On the Estimation of Stress-Strength Model Reliability Parameter of  Power Rayleigh Distribution

Abdulrhaman A.J. Ahmed; Feras Sh. M. Batah

doi:10.24996/ijs.2023.64.2.27

Authors

Abdulrhaman A.J. Ahmed Department of Mathematics, College of Education for pure Science, University Of Anbar, Anbar, Iraq
Feras Sh. M. Batah Department of Mathematics, College of Education for pure Science, University Of Anbar, Anbar, Iraq https://orcid.org/0000-0003-1254-3080

DOI:

https://doi.org/10.24996/ijs.2023.64.2.27

Keywords:

Power Rayleigh Distribution, Stress-Strength Reliability, Maximum Likelihood, Exact estimators of moments, Percentile, ordinary and weighted Least squares estimators, the Shrinkage method

Abstract

The aim of this paper is to estimate a single reliability system (R = P, Z > W) with a strength Z subjected to a stress W in a stress-strength model that follows a power Rayleigh distribution. It proposes, generates and examines eight methods and techniques for estimating distribution parameters and reliability functions. These methods are the maximum likelihood estimation(MLE), the exact moment estimation (EMME), the percentile estimation (PE), the least-squares estimation (LSE), the weighted least squares estimation (WLSE) and three shrinkage estimation methods (sh1) (sh2) (sh3). We also use the mean square error (MSE) Bias and the mean absolute percentage error (MAPE) to compare the estimation methods. Both theoretical comparison, simulation and real data are used. The results in light of this distribution show the advantage of the proposed methods.