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Aljohani HM. Estimation for the P( X > Y) of Lomax distribution under accelerated life tests. Heliyon 2024; 10:e25802. [PMID: 38371973 PMCID: PMC10873739 DOI: 10.1016/j.heliyon.2024.e25802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2023] [Revised: 01/06/2024] [Accepted: 02/02/2024] [Indexed: 02/20/2024] Open
Abstract
The system or unit survives when strength is more significant than the stress enjoined. This procedure is usually used in many companies to test their product. The reliability or the quality of the scheme or component is described by the parameters of stress-strength reliability (R = P ( X > Y )) where X denotes strength and Y indicates stress. In this article, we adopted the statistical inference of R while the two arbitrary factors X and Y are independent and approach the Lomax lifetime distribution with common scale parameters. Also, the strength and stress variables are subjected to a partial step-stress-quickened life experiment. The classical estimation and Bayes method create the point estimate of R. Confidence intervals of R are computed with asymptotic distribution, bootstrap technique, and Bayesian credible intervals. All results are evaluated and compared under an extensive simulation study. Finally, the lifetime data sets generated from the Lomax distribution are used to analyze the system's reliability by estimating R.
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Affiliation(s)
- Hassan M. Aljohani
- Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
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2
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Alharbi R, Garg R, Kumar I, Kumari A, Aldallal R. On estimation of P(Y < X) for inverse Pareto distribution based on progressively first failure censored data. PLoS One 2023; 18:e0287473. [PMID: 38032903 PMCID: PMC10688691 DOI: 10.1371/journal.pone.0287473] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2022] [Accepted: 07/04/2023] [Indexed: 12/02/2023] Open
Abstract
The stress-strength reliability (SSR) model ϕ = P(Y < X) is used in numerous disciplines like reliability engineering, quality control, medical studies, and many more to assess the strength and stresses of the systems. Here, we assume X and Y both are independent random variables of progressively first failure censored (PFFC) data following inverse Pareto distribution (IPD) as stress and strength, respectively. This article deals with the estimation of SSR from both classical and Bayesian paradigms. In the case of a classical point of view, the SSR is computed using two estimation methods: maximum product spacing (MPS) and maximum likelihood (ML) estimators. Also, derived interval estimates of SSR based on ML estimate. The Bayes estimate of SSR is computed using the Markov chain Monte Carlo (MCMC) approximation procedure with a squared error loss function (SELF) based on gamma informative priors for the Bayesian paradigm. To demonstrate the relevance of the different estimates and the censoring schemes, an extensive simulation study and two pairs of real-data applications are discussed.
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Affiliation(s)
- Randa Alharbi
- Department of Statistics, Faculty of Science, University of Tabuk, Tabuk, Saudia Arabia
| | - Renu Garg
- Department of Statistics, Kirori Mal College, University of Delhi, Delhi, India
| | - Indrajeet Kumar
- Department of Mathematics, Kalasalingam Academy of Research and Education, Krishnankoil, Tamilnadu, India
| | - Anita Kumari
- Department of Statistics, Central University of Haryana, Mahendergarh, India
| | - Ramy Aldallal
- Department of Accounting, College of Business Administration in Hawtat Bani Tamim, Prince Sattam Bin Abdulaziz University, Jeddah, Saudi Arabia
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3
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Yu Y, Wang L, Dey S, Liu J. Estimation of stress-strength reliability from unit-Burr Ⅲ distribution under records data. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:12360-12379. [PMID: 37501446 DOI: 10.3934/mbe.2023550] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/29/2023]
Abstract
This paper explores estimation of stress-strength reliability based on upper record values. When the strength and stress variables follow unit-Burr Ⅲ distributions, a generalized inferential approach is proposed for estimating stress-strength reliability (SSR). Under the common strength and stress parameter case, two types of pivotal quantities are constructed respectively, and then the generalized point and interval estimates for SSR are proposed in consequence, where the associated Monte-Carlo sampling approach is provided for computation. In addition, when strength and stress variables feature unequal model parameters, different generalized point and confidence interval estimates are also established in this regard. Extensive simulation studies are conducted to examine the behavior of proposed methods. Finally, a real-life data example is presented for illustration.
