Research

19 pages, 873 KiB

Open AccessArticle

An Evidential Software Risk Evaluation Model

by Xingyuan Chen and Yong Deng

Mathematics 2022, 10(13), 2325; https://0-doi-org.brum.beds.ac.uk/10.3390/math10132325 - 02 Jul 2022

Cited by 39 | Viewed by 2299

Software risk management is an important factor in ensuring software quality. Therefore, software risk assessment has become a significant and challenging research area. The aim of this study is to establish a data-driven software risk assessment model named DDERM. In the proposed model, [...] Read more.

Software risk management is an important factor in ensuring software quality. Therefore, software risk assessment has become a significant and challenging research area. The aim of this study is to establish a data-driven software risk assessment model named DDERM. In the proposed model, experts’ risk assessments of probability and severity can be transformed into basic probability assignments (BPAs). Deng entropy was used to measure the uncertainty of the evaluation and to calculate the criteria weights given by experts. In addition, the adjusted BPAs were fused using the rules of Dempster–Shafer evidence theory (DST). Finally, a risk matrix was used to get the risk priority. A case application demonstrates the effectiveness of the proposed method. The proposed risk modeling framework is a novel approach that provides a rational assessment structure for imprecision in software risk and is applicable to solving similar risk management problems in other domains. Full article

(This article belongs to the Special Issue Probability and Statistics in Quality and Reliability Engineering)

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26 pages, 1629 KiB

Open AccessArticle

Analysis of Modified Kies Exponential Distribution with Constant Stress Partially Accelerated Life Tests under Type-II Censoring

by Mazen Nassar and Farouq Mohammad A. Alam

Mathematics 2022, 10(5), 819; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050819 - 04 Mar 2022

Cited by 9 | Viewed by 2073

Abstract

This study investigates, for the first time, the product of spacing estimation of the modified Kies exponential distribution parameters as well as the acceleration factor using constant-stress partially accelerated life tests under the Type-II censoring scheme. Besides this approach, the conventional maximum likelihood [...] Read more.

This study investigates, for the first time, the product of spacing estimation of the modified Kies exponential distribution parameters as well as the acceleration factor using constant-stress partially accelerated life tests under the Type-II censoring scheme. Besides this approach, the conventional maximum likelihood method is also considered. The point estimates and the approximate confidence intervals of the unknown parameters are obtained using the two methods. In addition, two parametric bootstrap confidence intervals are discussed based on both estimation methods. Extensive simulation studies are conducted by considering different censoring schemes to examine the efficiency of each estimation method. Finally, two real data sets for oil breakdown times of insulating fluid and minority electron mobility are analyzed to show the applicability of the different methods. Moreover, the reliability function and the mean time-to-failure under the normal use condition are estimated using both methods. Based on Monte Carlo simulation outcomes and real data analysis, we recommend using the maximum product of spacing to evaluate both the point and interval estimates for the modified Kies exponential distribution parameters in the presence of constant-stress partially accelerated Type-II censored data. Full article

(This article belongs to the Special Issue Probability and Statistics in Quality and Reliability Engineering)

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15 pages, 1653 KiB

Open AccessArticle

Mathematical Modeling the Time-Delay Interactions between Tumor Viruses and the Immune System with the Effects of Chemotherapy and Autoimmune Diseases

by Hoang Pham

Mathematics 2022, 10(5), 756; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050756 - 27 Feb 2022

Cited by 8 | Viewed by 2150

Abstract

The immune system is the body’s defense against pathogens, which are complex living organisms found in many parts in the body including organs, tissues, cells, molecules, and proteins. When the immune system works properly, it can recognize and kill the abnormal cells and [...] Read more.

