Different Methods to Estimate Stress-Strength Reliability Function for Modified Exponentiated Lomax Distribution

When ensuring the reliability of device or the suitability of a material, it is necessary to take into consideration the stress cases in the operating environment. This means that the uncertainty about the reality environmental stress must be taken into as random. The stress-strength (S-S) model treated the stress and strength variables as random. In the simplest form of stress-strength model, y represents the stress put on the unit by the operating environment, and the strength of the unit represented by x. A unit is able to perform its required function if its stress imposed on it is less than the strength of the unit. In this paper, the stress-strength reliability estimation for the modified exponentiated Lomax distribution, which is generalization of the Lomax distribution, with an unknown shape parameter and a known scale parameters is studied using different methods. These methods include the maximum likelihood method, Bayesian estimation method under a quadratic loss function, and the least squares method for complete data. The estimators are compared based on Markov Chain Monte Carlo (MCMC) simulations using R-Studio, evaluated by the mean square error (MSE) criteria. The simulation results show that the maximum likelihood estimators are the best in two cases: the first is when the sample sizes are equal and the second is when the shape parameter of the strength variable is greater than the shape parameter of the stress variable. While least squares estimators are the beast if the strength sample size is smaller than the stress sample size. Finally when the strength sample size is greater than the stress sample size, then the best estimators differ between the maximum likelihood estimators and Bayesian estimators. Bayesian estimators become the best when the shape parameter of stress variable is larger than the shape parameter of the strength variable.