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Affiliation(s)
- Yarong Yu
- School of Mathematics, Yunnan Normal University, Kunming, China
| | - Liang Wang
- School of Mathematics, Yunnan Normal University, Kunming, China
| | - Sanku Dey
- Department of Statistics, St. Anthony's College, Shillong, Meghalaya, India
| | - Jia Liu
- School of Mathematics, Yunnan Normal University, Kunming, China
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4
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Krishnamoorthy K, Lv S. A report on the paper “xia cai, feng siman & yan liang (2022): generalized fiducial inference for the lower confidence limit of reliability based on weibull distribution, communications in statistics - simulation and computation, DOI: 10.1080/03610918.2022.2067873”. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2157013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
| | - Shanshan Lv
- Department of Statistics, Truman State University, Kirksville, Missouri, USA
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5
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Muhammad M, Liu L, Abba B, Muhammad I, Bouchane M, Zhang H, Musa S. A New Extension of the Topp-Leone-Family of Models with Applications to Real Data. ANNALS OF DATA SCIENCE 2022; 10:225-250. [PMID: 38625258 PMCID: PMC9579674 DOI: 10.1007/s40745-022-00456-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/13/2022] [Revised: 07/28/2022] [Accepted: 09/26/2022] [Indexed: 10/29/2022]
Abstract
In this article, we proposed a new extension of the Topp-Leone family of distributions. Some important properties of the model are developed, such as quantile function, stochastic ordering, model series representation, moments, stress-strength reliability parameter, Renyi entropy, order statistics, and moment of residual life. A particular member called new extended Topp-Leone exponential (NETLE) is discussed. Maximum likelihood estimation (MLE), least-square estimation (LSE), and percentile estimation (PE) are used for the model parameter estimation. Simulation studies were conducted using NETLE to assess the MLE, LSE, and PE performance by examining their bias and mean square error (MSE), and the result was satisfactory. Finally, the applications of the NETLE to two real data sets are provided to illustrate the importance of the NETLG families in practice; the data sets consist of daily new deaths due to COVID-19 in California and New Jersey, USA. The new model outperformed many other existing Topp-Leone's and exponential related distributions based on the real data illustrations.
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Affiliation(s)
- Mustapha Muhammad
- Department of Mathematics, Guangdong University of Petrochemical Technology, Maoming, 525000 China
| | - Lixia Liu
- School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, 050024 People’s Republic of China
| | - Badamasi Abba
- School of Mathematics and Statistics, Central South University, Changsha, China
- Department of Mathematics, Yusuf Maitama Sule University, Kano, Nigeria
| | - Isyaku Muhammad
- School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu, 611731 China
| | - Mouna Bouchane
- Key Laboratory of Augmented Reality College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, China
| | - Hexin Zhang
- School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, 050024 People’s Republic of China
| | - Sani Musa
- Department of Mathematics and Computer Science, Sule Lamido University, Kafin-Hausa, Jigawa Nigeria
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6
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Kumari R, Lodhi C, Tripathi YM, Sinha RK. Estimation of stress–strength reliability for inverse exponentiated distributions with application. INTERNATIONAL JOURNAL OF QUALITY & RELIABILITY MANAGEMENT 2022. [DOI: 10.1108/ijqrm-06-2021-0182] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
PurposeInferences for multicomponent reliability is derived for a family of inverted exponentiated densities having common scale and different shape parameters.Design/methodology/approachDifferent estimates for multicomponent reliability is derived from frequentist viewpoint. Two bootstrap confidence intervals of this parametric function are also constructed.FindingsForm a Monte-Carlo simulation study, the authors find that estimates obtained from maximum product spacing and Right-tail Anderson–Darling procedures provide better point and interval estimates of the reliability. Also the maximum likelihood estimate competes good with these estimates.Originality/valueIn literature several distributions are introduced and studied in lifetime analysis. Among others, exponentiated distributions have found wide applications in such studies. In this regard the authors obtain various frequentist estimates for the multicomponent reliability by considering inverted exponentiated distributions.
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7
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Inferences of the Multicomponent Stress–Strength Reliability for Burr XII Distributions. MATHEMATICS 2022. [DOI: 10.3390/math10142478] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
Multicomponent stress–strength reliability (MSR) is explored for the system with Burr XII distributed components under Type-II censoring. When the distributions of strength and stress variables have Burr XII distributions with common or unequal inner shape parameters, the existence and uniqueness of the maximum likelihood estimators are investigated and established. The associated approximate confidence intervals are obtained by using the asymptotic normal distribution theory along with the delta method and parametric bootstrap procedure, respectively. Moreover, alternative generalized pivotal quantities-based point and confidence interval estimators are developed. Additionally, a likelihood ratio test is presented to diagnose the equivalence of both inner shape parameters or not. Conclusively, Monte Carlo simulations and real data analysis are conducted for illustration.
