Stress-strength reliability estimation based on probability weighted moments in small sample scenario with three-parameter Weibull distribution

Stress-strength reliability is a fundamental concept in engineering and reliability analysis, crucial for assessing whether a system or component will perform adequately under given stress and strength conditions. The three-parameter Weibull distribution, a mainstay in reliability engineering and life testing, is renowned for its effectiveness in modeling failure data across a spectrum of engineering and scientific disciplines. Despite its utility, traditional parameter estimation methods, such as maximum likelihood estimation (MLE), are constrained by the absence of estimators for shape parameters below one and by inefficiency for those between one and two. Additionally, these methods often necessitate extensive sample sizes for achieving reliable outcomes. Bridging this gap, we introduce a reliability analysis framework anchored in the probability weighted moments (PWM) method, which are efficient in handling heavy-tailed or skewed distributions, ensuring the existence of estimators for arbitrary parameter scenarios. Our comprehensive evaluation using diverse datasets, including Monte Carlo simulations and real-world experimental data, demonstrates that the PWM method excels in robust parameter estimation, performs exceptionally well with small and moderate sample sizes. These advantages make the proposed analysis framework particularly effective for evaluating the stress-strength reliability of engineering structures under the three-parameter Weibull distribution.