Empirical Comparison of Sampling Techniques for Stress-Strength Reliability: Quasi-XLindley and Power Function Distributions

A novel combination of Monte Carlo simulation and real-world aerospace data is used to demonstrate that Ranked Set Sampling significantly improves the efficiency and accuracy of stress-strength reliability estimation compared to simple random sampling. In this study, we examine the probability of disaster and evaluate the efficiency of ranked set sampling (RSS) against simple random sampling (SRS) for estimating stress-strength reliability p = Pr(Y > X), where strength Y follows the power function distribution and stress X is modeled by the Quasi-XLindley distribution (QXL). Through Monte Carlo simulations, we compare the performance of maximum likelihood estimators under both sampling schemes. The methodology is validated using the NASA C-MAPSS turbofan engine dataset, illustrating RSS effectiveness in cost-optimized reliability assessments. Our findings advocate RSS as a resource-efficient alternative for real-world applications requiring robust stress-strength analysis.