Reliability Estimation of Parallel Stress-Strength Systems with Power Rayleigh Distribution

What is it about?

This paper discusses the estimation of the reliability of two parallel systems with stress-strength models when Rp = p[x < max(y1, y2, y3, … … . yn)]. The authors consider the Power Rayleigh Distribution (PR(α, β)) and present six estimation techniques, including Maximum Likelihood Estimator (MLE), Expectation-Maximization Estimator (EMME), Least Squares Estimator (LSE), and three shrinkage estimation methods (sh1, sh2, sh3). The paper compares these methods using three criteria: Bias, Mean Squared Error (MSE), and Mean Absolute Percentage Error (MAPE). The authors generate theoretical comparisons and conduct a simulation study to determine the best estimation methods. The paper concludes that the MLE method is the best overall, although the performance of the estimators varies depending on the sample size and distribution parameters. In summary, the paper provides an in-depth analysis of estimating the reliability of two parallel systems using the Power Rayleigh Distribution and compares various estimation techniques based on their accuracy and efficiency.

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Why is it important?

The paper discusses the reliability of parallel systems with two stress-strength models and the estimation of parameters using various methods. It is important because it helps in understanding the behavior and performance of systems that depend on two independent factors, which is useful in various fields like engineering and medical sciences. Key Takeaways: 1. The paper uses the power Rayleigh distribution (PR(α, β)) as a model for parallel reliability systems. 2. The estimation methods include Maximum Likelihood Estimator (MLE), Exact Moment Estimator (EMME), Least Squares Estimator (LSE), and three shrinkage estimation methods (sh1, sh2, sh3). 3. The comparison of these methods is done using criteria like bias, mean squared error (MSE), and mean absolute percentage error (MAPE). 4. The paper highlights the importance of understanding reliability in systems and the significance of selecting the appropriate estimation method for better performance. 5. This research contributes to the field of reliability engineering by investigating various estimation techniques and their performance in modeling parallel systems with two independent factors. The results of the study can be used to make informed decisions when designing and maintaining such systems.