Estimating the Reliability Function (2+1) Cascade Model for Inverse Chen Distribution

<ns7:p> Background A cascaded model in machine learning denotes a system in which numerous models are successively organized, with the result of one model functioning as the input for the subsequent model. This method enables the utilization of the strengths of individual models to enhance overall performance, especially in intricate tasks such as image production or named entity recognition. This research examines the reliability R of a certain (2+1) cascade Stress-Strength model about the Inverse Chen distribution. When the Strength and Stress adhere to Inverse Chen random variables with unspecified shape parameter α and known parameter β. Methods Five distinct methods (Maximum Likelihood Estimator (ML), Shrinkage Estimation Method with Shrinkage Weight Factor Estimators ( <ns7:italic> sh <ns7:sub>1</ns7:sub> </ns7:italic> ) and Trigonometric Shrinkage Weight Function ( <ns7:italic> sh <ns7:sub>2</ns7:sub> </ns7:italic> ), Least Square Estimation Method (LS) <ns7:bold>,</ns7:bold> Weighted Least Square Estimation Method (WLS)) are employed to estimate the specified reliability and to facilitate a comparison among them in a simulation conducted using the MATLAB(2023b) program, numerical simulation is employed after generating random samples of sizes 25, 50, 75, and 100 from the Inverse Chen Distribution to apply the Mean Square Error (MSE) criterion for comparison. Results The reliability results estimated by the five methods were recorded in tables, and the numerical simulation results were recorded in tables and graphs illustrating the suitability of data with respect to all the distributions under study. Conclusions Compared the inverse Chen distribution to some distributions such as the log-logistic, uniform, exponential, Rayleigh, Chi-Square Half-Normal, Gumbel, and Cauchy distributions, using real data for the diamonds from a major mining zone in Southwest Africa, the inverse Chen distribution seems to be a more competitive model for this data of diamonds than the other distributions. The optimal estimation approach for the reliability via MSE is the trigonometric shrinkage weight function estimator ( <ns7:italic> sh <ns7:sub>2</ns7:sub> </ns7:italic> ). </ns7:p>