Applied Probability and Statistical Inference in Reliability Engineering

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

Deadline for manuscript submissions: 28 February 2025 | Viewed by 2726

Special Issue Editors


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Guest Editor
Department of Statistics and Insurance Science, University of Piraeus, 185 34 Piraeus, Greece
Interests: nonparametric statistical inference; statistical reliability theory; statistical process control; order statistics; applied probability
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Guest Editor
Laboratory of Statistics and Data Analysis, Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, GR-83200 Karlovasi, Greece
Interests: model selection; applied probability; reliability theory; medical statistics; time series; biostatistics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Probability theory and statistics play a fundamental role in the research of various scientific fields, such as engineering, computer science, medicine, biology, or economics. Several statistical methods and probabilistic approaches, such as order statistics, Markov chain imbedding, computational statistics, generating functions approaches, or nonparametric statistics have attracted a considerable research interest during recent decades.

The aim of this Special Issue is to provide some evidence which reflects the importance of statistical techniques and probabilistic modelling in applied scientific areas, related to reliability engineering. We welcome articles establishing theoretical methodologies in these fields, but papers providing interesting and innovative applications, including solutions of important practical problems and case studies, of probability and statistics shall also be considered. Thus, the Special Issue is expected to be a collective work by a number of leading researchers and practitioners in their respective fields of expertise and, in general, experts who have been working at the forefront of applied probability, statistics, and reliability theory.

Dr. Ioannis S. Triantafyllou
Prof. Dr. Karagrigoriou Alexandros
Guest Editors

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Keywords

  • reliability modelling
  • nonparametric statistics
  • probabilistic methods
  • statistical models and methods
  • reliability and risk analysis
  • stochastic models and methods
  • probabilistic models in reliability
  • nonparametric methods in reliability
  • software reliability
  • Markov and semi-Markov processes in reliability
  • stochastic problems in reliability
  • multi-state systems
  • maintenance policies in reliability
  • order statistics in reliability

Published Papers (4 papers)

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Research

27 pages, 1397 KiB  
Article
Aging Renewal Point Processes and Exchangeability of Event Times
by Fabio Vanni and David Lambert
Mathematics 2024, 12(10), 1529; https://doi.org/10.3390/math12101529 - 14 May 2024
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Abstract
In this paper, we investigate the impact of latency aging on exchangeable (invariant under permutation of indices) inter-arrival times arising from mixed renewal point processes (statistical mixtures of point processes with renewal inter-arrival times) and explore the implications for reliability and survival analysis. [...] Read more.
In this paper, we investigate the impact of latency aging on exchangeable (invariant under permutation of indices) inter-arrival times arising from mixed renewal point processes (statistical mixtures of point processes with renewal inter-arrival times) and explore the implications for reliability and survival analysis. We prove that aging preserves the exchangeability of inter-arrival times. Our data analysis, which includes both surrogate data and a Bayesian approach to high-frequency currency exchange-rate data, shows how aging impacts key survival analysis metrics such as failure survival, renewal, and hazard rate functions. Full article
18 pages, 2818 KiB  
Article
Reliability of Partitioning Metric Space Data
by Yariv N. Marmor and Emil Bashkansky
Mathematics 2024, 12(4), 603; https://doi.org/10.3390/math12040603 - 18 Feb 2024
Viewed by 517
Abstract
The process of sorting or categorizing objects or information about these objects into clusters according to certain criteria is a fundamental procedure in data analysis. Where it is feasible to determine the distance metric for any pair of objects, the significance and reliability [...] Read more.
The process of sorting or categorizing objects or information about these objects into clusters according to certain criteria is a fundamental procedure in data analysis. Where it is feasible to determine the distance metric for any pair of objects, the significance and reliability of the separation can be evaluated by calculating the separation/segregation power (SP) index proposed herein. The latter index is the ratio of the average inter distance to the average intra distance, independent of the scale parameter. Here, the calculated SP value is compared to its statistical distribution obtained by a simulation study for a given partition under the homogeneity null hypothesis to draw a conclusion using standard statistical procedures. The proposed concept is illustrated using three examples representing different types of objects under study. Some general considerations are given regarding the nature of the SP distribution under the null hypothesis and its dependence on the number of divisions and the amount of data within them. A detailed modus operandi (working method) for analyzing a metric data partition is also offered. Full article
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28 pages, 408 KiB  
Article
Relative Orderings of Modified Proportional Hazard Rate and Modified Proportional Reversed Hazard Rate Models
by Mansour Shrahili, Mohamed Kayid and Mhamed Mesfioui
Mathematics 2023, 11(22), 4652; https://doi.org/10.3390/math11224652 - 15 Nov 2023
Viewed by 637
Abstract
In this paper, we identify several relative ordering properties of the modified proportional hazard rate and modified proportional reversed hazard rate models. For this purpose, we use two well-known relative orderings, namely the relative hazard rate ordering and the relative reversed hazard rate [...] Read more.
In this paper, we identify several relative ordering properties of the modified proportional hazard rate and modified proportional reversed hazard rate models. For this purpose, we use two well-known relative orderings, namely the relative hazard rate ordering and the relative reversed hazard rate ordering. The investigation is to see how a relative ordering between two possible base distributions for the response distributions in these models is preserved when the parameters of the underlying models are changed. We will give some examples to illustrate the results and the conditions under which they are obtained. Numerical simulation studies have also been provided to examine the examples presented. Full article
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19 pages, 493 KiB  
Article
Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored δ Shock Model
by Lina Bian, Bo Peng and Yong Ye
Mathematics 2023, 11(21), 4560; https://doi.org/10.3390/math11214560 - 6 Nov 2023
Viewed by 848
Abstract
A fresh censored δ shock model is investigated. The arrival of random shocks follows a generalized Pólya process, and the failure mechanism of the system occurs based on the censored δ shock model. The generalized Pólya process is used for modeling because the [...] Read more.
A fresh censored δ shock model is investigated. The arrival of random shocks follows a generalized Pólya process, and the failure mechanism of the system occurs based on the censored δ shock model. The generalized Pólya process is used for modeling because the generalized Pólya process has excellent properties, including the homogeneous Poisson process, the non-homogeneous Poisson process, and the Pólya process. Thus far, the lifetime properties of the censored δ shock model under the generalized Pólya process have not been studied. Therefore, for the established generalized Pólya censored δ shock model, the corresponding reliability function, the upper bound of the reliability function, the mean lifetime, the failure rate, and the class of life distribution are obtained. In addition, a replacement strategy N, based on the number of failures of the system, is considered using a geometric process. We determined the optimal replacement policy N* by objective function minimization. Finally, a numerical example is presented to verify the rationality of the model. Full article
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