The immune system is the body’s defense against pathogens, which are complex living organisms found in many parts in the body including organs, tissues, cells, molecules, and proteins. When the immune system works properly, it can recognize and kill the abnormal cells and the infected cells. Otherwise, it can attack the body’s healthy cells even if there is no invader. Many researchers have developed immunotherapy (or cancer vaccines) and have used chemotherapy for cancer treatment that can kill fast-growing cancer cells or at least slow down tumor growth. However, chemotherapy drugs travel throughout the body and tend to kill both healthy cells and cancer cells. In this study, we consider the fact that chemotherapy can kill tumor cells and that the loss of the immune cells may at the same time stir up cancer growth. We present a dynamic time-delay tumor-immune model with the effects of chemotherapy drugs and autoimmune disease. The modeling results can be used to determine the progression of tumor cells in the human body with the effect of chemotherapy, autoimmune diseases, and time delays based on partial differential equations. It can also be used to predict when the tumor viruses’ free state can be reached as time progresses, as well as the state of the body’s healthy cells as time progresses. We also present a few numerical cases that illustrate that the model can be used to monitor the effects of chemotherapy drug treatment and the growth rate of tumor virus-infected cells and the autoimmune disease. Full article

(This article belongs to the Special Issue Probability and Statistics in Quality and Reliability Engineering)

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25 pages, 833 KiB

Open AccessArticle

Methodology for the Assessment of Imprecise Multi-State System Availability

by Joanna Akrouche, Mohamed Sallak, Eric Châtelet, Fahed Abdallah and Hiba Hajj Chehade

Mathematics 2022, 10(1), 150; https://0-doi-org.brum.beds.ac.uk/10.3390/math10010150 - 04 Jan 2022

Cited by 1 | Viewed by 1424

Abstract

Most existing studies of a system’s availability in the presence of epistemic uncertainties assume that the system is binary. In this paper, a new methodology for the estimation of the availability of multi-state systems is developed, taking into consideration epistemic uncertainties. This paper [...] Read more.

Most existing studies of a system’s availability in the presence of epistemic uncertainties assume that the system is binary. In this paper, a new methodology for the estimation of the availability of multi-state systems is developed, taking into consideration epistemic uncertainties. This paper formulates a combined approach, based on continuous Markov chains and interval contraction methods, to address the problem of computing the availability of multi-state systems with imprecise failure and repair rates. The interval constraint propagation method, which we refer to as the forward–backward propagation (FBP) contraction method, allows us to contract the probability intervals, keeping all the values that may be consistent with the set of constraints. This methodology is guaranteed, and several numerical examples of systems with complex architectures are studied. Full article

(This article belongs to the Special Issue Probability and Statistics in Quality and Reliability Engineering)

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15 pages, 2601 KiB

Open AccessArticle

Robust Multivariate Shewhart Control Chart Based on the Stahel-Donoho Robust Estimator and Mahalanobis Distance for Multivariate Outlier Detection

by Ishaq Adeyanju Raji, Nasir Abbas, Mu’azu Ramat Abujiya and Muhammad Riaz

Mathematics 2021, 9(21), 2772; https://0-doi-org.brum.beds.ac.uk/10.3390/math9212772 - 01 Nov 2021

Cited by 1 | Viewed by 1641

Abstract

While researchers and practitioners may seamlessly develop methods of detecting outliers in control charts under a univariate setup, detecting and screening outliers in multivariate control charts pose serious challenges. In this study, we propose a robust multivariate control chart based on the Stahel-Donoho [...] Read more.

While researchers and practitioners may seamlessly develop methods of detecting outliers in control charts under a univariate setup, detecting and screening outliers in multivariate control charts pose serious challenges. In this study, we propose a robust multivariate control chart based on the Stahel-Donoho robust estimator (SDRE), whilst the process parameters are estimated from phase-I. Through intensive Monte-Carlo simulation, the study presents how the estimation of parameters and presence of outliers affect the efficacy of the Hotelling T² chart, and then how the proposed outlier detector brings the chart back to normalcy by restoring its efficacy and sensitivity. Run-length properties are used as the performance measures. The run length properties establish the superiority of the proposed scheme over the default multivariate Shewhart control charting scheme. The applicability of the study includes but is not limited to manufacturing and health industries. The study concludes with a real-life application of the proposed chart on a dataset extracted from the manufacturing process of carbon fiber tubes. Full article

(This article belongs to the Special Issue Probability and Statistics in Quality and Reliability Engineering)

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26 pages, 492 KiB

Open AccessArticle

The Exponentiated Burr–Hatke Distribution and Its Discrete Version: Reliability Properties with CSALT Model, Inference and Applications

by Mahmoud El-Morshedy, Hassan M. Aljohani, Mohamed S. Eliwa, Mazen Nassar, Mohammed K. Shakhatreh and Ahmed Z. Afify

Mathematics 2021, 9(18), 2277; https://0-doi-org.brum.beds.ac.uk/10.3390/math9182277 - 16 Sep 2021

Cited by 9 | Viewed by 1720

Abstract

Continuous and discrete distributions are essential to model both continuous and discrete lifetime data in several applied sciences. This article introduces two extended versions of the Burr–Hatke model to improve its applicability. The first continuous version is called the exponentiated Burr–Hatke (EBuH) distribution. [...] Read more.