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Saini S, Tomer S, Garg R. Inference of multicomponent stress-strength reliability following Topp-Leone distribution using progressively censored data. J Appl Stat 2022; 50:1538-1567. [PMID: 37197757 PMCID: PMC10184616 DOI: 10.1080/02664763.2022.2032621] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Abstract
In this paper, the inference of multicomponent stress-strength reliability has been derived using progressively censored samples from Topp-Leone distribution. Both stress and strength variables are assumed to follow Topp-Leone distributions with different shape parameters. The maximum likelihood estimate along with the asymptotic confidence interval are developed. Boot-p and Boot-t confidence intervals are also constructed. The Bayes estimates under generalized entropy loss function based on gamma priors using Lindley's, Tierney-Kadane's approximation and Markov chain Monte Carlo methods are derived. A simulation study is considered to check the performance of various estimation methods and different censoring schemes. A real data study shows the applicability of the proposed estimation methods.
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Affiliation(s)
- Shubham Saini
- Department of Statistics, University of Delhi, Delhi, India
| | - Sachin Tomer
- Department of Statistics, Ramanujan College, University of Delhi, Delhi, India
| | - Renu Garg
- Department of Statistics, University of Delhi, Delhi, India
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9
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Estimation of Stress-Strength Reliability for Multicomponent System with Rayleigh Data. ENERGIES 2021. [DOI: 10.3390/en14237917] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Inference is investigated for a multicomponent stress-strength reliability (MSR) under Type-II censoring when the latent failure times follow two-parameter Rayleigh distribution. With a context that the lifetimes of the strength and stress variables have common location parameters, maximum likelihood estimator of MSR along with the existence and uniqueness is established. The associated approximate confidence interval is provided via the asymptotic distribution theory and delta method. Meanwhile, alternative generalized pivotal quantities-based point and confidence interval estimators are also constructed for MSR. More generally, when the lifetimes of strength and stress variables follow Rayleigh distributions with unequal location parameters, likelihood and generalized pivotal-based estimators are provided for MSR as well. In addition, to compare the equivalence of different strength and stress parameters, a likelihood ratio test is provided. Finally, simulation studies and a real data example are presented for illustration.
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10
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Analysis for Xgamma Parameters of Life under Type-II Adaptive Progressively Hybrid Censoring with Applications in Engineering and Chemistry. Symmetry (Basel) 2021. [DOI: 10.3390/sym13112112] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Censoring mechanisms are widely used in various life tests, such as medicine, engineering, biology, etc., as they save (overall) test time and cost. In this context, we consider the problem of estimating the unknown xgamma parameter and some survival characteristics, such as reliability and failure rate functions in the presence of adaptive type-II progressive hybrid censored data. For this purpose, the maximum likelihood and Bayesian inferential approaches are used. Using the observed Fisher information under s-normal approximation, different asymptotic confidence intervals for any function of the unknown parameter were constructed. Using the gamma flexible prior, Bayes estimators against the squared-error loss were developed. Two procedures of Bayesian approximations—Lindley’s approximation and Metropolis–Hastings algorithm—were used to carry out the Bayes estimates and to construct the associated credible intervals. An extensive simulation study was implemented to compare the performance of the different methods. To validate the proposed methodologies of inference—two practical studies using datasets that form engineering and chemical fields are discussed.
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11
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Abstract
In this article, we introduce a new extended cosine family of distributions. Some important mathematical and statistical properties are studied, including asymptotic results, a quantile function, series representation of the cumulative distribution and probability density functions, moments, moments of residual life, reliability parameter, and order statistics. Three special members of the family are proposed and discussed, namely, the extended cosine Weibull, extended cosine power, and extended cosine generalized half-logistic distributions. Maximum likelihood, least-square, percentile, and Bayes methods are considered for parameter estimation. Simulation studies are used to assess these methods and show their satisfactory performance. The stress–strength reliability underlying the extended cosine Weibull distribution is discussed. In particular, the stress–strength reliability parameter is estimated via a Bayes method using gamma prior under the square error loss, absolute error loss, maximum a posteriori, general entropy loss, and linear exponential loss functions. In the end, three real applications of the findings are provided for illustration; one of them concerns stress–strength data analyzed by the extended cosine Weibull distribution.
