In this paper endeavors to submit reliability (R) of a special (2+1) stress-strength Cascade model for Weibull distribution. Expressions for the model reliability are obtained when the strength and stress are weibull random variables with known shape and unknown scale parameters. Four different methods (ML, Mo, LS and WLS) are used to estimate the reliability and make a comparison between them in simulation study with program made by MATLAB 2016 using criterion MSE, where it found that the best estimator between the four estimators was ML.

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In this paper, we find the reliability R of a component when it is exposed to four independent stresses and it having one strength for Lomax distribution. the reliability R was estimated by using four different estimations (MLE, RgE, LSE, and WLSE) methods. A comparison was made between the results of estimating the reliability function by MSE and MAPE criteria, that will get from a Monte Carlo simulation study. We found that the performance of ML is the best to.

This paper discusses reliability R of the (2+1) Cascade model of inverse Weibull distribution. Reliability is to be found when strength-stress distributed is inverse Weibull random variables with unknown scale parameter and known shape parameter. Six estimation methods (Maximum likelihood, Moment, Least Square, Weighted Least Square, Regression and Percentile) are used to estimate reliability. There is a comparison between six different estimation methods by the simulation study by MATLAB 2016, using two statistical criteria Mean square error and Mean Absolute Percentage Error, where it is found that best estimator between the six estimators is Maximum likelihood estimation method.