In this paper, a Bayesian analysis is made to estimate the Reliability of two stress-strength model systems. First: the reliability  of a one component strengths X under stress Y. Second, reliability  of one component strength under three stresses. Where X and Y are independent generalized exponential-Poison random variables with parameters (α,λ,θ) and (β,λ,θ) . The analysis is concerned with and based on doubly type II censored samples using gamma prior under four different loss functions, namely   quadratic loss function, weighted loss functions,  linear and non-linear exponential loss function. The estimators are compared by mean squared error criteria due to a simulation study. We also find that the mean square error is the best performance of the estimator from that found in  quadratic, weighted, linear and non-linear exponential loss functions.

In this paper, a Bayesian analysis is made to estimate the Reliability of two stress-strength model systems. First: the reliability R 1 of a two component strengths X 1 and X 2 under common stress Y. Second: reliability R 2 of two components strength under two stresses. Where X and Y are independent Generalized Exponential-poison random variables with(α,λ,θ) and (β,λ,θ), respectively. The analysis is concerned based on left censored samples using gamma prior under four different loss functions (Quadratic, Weighted, Linear exponential and non-Linear exponential). The estimators are compared by Mean squared error criteria due to a simulation study and find that the best performance of the estimators found in order as (Quadratic, Weighted, Linear exponential and non-Linear exponential).