Truncated distributions arise naturally in many practical situations. It’s a conditional distribution that develops when the parent distribution's domain is constrained to a smaller area. The distribution of a right truncated is one of the types of a single truncated that is restricted within a specific field and usually occurs when the specified period for the study is complete.  Hence, this paper introduces Right Truncated Inverse Generalized Rayleigh Distribution (RTIGRD) with two parameters  is introduced. Then, provided some properties such as; (probability density function, cumulative distribution function (CDF), survival function, hazard function, ‎rth moment, mean,   variance, Moment Generating Function, Skewness, kurtosi

 The reliability of the stress-strength model attracted many statisticians for several years owing to its applicability in different and diverse parts such as engineering, quality control, and economics. In this paper, the system reliability estimation in the stress-strength model containing Kth parallel components will be offered by four types of shrinkage methods: constant Shrinkage Estimation Method, Shrinkage Function Estimator, Modified Thompson Type Shrinkage Estimator, Squared Shrinkage Estimator. The Monte Carlo simulation study is compared among proposed estimators using the mean squared error. The result analyses of the shrinkage estimation methods showed that the shrinkage functions estimator was the best since

This paper discusses reliability of the stress-strength model. The reliability functions 𝑅1 and 𝑅2 were obtained for a component which has an independent strength and is exposed to two and three stresses, respectively. We used the generalized inverted Kumaraswamy distribution GIKD with unknown shape parameter as well as known shape and scale parameters. The parameters were estimated from the stress- strength models, while the reliabilities 𝑅1, 𝑅2 were estimated by three methods, namely the Maximum Likelihood,  Least Square, and Regression.

 A numerical simulation study a comparison between the three estimators by mean square error is performed. It is found that best estimator between

       A reliability system of the multi-component stress-strength model R_(s,k) will be considered in the present paper ,when the stress and strength are independent and non-identically distribution have the Exponentiated Family Distribution(FED) with the unknown  shape parameter α and known scale parameter λ  equal to two and parameter θ equal to three. Different estimation methods of R_(s,k) were introduced corresponding to Maximum likelihood and Shrinkage estimators. Comparisons among the suggested estimators were prepared depending on simulation established on mean squared error (MSE) criteria.

     In this paper, Bayesian estimator for the parameter and reliability function of inverse Rayleigh distribution (IRD) were obtained Under three types of loss function, namely, square error loss function (SELF), Modified Square error loss function (MSELF) and Precautionary loss function (PLF),taking into consideration the  informative and non- informative  prior. The performance of such estimators was assessed on the basis of mean square error (MSE) criterion by performing a Monte Carlo simulation technique.