Estimation for reliability function and prediction. Based on record values from Rayleigh distribution

      Аннотация: In the statistical literature R = P(Y<X) is known as the stress-strength parameter and it has received significant attention in the last few decades. The parameter R is referred to as the reliability parameter. This problem arises in the classical stress-strength reliability where one is interested in assessing the proportion of the times the random strength X of a component exceeds the random stress Y to which the component is subjected. This problem also arises in situations where X and Y represent lifetimes of two devices and one wants to estimate the probability that one fails before the other. As can be seen from the cited literature, the developments in this field covered a variety of data types including complete data, censored data as well as data with explanatory variables. This thesis is divided into two parts. The first part consists of two chapters dealing with the estimation problem of the stress strength reliability model for Rayleigh distribution (RD). The second part (one chapter) dealing with the problems of one-sample and two-sample predictions using various type of data from RD.

Ключевые слова: prediction, Estimation, Random removals, Life testing, Expected test time.