Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.6
2.2
Journals
Mathematics
Special Issues
Reliability Estimation and Mathematical Statistics, 2nd Edition
share announcement

Reliability Estimation and Mathematical Statistics, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 31 October 2026 | Viewed by 1570

Special Issue Editor

Prof. Dr. Kamel Rekab

E-Mail Website
Guest Editor
Division of Computing Analytics and Mathematics, School of Science and Engineering, University of Missouri Kansas City, 5110 Rockhill Road, Kansas City, MO 64110, USA
Interests: statistical software testing and reliability; network security; biostatistics; statistics in advanced manufacturing; statistical quality improvement; design of industrial experiments; sequential analysis; mathematical statistics; probability theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Reliability estimation and mathematical statistics are two closely intertwined fields that play a crucial role in various scientific disciplines and industries. Reliability estimation focuses on assessing the dependability and performance of systems, products, or processes over time. It involves the analysis of failure data to make informed predictions about future reliability. Mathematical statistics, on the other hand, provides the theoretical framework and tools for drawing meaningful conclusions from data, making it an indispensable component of reliability analysis.

In reliability estimation, engineers and statisticians utilize various statistical techniques such as survival analysis, hazard functions, and probability distributions to model and quantify the likelihood of failures or breakdowns. This information is invaluable for decision-making in fields like engineering, manufacturing, healthcare, and finance, where reliability is a critical concern.

Mathematical statistics underpins these reliability assessments by offering methods for data collection, hypothesis testing, and parameter estimation. It involves concepts like sampling theory, probability theory, and statistical inference to extract meaningful insights from empirical data. By applying mathematical statistics, analysts can make informed decisions about system maintenance, quality control, and risk management.

In conclusion, reliability estimation and mathematical statistics are integral components of modern problem-solving and decision-making processes. Their symbiotic relationship empowers industries and researchers to improve the dependability and performance of systems, products, and processes, ultimately leading to safer and more efficient outcomes across a wide range of applications.

This Special Issue, as a follow up of the previous edition, is intended to be our commitment to excellence and innovation in the field has led us to a momentous juncture, and I invite you all to be a part of this exciting journey.

We extend a warm invitation to contribute your work and insights to Reliability Estimation and Mathematical Statistics, 2nd Edition. The hope is to offer readers fresh insights and address topics of critical importance in reliability estimation and mathematical statistics.

I encourage you to explore our submission guidelines and consider joining us as contributors, and for our dedicated readers, please continue to engage with us by providing feedback and sharing your thoughts on our content.

Thank you for your continued support, and I look forward to our shared exploration of ideas and insights.

Prof. Dr. Kamel Rekab
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • estimation
  • reliability
  • sequential
  • Bayesian
  • classical
  • decision rule
  • simulation
  • software
  • statistics
  • system

