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Mathematics
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Reliability Estimation and Mathematical Statistics
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Reliability Estimation and Mathematical Statistics

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

Deadline for manuscript submissions: 31 July 2024 | Viewed by 1148

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 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. 

It is with great enthusiasm and anticipation that I write to you today as the Guest Editor of the upcoming Special Issue Reliability Estimation and Mathematical Statistics. 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. 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 100 words) can be sent to the Editorial Office for announcement on this website.

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
  • system

Published Papers (2 papers)

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25 pages, 1072 KiB  
Article
Multivariate Structural Equation Modeling Techniques for Estimating Reliability, Measurement Error, and Subscale Viability When Using Both Composite and Subscale Scores in Practice
by Walter Peter Vispoel, Hyeryung Lee and Tingting Chen
Mathematics 2024, 12(8), 1164; https://doi.org/10.3390/math12081164 - 12 Apr 2024
Viewed by 275
Abstract
We illustrate how structural equation models (SEMs) can be used to assess the reliability and generalizability of composite and subscale scores, proportions of multiple sources of measurement error, and subscale added value within multivariate designs using data from a popular inventory measuring hierarchically [...] Read more.
We illustrate how structural equation models (SEMs) can be used to assess the reliability and generalizability of composite and subscale scores, proportions of multiple sources of measurement error, and subscale added value within multivariate designs using data from a popular inventory measuring hierarchically structured personality traits. We compare these techniques between standard SEMs representing congeneric relations between indicators and underlying factors versus SEM-based generalizability theory (GT) designs with simplified essential tau-equivalent constraints. Results strongly emphasized the importance of accounting for multiple sources of measurement error in both contexts and revealed that, in most but not all instances, congeneric designs yielded higher score accuracy, lower proportions of measurement error, greater average subscale score viability, stronger model fits, and differing magnitudes of disattenuated subscale intercorrelations. Extending the congeneric analyses to the item level further highlighted consistent weaknesses in the psychometric properties of negatively versus positively keyed items. Collectively, these findings demonstrate the practical value and advantages of applying GT-based principles to congeneric SEMs that are much more commonly encountered in the research literature and more directly linked to the specific measures being analyzed. We also provide prophecy formulas to estimate reliability and generalizability coefficients, proportions of individual sources of measurement error, and subscale added-value indices for changes made to measurement procedures and offer guidelines and examples for running all illustrated analyses using the lavaan (Version 0.6-17) and semTools (Version 0.5-6) packages in R. The methods described for the analyzed designs are applicable to any objectively or subjectively scored assessments for which both composite and subcomponent scores are reported. Full article
(This article belongs to the Special Issue Reliability Estimation and Mathematical Statistics)
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15 pages, 2474 KiB  
Article
Traffic Safety Assessment and Injury Severity Analysis for Undivided Two-Way Highway–Rail Grade Crossings
by Qiaoqiao Ren, Min Xu, Bojian Zhou and Sai-Ho Chung
Mathematics 2024, 12(4), 519; https://doi.org/10.3390/math12040519 - 07 Feb 2024
Cited by 1 | Viewed by 631
Abstract
The safety and reliability of undivided two-way highway–rail grade crossings (HRGCs) are of paramount importance in transportation systems. Utilizing crash data from the Federal Railroad Administration between 2020 and 2021, this study aims to predict crash injury severity outcomes and investigate various factors [...] Read more.
The safety and reliability of undivided two-way highway–rail grade crossings (HRGCs) are of paramount importance in transportation systems. Utilizing crash data from the Federal Railroad Administration between 2020 and 2021, this study aims to predict crash injury severity outcomes and investigate various factors influencing injury severities. The χ2 test was first used to select variables that were significantly associated with injury outcomes. By employing the eXtreme Gradient Boosting (XGBoost) model and interpretable SHapley Additive exPlanations (SHAP), a cross-category safety assessment that offers an evidence-based hierarchy and statistical inference of risk factors associated with crashes, crossings, vehicles, drivers, and environment was provided for killed, injured, and uninjured outcomes. Some significant predictors overlapped between the killed and injured models, such as old driver, driver was in vehicle, main track, went around the gate, adverse crossing surface, and truck, while the other different significant factors revealed that the model could distinguish between different severity levels. Additionally, the results suggested that the model has varying performances in predicting different injury severities, with the killed model having the highest accuracy of 93.36%. The SHAP dependency plots for the top three features also ensure reliable predictions and inform potential interventions aimed at strengthening traffic safety and risk management practices, such as enhanced warning systems and targeted educational campaigns for older drivers. Full article
(This article belongs to the Special Issue Reliability Estimation and Mathematical Statistics)
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