Estimation of the reliability parameter of a two-component system.

[М. Ж. Јовановић]

[10], 141 лист

Matematika - Verovatnoa i statistika / Mathematics - Probability and Statistics

Prvi radovi iz tzv. stress-strength problematike pojavili su se polovinom dvadesetog veka, a ova oblast koja pripada teoriji pouzda- nosti je veoma iva i danas, qemu u prilog govori i to da se svake godine objavi po desetak radova na ovu temu. U disertaciji su predstav eni metodi za oceivae parametra pouzdanosti kod sistema sa nezavisnim stresom i snagom. Takoe su uvedena dva nova modela i izvedene su razne ocene parametra pouzdanosti svakog od modela. Disertacija je pode ena u qetiri glave. U prvoj glavi se uvode osnovni pojmovi i daju primeri iz realnog ivota koji pokazuju veliku mogunost praktiqne primene rezultata iz ove oblasti. Sortirano po raspodelama stresa i snage hronoloxki se daje pregled svih istraivaa, poznatih autoru, iz ove oblasti. Navode se specijalne funkcije i ihove glavne osobine koje se kasnije koriste u izraqunavaima. Izvode se ili navode izrazi za parametar pouzdanosti za razne raspodele stresa i snage. Druga glava je posveena raznim metodima koji se koriste kako za taqkasto, tako i za intervalno oceivae parametra pouzdanosti si- stema. Za svaki od metoda izvedene su ili navedene ocene parametra pouzdanosti za razne raspodele stresa i snage. U treoj glavi se uvodi novi model kod koga stres ima geometrijsku, a snaga Puasonovu raspodelu. To je jedan od prvih, ako ne i prvi put u literaturi da raspodele stresa i snage nisu iz iste familije raspodela. Za taj model parametar pouzdanosti se oceuje raznim metodima i na osnovu simulacija se donosi zak uqak o tome koje bi ocene trebalo ko- ristiti u praksi...

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...

stres-snaga, pouzdanost, geometrijska raspodela, Pua- sonova raspodela, eksponencijalna raspodela, ocena maksimalne vero- dostojnosti, jedinstvena nepristrasna ocena sa uniformno minimalnom disperzijom, Bajesova ocena, intervali poverea

stress-strength, reliability, geometric distribution, Poisson dis- tribution, exponential distribution, maximum likelihood estimator, uniformly minimum variance unbiased estimator, Bayes estimator, condence intervals, bootstrap

519.248(043.3)

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