practice is based on the
simulations.
In the fourth chapter, another model is introduced, with the stress and
strength distributions which are not only from different families of distribu-
tions, but also do not belong to the same type of distributions. The stress
has geometric, while the strength has exponential distribution. The reliabil-
ity parameter for this model is also estimated using different methods, and
the decision on optimal estimators for usage in practice is once again based
on the simulations. |