Employ Shrinkage Estimation Technique for the Reliability System in Stress-Strength Models: special case of Exponentiated Family Distribution

Abstract

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.

Keywords

• Exponentiated Family Distribution, Reliability of multicomponent Stress–Strength models, Maximum likelihood estimator, Shrinkage estimator and mean squared error.