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The present paper concerns with the problem of estimating the reliability system in the stress – strength model under the consideration non identical and independent of stress and strength and follows Lomax Distribution. Various shrinkage estimation methods were employed in this context depend on Maximum likelihood, Moment Method and shrinkage weight factors based on Monte Carlo Simulation. Comparisons among the suggested estimation methods have been made using the mean absolute percentage error criteria depend on MATLAB program.

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This paper is concerned with double stage shrinkage estimator (DSSE) for lowering the mean squared error of classical estimator (MLE) for the shape parameter (α) of generalized Exponential (GE) distribution in a region (R) around available prior knowledge (α 0 ) about the actual value (α) as initial estimate in case when a scale parameter (λ) is known as well as to reduce the cost of experimentations.In situation where the experimentations are time consuming or very costly, a double stage procedure can be used to reduce the expected sample size needed to obtain the estimator.This estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor ψ(⋅) and for acceptance mentioned region R.Expressions for Bias, Mean square error (MSE), Expected sample size [E(n/α,R)], Expected sample size proportion [E(n/α,R)/n], probability for avoiding the second sample

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