Special Issue "Reliability and Statistical Learning and Its Applications"

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

Deadline for manuscript submissions: closed (1 December 2021) | Viewed by 8258

Special Issue Editor

Prof. Dr. Hoang Pham
E-Mail Website
Guest Editor
Department of Industrial and Systems Engineering, Rutgers University, Piscataway, NJ, USA
Interests: reliability engineering; software reliability; statistical inferences; fault-tolerant computing
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Special Issue Information

Dear Colleagues,

Growing international competition has increased the need for all industries and businesses to produce high-quality products as well as better services. Articles concerning new theoretical research and methods on statistical reliability, applied mathematics and methods in modeling and prediction, and statistical learning are solicited. Preference will be given to papers with real-world applications over purely theoretical papers. Topics of interest include but are not limited to the following:

  • Statistical methods in machine learning;
  • Reliability modeling and optimization;
  • Reliability of intelligent systems;
  • Statistical learning algorithms, models, and theories;
  • Applied mathematics and methods in statistical learning;
  • Feature selection and development;
  • Causal embeddings for recommendation;
  • Statistical inference for recommendation systems;
  • Case studies on statistical modeling and analysis of real-world applications.

Prof. Dr. Hoang Pham
Guest Editor

Manuscript Submission Information

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Published Papers (3 papers)

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Research

Article
Software Reliability Modeling Incorporating Fault Detection and Fault Correction Processes with Testing Coverage and Fault Amount Dependency
Mathematics 2022, 10(1), 60; https://doi.org/10.3390/math10010060 - 24 Dec 2021
Cited by 2 | Viewed by 664
Abstract
This paper presents a general testing coverage software reliability modeling framework that covers imperfect debugging and considers not only fault detection processes (FDP) but also fault correction processes (FCP). Numerous software reliability growth models have evaluated the reliability of software over the last [...] Read more.
This paper presents a general testing coverage software reliability modeling framework that covers imperfect debugging and considers not only fault detection processes (FDP) but also fault correction processes (FCP). Numerous software reliability growth models have evaluated the reliability of software over the last few decades, but most of them attached importance to modeling the fault detection process rather than modeling the fault correction process. Previous studies analyzed the time dependency between the fault detection and correction processes and modeled the fault correction process as a delayed detection process with a random or deterministic time delay. We study the quantitative dependency between dual processes from the viewpoint of fault amount dependency instead of time dependency, then propose a generalized modeling framework along with imperfect debugging and testing coverage. New models are derived by adopting different testing coverage functions. We compared the performance of these proposed models with existing models under the context of two kinds of failure data, one of which only includes observations of faults detected, and the other includes not only fault detection but also fault correction data. Different parameter estimation methods and performance comparison criteria are presented according to the characteristics of different kinds of datasets. No matter what kind of data, the comparison results reveal that the proposed models generally give improved descriptive and predictive performance than existing models. Full article
(This article belongs to the Special Issue Reliability and Statistical Learning and Its Applications)
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Article
Comparisons of Parallel Systems with Components Having Proportional Reversed Hazard Rates and Starting Devices
Mathematics 2021, 9(8), 856; https://doi.org/10.3390/math9080856 - 14 Apr 2021
Cited by 1 | Viewed by 445
Abstract
In this paper, we consider stochastic comparisons of parallel systems with proportional reversed hazard rate (PRHR) distributed components equipped with starting devices. By considering parallel systems with two components that PRHR and starting devices, we prove the hazard rate and reversed hazard rate [...] Read more.
In this paper, we consider stochastic comparisons of parallel systems with proportional reversed hazard rate (PRHR) distributed components equipped with starting devices. By considering parallel systems with two components that PRHR and starting devices, we prove the hazard rate and reversed hazard rate orders. These results are then generalized for such parallel systems with n components in terms of usual stochastic order. The establish results are illustrated with some examples. Full article
(This article belongs to the Special Issue Reliability and Statistical Learning and Its Applications)
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Article
On Estimating the Number of Deaths Related to Covid-19
Mathematics 2020, 8(5), 655; https://doi.org/10.3390/math8050655 - 26 Apr 2020
Cited by 22 | Viewed by 6683
Abstract
In this paper, we discuss an explicit model function that can estimate the total number of deaths in the population, and particularly, estimate the cumulative number of deaths in the United States due to the current Covid-19 virus. We compare the modeling results [...] Read more.
In this paper, we discuss an explicit model function that can estimate the total number of deaths in the population, and particularly, estimate the cumulative number of deaths in the United States due to the current Covid-19 virus. We compare the modeling results to two related existing models based on a new criteria and several existing criteria for model selection. The results show the proposed model fits significantly better than the other two related models based on the U.S. Covid-19 death data. We observe that the errors of the fitted data and the predicted data points on the total number of deaths in the U.S. on the last available data point and the next coming day are less than 0.5% and 2.0%, respectively. The results show very encouraging predictability for the model. The new model predicts that the maximum total number of deaths will be approximately 62,100 across the United States due to the Covid-19 virus, and with a 95% confidence that the expected total death toll will be between 60,951 and 63,249 deaths based on the data until 22 April, 2020. If there is a significant change in the coming days due to various testing strategies, social-distancing policies, the reopening of community strategies, or a stay-home policy, the predicted death tolls will definitely change. Future work can be explored further to apply the proposed model to global Covid-19 death data and to other applications, including human population mortality, the spread of disease, and different topics such as movie reviews in recommender systems. Full article
(This article belongs to the Special Issue Reliability and Statistical Learning and Its Applications)
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