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12
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A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies. ENTROPY 2021; 23:e23111394. [PMID: 34828091 PMCID: PMC8619665 DOI: 10.3390/e23111394] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/13/2021] [Revised: 10/12/2021] [Accepted: 10/15/2021] [Indexed: 11/17/2022]
Abstract
In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength reliability, and Rényi entropy. A particular member, called the exponentiated sine Weibull distribution, is highlighted; we analyze its skewness and kurtosis, moments, quantile function, residual mean and reversed mean residual life functions, order statistics, and extreme value distributions. Maximum likelihood estimation and Bayes estimation under the square error loss function are considered. Simulation studies are used to assess the techniques, and their performance gives satisfactory results as discussed by the mean square error, confidence intervals, and coverage probabilities of the estimates. The stress-strength reliability parameter of the exponentiated sine Weibull model is derived and estimated by the maximum likelihood estimation method. Also, nonparametric bootstrap techniques are used to approximate the confidence interval of the reliability parameter. A simulation is conducted to examine the mean square error, standard deviations, confidence intervals, and coverage probabilities of the reliability parameter. Finally, three real applications of the exponentiated sine Weibull model are provided. One of them considers stress-strength data.
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Çetinkaya Ç. Reliability estimation of the stress–strength model with non-identical jointly type-II censored Weibull component strengths. J STAT COMPUT SIM 2021. [DOI: 10.1080/00949655.2021.1910948] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Çagatay Çetinkaya
- Department of Accounting and Taxation, Bingöl Üniversitesi, Bingöl, Turkey
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La-Ongkaew M, Niwitpong SA, Niwitpong S. Confidence intervals for the difference between the coefficients of variation of Weibull distributions for analyzing wind speed dispersion. PeerJ 2021; 9:e11676. [PMID: 34249509 PMCID: PMC8256813 DOI: 10.7717/peerj.11676] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Accepted: 06/04/2021] [Indexed: 11/20/2022] Open
Abstract
Wind energy is an important renewable energy source for generating electricity that has the potential to replace fossil fuels. Herein, we propose confidence intervals for the difference between the coefficients of variation of Weibull distributions constructed using the concepts of the generalized confidence interval (GCI), Bayesian methods, the method of variance estimates recovery (MOVER) based on Hendricks and Robey's confidence interval, a percentile bootstrap method, and a bootstrap method with standard errors. To analyze their performances, their coverage probabilities and expected lengths were evaluated via Monte Carlo simulation. The simulation results indicate that the coverage probabilities of GCI were greater than or sometimes close to the nominal confidence level. However, when the Weibull shape parameter was small, the Bayesian- highest posterior density interval was preferable. All of the proposed confidence intervals were applied to wind speed data measured at 90-meter wind energy potential stations at various regions in Thailand.
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Affiliation(s)
- Manussaya La-Ongkaew
- Department of Applied Statistics, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand
| | - Sa-Aat Niwitpong
- Department of Applied Statistics, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand
| | - Suparat Niwitpong
- Department of Applied Statistics, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand
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Ma J, Wang L, Tripathi YM, Rastogi MK. Reliability inference for stress-strength model based on inverted exponential Rayleigh distribution under progressive Type-II censored data. COMMUN STAT-SIMUL C 2021. [DOI: 10.1080/03610918.2021.1908552] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Jin’ge Ma
- School of Mathematics and Statistics, Xidian University, Xi’an, P.R. China
| | - Liang Wang
- School of Mathematics, Yunnan Normal University, Kunming, P.R. China
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Muhammad I, Wang X, Li C, Yan M, Chang M. Estimation of the Reliability of a Stress-Strength System from Poisson Half Logistic Distribution. ENTROPY 2020; 22:e22111307. [PMID: 33287072 PMCID: PMC7711519 DOI: 10.3390/e22111307] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/11/2020] [Revised: 11/09/2020] [Accepted: 11/12/2020] [Indexed: 11/16/2022]
Abstract
This paper discussed the estimation of stress-strength reliability parameter R=P(Y<X) based on complete samples when the stress-strength are two independent Poisson half logistic random variables (PHLD). We have addressed the estimation of R in the general case and when the scale parameter is common. The classical and Bayesian estimation (BE) techniques of R are studied. The maximum likelihood estimator (MLE) and its asymptotic distributions are obtained; an approximate asymptotic confidence interval of R is computed using the asymptotic distribution. The non-parametric percentile bootstrap and student’s bootstrap confidence interval of R are discussed. The Bayes estimators of R are computed using a gamma prior and discussed under various loss functions such as the square error loss function (SEL), absolute error loss function (AEL), linear exponential error loss function (LINEX), generalized entropy error loss function (GEL) and maximum a posteriori (MAP). The Metropolis–Hastings algorithm is used to estimate the posterior distributions of the estimators of R. The highest posterior density (HPD) credible interval is constructed based on the SEL. Monte Carlo simulations are used to numerically analyze the performance of the MLE and Bayes estimators, the results were quite satisfactory based on their mean square error (MSE) and confidence interval. Finally, we used two real data studies to demonstrate the performance of the proposed estimation techniques in practice and to illustrate how PHLD is a good candidate in reliability studies.
