Documents published in Scipedia

• Bayesian and Non-Bayesian Inference for Discrete Model Based on Censored Samples with Optimal Test Plan

  R. Alotaibi, H. Rezk, E. Almetwally

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 20

  
  

  Abstract

  In reliability and lifetime studies, it is often impractical to observe the failure times of all units in a sample, particularly when the process is timeconsuming or expensive. Type II censoring addresses this by terminating the experiment after a predetermined number of failures from a total sample of size. The Discrete Alpha Power Extended Inverted Weibull distribution is particularly suitable for modeling such censored discrete lifetime data. Its flexible shape parameters allow it to capture a wide range of failure behaviors, including over-dispersion, which is common in censored datasets. In this context, the likelihood function and estimation procedures (maximum likelihood and Bayesian) explicitly account for the censoring, ensuring unbiased parameter estimates and reliable predictive inferences. Consequently, the Discrete Alpha Power Extended Inverted Weibull distribution provides a practical and statistically robust framework for analyzing discrete lifetimes under type II censoring.OPEN ACCESS Received: 28/07/2025 Accepted: 19/09/2025 Published: 23/01/2026

  Abstract
  In reliability and lifetime studies, it is often impractical to observe the failure times of all units in a sample, particularly when the process is timeconsuming or expensive. [...]

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• Analysis of Burr-XII Lifespan Using Adaptive Progressive Type-II Hybrid Binomial Censoring with Physical Modeling of Polyester and Carbon Fibers

  R. Alotaibi, H. Rezk, A. Elshahhat

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 4

  
  

  Abstract

  This study introduces advanced statistical methods, allowing for more efficient and accurate reliability testing of fibers such as polyester and carbon. Polyester ficbers are suitable for textiles and industrial use due to their wrinkle resistance and affordability, while carbon fibers offer superior strength, thermal stability, and corrosion resistance. To guarantee greater efficiency of inference methodologies and reduce overall testing time, the adaptive Type-II progressive hybrid censoring via binomial removals has gained popularity in reliability analysis and life-testing problems. The proposed scheme allows survival units to be removed at random stages according to a binomial law, thereby reducing experimental time while preserving statistical efficiency. When lifetimes are gathered using the suggested censoring technique, point and interval estimates of the unknown parameters of the Burr-XII model are obtained using both classical and Bayesian approaches. We obtain various Bayesian estimates using the squared loss function. Some numerical methods are employed to obtain the suggested estimators due to their complexity. The various Bayes estimates and related credible intervals are created using Markov chain Monte Carlo techniques. To assess estimator performance, extensive simulation studies are conducted, comparing bias, mean squared error, coverage probabilities, and interval lengths under varying censoring and removal settings. The simulation results confirm that the Bayesian framework, particularly with informative priors, provides more accurate and stable estimates than asymptotic likelihood-based methods. We examine two physics data sets representing polyester and carbon fibers to demonstrate the relevance of the suggested approaches in a real-world setting. These applications highlight the practical value of the proposed approach for material design, maintenance planning, and broader reliability engineering problems.OPEN ACCESS Received: 13/06/2025 Accepted: 12/09/2025 Published: 23/01/2026

  Abstract
  This study introduces advanced statistical methods, allowing for more efficient and accurate reliability testing of fibers such as polyester and carbon. Polyester ficbers [...]

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• Statistical Analysis of Progressive Interval Type-I Partially Accelerated Test and Its Inspection of Optimum Periods

  R. Alotaibi, C. Park, H. Rezk, A. Elshahhat

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (3), 54

  
  

  Abstract

  This study explores a general framework for reliability analysis named progressive interval Type-I censoring within a multi-stage step-stress partially accelerated life testing setting. A more flexible alternative to the traditional exponential model, known as the length-biased exponential (LBE) distribution, is employed to model failure times. Due to its symmetrical feature, it has extensive applications in real-world domains such as survival analysis, actuarial science, reliability, and mathematical finance. The maximum likelihood approach of estimation is utilized to estimate the model parameters, along with bootstrapping techniques to assess estimation efficiency. Confidence intervals for the LBE parameters are also derived based on asymptotic variances. To optimize the inspection period, two competing optimality criteria—variance minimization (Varoptimality) and determinant maximization (D-optimality)—are investigated. A comprehensive Monte Carlo simulation study is conducted to evaluate the performance of different estimation strategies, demonstrating the superiority of the proposed methodology. Steel is particularly valued for its toughness, wear resistance, and hardness, all of which can be significantly modified through heat treatment and annealing processes. So, a real-world application using hardened steel failure data validates the practical relevance of the developed inferential framework. The findings offer valuable insights for statisticians and reliability engineers in designing efficient life-testing experiments under constrained resources.OPEN ACCESS Received: 21/03/2025 Accepted: 07/05/2025 Published: 22/09/2025

  Abstract
  This study explores a general framework for reliability analysis named progressive interval Type-I censoring within a multi-stage step-stress partially accelerated life testing [...]

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  •  read