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

22 pages, 713 KB  
Article
Bridging Markov Chain Monte Carlo Techniques and Tierney–Kadane Approximations for Progressively Censored Garhy Reliability Models: Simulation Insights and a Medical Application
by Abdullah H. Alenezy, Anis Ben Ghorbal, Khudhayr A. Rashedi and Ghareeb A. Marei
Mathematics 2026, 14(10), 1777; https://doi.org/10.3390/math14101777 - 21 May 2026
Abstract
This paper investigates the estimation of the stress–strength reliability parameter R=P(Y<X) when both stress and strength follow independent Garhy distributions under progressive Type-II censoring schemes. A closed-form expression for R is explicitly derived, enabling effective [...] Read more.
This paper investigates the estimation of the stress–strength reliability parameter R=P(Y<X) when both stress and strength follow independent Garhy distributions under progressive Type-II censoring schemes. A closed-form expression for R is explicitly derived, enabling effective and precise calculation without numerical integration. The Garhy distribution, a flexible one-parameter lifetime model with an increasing hazard function, is confirmed by full-scale goodness-of-fit diagnostics. A Bayesian estimation model is trained on non-informative priors (normal and extended Jeffreys priors) under squared error loss. The posterior expectations are analytically intractable; we adopt two complementary methods of computation: (i) Markov Chain Monte Carlo (MCMC) using the Metropolis–Hastings algorithm and (ii) the Tierney–Kadane (TK) approximation, which provides extremely precise analytical estimates with significantly reduced computational burden. Monte Carlo simulations are large-scale and compare the proposed estimators under different censoring schemes, sample sizes, and parameter configurations in terms of bias and mean squared error (MSE). The methodology is further applied to a real medical dataset comprising kidney dialysis patient survival times, demonstrating its practical relevance in clinical reliability assessment. Results consistently indicate that Bayesian methods, particularly with the extended Jeffreys prior, outperform classical MLEs in terms of stability and accuracy, especially under heavy censoring. Moreover, the TK approximation yields estimates virtually identical to MCMC while requiring only a fraction of the computational effort. We further extend the TK framework to approximate the posterior variance of R and the expected log-likelihood, providing a fully analytical alternative to MCMC for comprehensive Bayesian inference. Full article
(This article belongs to the Special Issue Reliability Estimation and Mathematical Statistics, 2nd Edition)
15 pages, 286 KB  
Article
Reliability Inference and Remaining Useful Life Prediction Based on the Two-Parameter Bathtub-Shaped Lifetime Distribution Under Progressive Type-II Censoring
by Xiaofei Wang, Biwu Zhang, Peihua Jiang and Yaqun Zhou
Mathematics 2026, 14(7), 1109; https://doi.org/10.3390/math14071109 - 26 Mar 2026
Viewed by 394
Abstract
The two-parameter bathtub-shaped distribution is an important lifetime distribution. In this paper, we are interested in developing reliability inference and remaining useful life prediction methods for the two-parameter bathtub-shaped lifetime distribution under progressive type-II censoring. By constructing generalized pivotal quantities, the generalized confidence [...] Read more.
The two-parameter bathtub-shaped distribution is an important lifetime distribution. In this paper, we are interested in developing reliability inference and remaining useful life prediction methods for the two-parameter bathtub-shaped lifetime distribution under progressive type-II censoring. By constructing generalized pivotal quantities, the generalized confidence intervals for both model parameters and key reliability metrics, including quantiles, reliability functions, and remaining useful life are exploited. The proposed methods are further extended to accelerated life testing scenarios. The corresponding accelerated life testing model is constructed based on the two-parameter bathtub-shaped distribution. Furthermore, the generalized confidence intervals for model parameters, quantiles, reliability functions, and remaining useful life are also exploited under the designed stress level. Through comprehensive Monte Carlo simulations, and comparing our approach with Wald confidence intervals and bootstrap-p confidence intervals across moderate and large sample sizes, we confirm the superior coverage probability performance of the generalized confidence interval procedures. The practical applicability of our methodology is validated through two illustrative examples. Full article
(This article belongs to the Special Issue Reliability Estimation and Mathematical Statistics, 2nd Edition)
26 pages, 2418 KB  
Article
The Marshall–Olkin Power Half-Logistic Distribution for Reliability Modeling of Degradation Data Under Generalized Hybrid Censoring
by Ridab Adlan, Hanan Haj Ahmad and Mohamed Aboshady
Mathematics 2026, 14(6), 973; https://doi.org/10.3390/math14060973 - 13 Mar 2026
Viewed by 382
Abstract
The prediction of material lifetime is central to nanomaterial engineering and reliability analysis. We propose the Marshall–Olkin Power Half-Logistic (MOPHL) distribution, obtained by applying a Marshall–Olkin transform to the Power Half-Logistic baseline. We derive core properties—including moments, hazard rate characterization, and Rényi entropy—and [...] Read more.
The prediction of material lifetime is central to nanomaterial engineering and reliability analysis. We propose the Marshall–Olkin Power Half-Logistic (MOPHL) distribution, obtained by applying a Marshall–Olkin transform to the Power Half-Logistic baseline. We derive core properties—including moments, hazard rate characterization, and Rényi entropy—and develop inference under generalized progressive hybrid censoring. Estimation is carried out via maximum likelihood and Bayesian methods using a Metropolis–Hastings sampler. Asymptotic results, Fisher information, and corresponding confidence/credible intervals are provided. A Monte Carlo study assesses bias, the mean squared error, and coverage across censoring scenarios and hazard regimes. In a case study on hydroxylated fullerene degradation, MOPHL outperforms nine competing models in goodness-of-fit and predictive reliability. We also report the mean time to failure and mean residual life to support engineering decision-making. The proposed framework offers a tractable and robust tool for degradation analysis under censored data, with applicability to materials, mechanical components, biomedical devices, and environmental monitoring. Full article
(This article belongs to the Special Issue Reliability Estimation and Mathematical Statistics, 2nd Edition)
►▼ Show Figures

Figure 1

38 pages, 25290 KB  
Article
A New Multi-Progressive Generalized Type-II Censoring: Theory, Reliability Inference, and Multidisciplinary Applications
by Heba S. Mohammed and Ahmed Elshahhat
Mathematics 2026, 14(5), 862; https://doi.org/10.3390/math14050862 - 3 Mar 2026
Viewed by 514
Abstract
Modern reliability experiments frequently face operational constraints that require balancing test duration, precision, and removal strategies, rendering classical censoring schemes inadequate for contemporary multidisciplinary applications. This study introduces a novel multi-progressive generalized Type-II censoring (MP-GC-T2) framework that unifies and extends existing progressive and [...] Read more.
Modern reliability experiments frequently face operational constraints that require balancing test duration, precision, and removal strategies, rendering classical censoring schemes inadequate for contemporary multidisciplinary applications. This study introduces a novel multi-progressive generalized Type-II censoring (MP-GC-T2) framework that unifies and extends existing progressive and generalized censoring structures through the integration of staged failure-proportion controls, dual temporal termination thresholds, and adaptive withdrawal of surviving units. The proposed mechanism provides enhanced flexibility in experiment design while retaining analytical tractability for statistical inference. Assuming Weibull lifetimes, we develop a complete inferential framework including maximum likelihood estimation, asymptotic interval construction, and Bayesian estimation via hybrid Metropolis–Hastings–Gibbs sampling with informative gamma priors, together with multiple interval estimation strategies for reliability characteristics. Extensive Monte Carlo investigations assess estimator bias, precision, coverage behaviour, and interval efficiency across diverse censoring configurations, demonstrating robustness and inferential gains relative to conventional schemes. Furthermore, optimal progressive-removal planning criteria are explored to guide practitioners in selecting censoring patterns that maximize inferential accuracy under practical constraints. The versatility and practical relevance of the MP-GC-T2 design are illustrated through applications to heterogeneous real datasets arising from clinical, chemical, geological, physical, and petroleum sciences, confirming its adaptability to distinct reliability structures and data-generation mechanisms. Collectively, the proposed methodology contributes a unified experimental and inferential platform that advances censoring design, reliability estimation, and cross-disciplinary statistical modelling. Full article
(This article belongs to the Special Issue Reliability Estimation and Mathematical Statistics, 2nd Edition)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-4
Back to TopTop