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Affiliation(s)
- Isyaku Muhammad
- School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China; (I.M.); (M.Y.); (M.C.)
| | - Xingang Wang
- College of Mechanical and Electrical Engineering, Guangdong University of Petrochemical Technology, Maoming 525000, China
- School of Control and Engineering, Northeastern University, Qinhunangdao 066004, China
- Correspondence: (X.W.); (C.L.)
| | - Changyou Li
- School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China; (I.M.); (M.Y.); (M.C.)
- Correspondence: (X.W.); (C.L.)
| | - Mingming Yan
- School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China; (I.M.); (M.Y.); (M.C.)
| | - Miaoxin Chang
- School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China; (I.M.); (M.Y.); (M.C.)
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Kotb MS, Raqab MZ. Estimation of reliability for multi-component stress–strength model based on modified Weibull distribution. Stat Pap (Berl) 2020. [DOI: 10.1007/s00362-020-01213-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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18
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Wang L, Wu K, Tripathi YM, Lodhi C. Reliability analysis of multicomponent stress–strength reliability from a bathtub-shaped distribution. J Appl Stat 2020; 49:122-142. [DOI: 10.1080/02664763.2020.1803808] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Liang Wang
- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, People's Republic of China
- School of Mathematics, Yunnan Normal University, Kunming, People's Republic of China
| | - Ke Wu
- School of Mathematics, Yunnan Normal University, Kunming, People's Republic of China
| | | | - Chandrakant Lodhi
- Department of Mathematics, Indian Institute of Technology Patna, Bihta, India
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19
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Stress–strength reliability models involving generalized gamma and Weibull distributions. INTERNATIONAL JOURNAL OF QUALITY & RELIABILITY MANAGEMENT 2020. [DOI: 10.1108/ijqrm-06-2019-0190] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
PurposeThis paper deals with the estimation of the stress–strength reliability R = P(X < Y), when X and Y follow (1) independent generalized gamma (GG) distributions with only a common shape parameter and (2) independent Weibull random variables with arbitrary scale and shape parameters and generalize the proposal from Kundu and Gupta (2006), Kundu and Raqab (2009) and Ali et al. (2012).Design/methodology/approachFirst, a closed form expression for R is derived under the conditions (1) and (2). Next, sufficient conditions are given for the convergence of the infinite series expansions used to calculate the value of R in case (2). The models GG and Weibull are fitted by maximum likelihood using Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton method. Confidence intervals and standard errors are calculated using bootstrap. For illustration purpose, two real data sets are analyzed and the results are compared with the existing recent results available in the literature.FindingsThe proposed approaches improve the estimation of the R by not using transformations in the data and flexibilize the modeling with Weibull distributions with arbitrary scale and shape parameters.Originality/valueThe proposals of the paper eliminate the misestimation of R caused by subtracting a constant value from the data (Kundu and Raqab, 2009) and treat the estimation of R in a more adequate way by using the Weibull distributions without restrictions in the parameters. The two cases covered generalize a number of distributions and unify a number of stress–strength probability P(X < Y) results available in the literature.
