The Laplace Residual Power Series Method for Solving Fractional Fifth-Order Korteweg–de Vries Equations

Shasta Reservoir is the largest in California, formed by Shasta Dam on the Sacramento River, and plays a major role in the Central Valley Project (CVP) by providing water storage, flood control, hydroelectric power, and irrigation. This study employs advanced statistical methods to evaluate the reservoir’s reliability and operational risks using censored hydrological data. We propose an improved adaptive progressive censoring plan and apply established statistical techniques, maximum likelihood and maximum product of spacings, alongside Bayesian estimation. The Bayes estimates are obtained through the squared error loss function and based on two sources for the observed data, namely the likelihood and spacing functions. The focus is on estimating the distribution’s scale parameter and two critical reliability metrics: the reliability function and the hazard rate function. The approximate confidence intervals based on the two classical approaches of the scale parameter and reliability metrics are studied. The highest posterior density credible intervals are also discussed. A simulation study evaluates the model’s accuracy under diverse data scenarios, and its practical utility is demonstrated through real-world data from Shasta Reservoir. The problem of optimizing data collection strategies is discussed with the same real data. The findings underscore the model’s value in enhancing reservoir reliability assessments, offering actionable insights for hydrology, disaster preparedness, and sustainable resource management.OPEN ACCESS Received: 15/03/2025 Accepted: 12/06/2025 Published: 22/09/2025