Point and Interval Estimators of R=P[Y < X] Based on Gompertz Distribution and Ranked Set Sampling Data

Abstract

The stress-strength model R= P[Y<X] is defined as the probability that the stress variable  is less than the strength variable  Although the main use of stress-strength model in physics and engineering fields. It has also more uses in economics, quality control, psychology, medicine, and agricultural. Traditionally, simple random sampling (SRS) is used for estimating the reliability model. In recent years, the ranked set sampling (RSS) is used for estimating reliability model because it is more efficient than (SRS). In this paper, we present the point and interval estimators for reliability model when the strength and stress variables are two independent Gompertz distribution based on (RSS). Monte Carlo simulation study is used to compare the maximum likelihood estimator based on (RSS) with the maximum likelihood estimator based on (SRS) and construct an asymptotic confidence interval (ACI) and bootstrap confidence (BCI). Finally, real data in medicine is used for illustrative our proposed method.