Methods For Estimating 𝑹(𝑺,𝑲) Based On Rayleigh-Pareto Distribution

Abstract

This paper considers with the reliability of a multicomponent system of k components 𝑅(𝑆,𝐾) estimation problem of a stress-strength model. 𝑅(𝑆,𝐾) is obtained when the strength and stress variables have the two-parameters Rayleigh-Pareto distribution 𝑅𝑃(𝜎,𝜌). (𝜎) is the known scale parameter and (𝜌) is an unknown shape parameter for stress - strength distribution of Rayleigh-Pareto. The system contains (K) components with its strength (𝑌1,𝑌2,…..,𝑌𝐾), which represent random variables distributed independently and symmetrically, and each component suffers from random stress is (X). The system regards as active system only if at least strength components exceed the stress. Parameter estimation using Least Squares (LS) , Relative Least Squares RLS , Wight Least Squares (WLS) and Ridge Regression Method (RRM) have discussed. The estimating of reliability parameters obtained from all the approaches above are compared with the Mean Square Error (MSE) and Mean Absolute Percentage Error (MAPE) criteria based on Monte-Carlo simulation experiment. Significantly, WLS and LS estimators have shown better performance compared with other methods.