Abstract

Long testing times are usually required for the life testing of very reliable products or materials. The testing process can be hastened by using accelerated life tests. The lifespan of the items that accelerated life tests inspect is reduced since they test products in more severe circumstances than those found in regular use scenarios. Data that was censored and disclosed the precise timings of failure may point to accelerated life tests where all units assigned to test are unknown, or where all units assigned to test have not failed for a few reasons, including challenges with technology, tools, costs, and schedules. The step-stress partially accelerated life test was examined in this work using the type-I progressive hybrid censoring scheme and the type-II progressive censoring scheme. The influence of the stress shift is explained using the tempered random variable model, where the failure times of the items are assumed to follow the alpha power Lomax distribution. The unknown parameters are estimated using the maximum likelihood estimation and Bayesian methods. The asymptotic theory of maximum likelihood estimation is also employed in the construction of the approximate confidence intervals. While the point estimates under two censoring schemes are compared in terms of absolute biases and root mean squared errors, approximate confidence intervals and coverage probabilities are compared in terms of their lengths and coverage probabilities. Additionally, three possible optimal test strategies are investigated using different optimal criteria. The performance of the estimators was evaluated and contrasted with two censoring techniques with various sample sizes using a simulation study. Finally, a numerical example for insulating fluid between electrodes data is presented to illustrate how the methods will work in real-world scenarios.OPEN ACCESS Received: 11/06/2025 Accepted: 29/07/2025 Published: 23/01/2026

Abstract

In this paper, we extend the concepts of statistical convergence and strong summability for the sequences of fuzzy numbers using modulus functions. By introducing appropriate conditions on the modulus functions, we generalize and refine existing notions of convergence within the fuzzy setting. Additionally, we establish several interrelationships between these extended concepts, thereby contributing to the deeper understanding of summability and convergence behavior in the sequences of fuzzy numbers.OPEN ACCESS Received: 16/06/2025 Accepted: 20/08/2025 Published: 27/11/2025

Abstract

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

Abstract

This paper explores the dynamic behavior of optical soliton solutions for the modified Kawahara (mK) equation and the modified BenjaminBona-Mahony (mBBM) equation, two significant nonlinear evolution equations. Using an advanced analytical approach, a diverse set of soliton solutions is derived, including bell-shaped, anti-bell-shaped, W-shaped, M-shaped, and periodic waveforms. These solutions unveil the intricate nonlinear dynamics underlying the equations. The robustness of the method is demonstrated through comprehensive 2D, 3D, and contour visualizations, offering clear insights into the physical significance of the solitons. The study enhances the existing catalog of soliton solutions, contributing to a deeper understanding of nonlinear wave propagation and its potential applications in fields such as optical communication and fluid dynamics.OPEN ACCESS Received: 06/05/2025 Accepted: 09/06/2025 Published: 15/08/2025