Оцењивање параметара поузданости двокомпонентног система

Abstract

Први радови из тзв. stress-strength проблематике појавили су се половином двадесетог века, а ова област која припада теорији поузда- ности је веома жива и данас, чему у прилог говори и то да се сваке године објави по десетак радова на ову тему. У дисертацији су представљени методи за оцењивање параметра поузданости код система са независним стресом и снагом. Такође су уведена два нова модела и изведене су разне оцене параметра поузданости сваког од модела.

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 scientic 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...