Continuous and discrete distributions are essential to model both continuous and discrete lifetime data in several applied sciences. This article introduces two extended versions of the Burr–Hatke model to improve its applicability. The first continuous version is called the exponentiated Burr–Hatke (EBuH) distribution. We also propose a new discrete analog, namely the discrete exponentiated Burr–Hatke (DEBuH) distribution. The probability density and the hazard rate functions exhibit decreasing or upside-down shapes, whereas the reversed hazard rate function. Some statistical and reliability properties of the EBuH distribution are calculated. The EBuH parameters are estimated using some classical estimation techniques. The simulation results are conducted to explore the behavior of the proposed estimators for small and large samples. The applicability of the EBuH and DEBuH models is studied using two real-life data sets. Moreover, the maximum likelihood approach is adopted to estimate the parameters of the EBuH distribution under constant-stress accelerated life-tests (CSALTs). Furthermore, a real data set is analyzed to validate our results under the CSALT model. Full article

(This article belongs to the Special Issue Probability and Statistics in Quality and Reliability Engineering)

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13 pages, 458 KiB

Open AccessArticle

Residual Probability Function for Dependent Lifetimes

by Mhamed Mesfioui and Mohamed Kayid

Mathematics 2021, 9(15), 1782; https://0-doi-org.brum.beds.ac.uk/10.3390/math9151782 - 28 Jul 2021

Cited by 1 | Viewed by 1178

Abstract

In this paper, the residual probability function is applied to analyze the survival probability of two used components relative to each other in the case when their lifetimes are dependent. The expression of the function by copulas has been derived along with some [...] Read more.

In this paper, the residual probability function is applied to analyze the survival probability of two used components relative to each other in the case when their lifetimes are dependent. The expression of the function by copulas has been derived along with some examples of particular copulas. The behaviour of the residual probability function in terms of the underlying dependence is also discussed. The residual probability order is also considered in the dependent case. In the class of Archimedean survival copulas, we prove that the residual probability order implies the usual stochastic order in the reversed direction, and the hazard rate order concludes the residual probability order. Full article

(This article belongs to the Special Issue Probability and Statistics in Quality and Reliability Engineering)

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13 pages, 1269 KiB

Open AccessArticle

Analysis of Network Reliability Characteristics and Importance of Components in a Communication Network

by Soni Bisht, Akshay Kumar, Nupur Goyal, Mangey Ram and Yury Klochkov

Mathematics 2021, 9(12), 1347; https://0-doi-org.brum.beds.ac.uk/10.3390/math9121347 - 11 Jun 2021

Cited by 14 | Viewed by 2771

Abstract

Network reliability is one of the most important concepts in this modern era. Reliability characteristics, component significance measures, such as the Birnbaum importance measure, critical importance measure, the risk growth factor and average risk growth factor, and network reliability stability of the communication [...] Read more.

Network reliability is one of the most important concepts in this modern era. Reliability characteristics, component significance measures, such as the Birnbaum importance measure, critical importance measure, the risk growth factor and average risk growth factor, and network reliability stability of the communication network system have been discussed in this paper to identify the critical components in the network, and also to quantify the impact of component failures. The study also proposes an efficient algorithm to compute the reliability indices of the network. The authors explore how the universal generating function can work to solve the problems related to the network using the exponentially distributed failure rate. To illustrate the proposed algorithm, a numerical example has been taken. Full article

(This article belongs to the Special Issue Probability and Statistics in Quality and Reliability Engineering)

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14 pages, 2665 KiB

Open AccessArticle

Reliability Measures and Profit Exploration of Windmill Water-Pumping Systems Incorporating Warranty and Two Types of Repair

by Nupur Goyal, Mangey Ram, Akshay Kumar, Soni Bisht and Yury Klochkov

Mathematics 2021, 9(8), 822; https://0-doi-org.brum.beds.ac.uk/10.3390/math9080822 - 09 Apr 2021

Cited by 5 | Viewed by 1859

Abstract

Wind energy is a kind of renewable energy that plays a significant role in remote areas for pumping water. The windmill is also used to generate electricity. The windmill is also known as a wind pump when it is used for pumping water. [...] Read more.