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Hu X, Gui W. Assessing the lifetime performance index with Lomax distribution based on progressive type I interval censored sample. J Appl Stat 2019; 47:1757-1775. [DOI: 10.1080/02664763.2019.1693523] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Xuehua Hu
- Department of Mathematics, Beijing Jiaotong University, Beijing, People's Republic of China
| | - Wenhao Gui
- Department of Mathematics, Beijing Jiaotong University, Beijing, People's Republic of China
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21
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Chaturvedi A, Pathak A, Kumar N. Statistical inferences for the reliability functions in the proportional hazard rate models based on progressive type-II right censoring. J STAT COMPUT SIM 2019. [DOI: 10.1080/00949655.2019.1614182] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
| | - Anupam Pathak
- Department of Statistics, Ramjas College, University of Delhi, Delhi, India
| | - Narendra Kumar
- Department of Statistics, University of Delhi, Delhi, India
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23
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Condino F, Domma F, Latorre G. Likelihood and Bayesian estimation of $$P(Y{<}X)$$ P ( Y < X ) using lower record values from a proportional reversed hazard family. Stat Pap (Berl) 2016. [DOI: 10.1007/s00362-016-0772-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Affiliation(s)
- Bing Xing Wang
- Department of Statistics, Zhejiang Gongshang University, Hangzhou, China
| | - Xiu Kun Wang
- Department of Statistics, Zhejiang Gongshang University, Hangzhou, China
| | - Keming Yu
- Department of Mathematics, Brunel University, London, UK
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25
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Mokhlis NA, Ibrahim EJ, Gharieb DM. Stress−strength reliability with general form distributions. COMMUN STAT-THEOR M 2016. [DOI: 10.1080/03610926.2015.1014110] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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26
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Wu JW, Lee WC. Statistical Testing Procedure for Assessing The Quality Performance of Exponentiated Weibull Products with The Lower Record Values. JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS 2015. [DOI: 10.1080/09720510.2014.961760] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Ahmed EA. Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach. J Appl Stat 2013. [DOI: 10.1080/02664763.2013.847907] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Soliman AA, Abd-Ellah AH, Abou-Elheggag NA, Ahmed EA. Reliability estimation in stress–strength models: an MCMC approach. STATISTICS-ABINGDON 2013. [DOI: 10.1080/02331888.2011.637629] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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Li Y, Chen J, Liu J, Zhang L, Wang W, Zhang S. Estimation of the reliability of all-ceramic crowns using finite element models and the stress-strength interference theory. Comput Biol Med 2013; 43:1214-20. [PMID: 23930816 DOI: 10.1016/j.compbiomed.2013.06.007] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2010] [Revised: 06/05/2013] [Accepted: 06/07/2013] [Indexed: 11/29/2022]
Abstract
The reliability of all-ceramic crowns is of concern to both patients and doctors. This study introduces a new methodology for quantifying the reliability of all-ceramic crowns based on the stress-strength interference theory and finite element models. The variables selected for the reliability analysis include the magnitude of the occlusal contact area, the occlusal load and the residual thermal stress. The calculated reliabilities of crowns under different loading conditions showed that too small occlusal contact areas or too great a difference of the thermal coefficient between veneer and core layer led to high failure possibilities. There results were consistent with many previous reports. Therefore, the methodology is shown to be a valuable method for analyzing the reliabilities of the restorations in the complicated oral environment.
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Affiliation(s)
- Yan Li
- Department of Prosthodontics, School of Stomatology, The Fourth Military Medical University, 145 West Changle Road, Xi'an, PR China
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Ye RD, Ma TF, Luo K. Inferences on the reliability in balanced and unbalanced one-way random models. J STAT COMPUT SIM 2012. [DOI: 10.1080/00949655.2012.741598] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Min X, Sun D. A matching prior based on the modified profile likelihood in a generalized Weibull stress-strength model. CAN J STAT 2012. [DOI: 10.1002/cjs.11164] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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Xiao X, Hu Q, Yu D, Xie M. Study of an imputation algorithm for the analysis of interval-censored data. J STAT COMPUT SIM 2012. [DOI: 10.1080/00949655.2012.716441] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Domma F, Giordano S. A copula-based approach to account for dependence in stress-strength models. Stat Pap (Berl) 2012. [DOI: 10.1007/s00362-012-0463-0] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Domma F, Giordano S. A stress–strength model with dependent variables to measure household financial fragility. STAT METHOD APPL-GER 2012. [DOI: 10.1007/s10260-012-0192-5] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Barbiero A. Confidence Intervals for Reliability of Stress-Strength Models in the Normal Case. COMMUN STAT-SIMUL C 2011. [DOI: 10.1080/03610918.2011.560728] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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