Wind energy is a kind of renewable energy that plays a significant role in remote areas for pumping water. The windmill is also used to generate electricity. The windmill is also known as a wind pump when it is used for pumping water. In this work, the authors proposed a complex hybrid model of an example of combined system (windmill, rechargeable battery and pumping system) to evaluate the system’s performance. System performance was affected by system degradation due to system failure. These factors also affected the profit of the user. Two types of repair facilities for continuous and satisfactory performance of the system were assumed. To illustrate the system modeling using the Gumbel–Hougaard family of the copula, numerical examples were used for the exploration of Markov results of the reliability measures and the profit of the system with the warranty period, with this also being demonstrated graphically. Full article

(This article belongs to the Special Issue Probability and Statistics in Quality and Reliability Engineering)

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21 pages, 1046 KiB

Open AccessArticle

Bayesian Estimation Based on Sequential Order Statistics for Heterogeneous Baseline Gompertz Distributions

by Tzong-Ru Tsai, Hua Xin and Chiun-How Kao

Mathematics 2021, 9(2), 145; https://0-doi-org.brum.beds.ac.uk/10.3390/math9020145 - 11 Jan 2021

Cited by 3 | Viewed by 1775

Abstract

A composite dynamic system (CDS) is composed of multiple components. Each component failure can equally induce higher loading on the surviving components and, hence, enhances the hazard rate of each surviving component. The applications of CDS and the reliability evaluation of CDS has [...] Read more.

A composite dynamic system (CDS) is composed of multiple components. Each component failure can equally induce higher loading on the surviving components and, hence, enhances the hazard rate of each surviving component. The applications of CDS and the reliability evaluation of CDS has earned more attention in the recent two decades. Because the lifetime quality of components could be inconsistent, the lifetimes of components in the CDS is considered to follow heterogeneous baseline Gompertz distributions in this study. A power-trend hazard rate function is used in order to characterize the hazard rate of the CDS. In order to overcome the difficulty of obtaining reliable estimates of the parameters in the CDS model, the Bayesian estimation method utilizing a hybrid Gibbs sampling and Metropolis-Hasting algorithm to implement the Markov chain Monte Carlo approach is proposed for obtaining the Bayes estimators of the CDS parameters. An intensive simulation study is carried out to evaluate the performance of the proposed estimation method. The simulation results show that the proposed estimation method is reliable in providing reliability evaluation information for the CDS. An example regarding the service system of small electric carts is used for illustration. Full article

(This article belongs to the Special Issue Probability and Statistics in Quality and Reliability Engineering)

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12 pages, 655 KiB

Open AccessArticle

Stable and Unstable Pattern Recognition Using D² and SVM: A Multivariate Approach

by Pamela Chiñas-Sanchez, Ismael Lopez-Juarez, Jose Antonio Vazquez-Lopez, Abdelkader El Kamel and Jose Luis Navarro-Gonzalez

Mathematics 2021, 9(1), 10; https://0-doi-org.brum.beds.ac.uk/10.3390/math9010010 - 23 Dec 2020

Cited by 2 | Viewed by 1673

Abstract

Control charts are used to visually identify the signals that define the behavior of industrial processes in univariate cases. However, whenever the statistical quality of more than one critical variable needs to be monitored simultaneously, the procedure becomes much more complicated. This paper [...] Read more.

Control charts are used to visually identify the signals that define the behavior of industrial processes in univariate cases. However, whenever the statistical quality of more than one critical variable needs to be monitored simultaneously, the procedure becomes much more complicated. This paper presents a methodology on multivariate pattern recognition using the Mahalanobis distance

(D^{2})

and the Support Vector Machine (SVM) technique to recognise two multivariate patterns. The relevance of the study lies in the monitoring of the variables while considering the correlation between them and the effects of interchangeably using a stable multivariate case against an unstable pattern that results in recognition rates up to