Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling

Yousef, Manal M.; Hassan, Amal S.; Al-Nefaie, Abdullah H.; Almetwally, Ehab M.; Almongy, Hisham M.

doi:10.3390/math10173122

Cited by 14 publications

(7 citation statements)

References 44 publications

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“…Te study of stressstrength reliability in light of the ranked set sampling (RSS) technique has recently captured the interest of multiple writers due to its application in a variety of felds. Terefore, in our upcoming work, we want to address the problem of stress-strength estimation for a certain distribution in the class using the RSS method [26][27][28], and also, for applications of lifetime data [29][30][31].…”

Section: Discussionmentioning

confidence: 99%

A Compound Class of Unit Burr XII Model: Theory, Estimation, Fuzzy, and Application

Zayed

Hassan

Almetwally

et al. 2023

Scientific Programming

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The current research offers an enhanced three-parameter lifetime model that combines the unit Burr XII distribution with a power series distribution. The novel class of distribution is named the unit Burr XII power series (UBXIIPS). This compounding technique allows for the production of flexible distributions with strong physical meanings in domains such as biology and engineering. The UBXIIPS class includes the unit Burr XII Poisson (UBXIIP) distribution, the unit Burr XII binomial distribution, the unit Burr XII geometric distribution, and the unit Burr XII negative binomial distribution. The statistical properties of the class include formulas for the density and cumulative distribution functions, and limiting behaviour, moments and incomplete moments, entropy measures, and quantile function are provided. For estimating population parameters and fuzzy reliability for the UBXIIP model, maximum likelihood and Bayesian approaches are studied by the Metropolis–Hastings algorithm. For maximum likelihood estimators, the length of asymptotic confidence intervals is specified, whereas, for Bayesian estimators, the length of credible confidence intervals is assigned. A simulation investigation of the UBXIIP model was established to evaluate the performance of suggested estimates. In addition, the UBXIIP distribution is explored using real-world data. The UBXIIP distribution appears to offer some benefits in understanding lifetime data when compared to unit Weibull, beta, Kumaraswamy, Kumaraswamy Kumaraswamy, Marshall-Olkin Kumaraswamy, and Topp–Leone Weibull Lomax distributions.

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Section: Discussionmentioning

confidence: 99%

A Compound Class of Unit Burr XII Model: Theory, Estimation, Fuzzy, and Application

Zayed

Hassan

Almetwally

et al. 2023

Scientific Programming

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“…It should be noted that the parameters of the hybrid deteriorating function ( o , κ o , υ o , ψ o , p , κ p , υ p , and ψ p ) can be calculated by applying Equations ( 19)- (22). After getting the parameters' value, the expected failure numbers, E 27) and (28), and their form are as follows:…”

Section: Analysis By the Natural Conjugate Probability Distributionmentioning

confidence: 99%

“…They also compared the performance between maximum likelihood estimators and Bayesian estimators. Liu et al [28] applied a Bayesian estimation method to evaluate products' reliability. This method can achieve both point and confidence interval estimation for the critical parameters.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Statistical Method Enhance the Decision-Making for Imperfect Preventive Maintenance with a Hybrid Competing Failure Mode

Fang

Hsu

Liu

2022

Axioms

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The study aims to provide a Bayesian statistical method with natural conjugate for facilities’ preventive maintenance scheduling related to the hybrid competing failure mode. An effective preventive maintenance strategy not only can improve a system’s health condition but also can increase a system’s efficiency, and therefore a firm needs to make an appropriate strategy for increasing the utilization of a system with reasonable costs. In the last decades, preventive maintenance issues of deteriorating systems have been studied in the related literature, and hundreds of maintenance/replacement models have been created. However, few studies focused on the issue of hybrid deteriorating systems which are composed of maintainable and non-maintainable failure modes. Moreover, due to the situations of the scarcity of historical failure data, the related analyses of preventive maintenance would be difficult to perform. Based on the above two reasons, this study proposed a Bayesian statistical method to deal with such preventive maintenance problems. Non-homogeneous Poisson processes (NHPP) with power law failure intensity functions are employed to describe the system’s deterioration behavior. Accordingly, the study can provide useful ways to help managers to make effective decisions for preventive maintenance. To apply the proposed models in actual cases, the study provides solution algorithms and a computerized architecture design for decision-makers to realize the computerization of decision-making.

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“…The estimation of an MSSR from a generalised inverted exponential distribution using RSS was discussed in [30]. Reference [31] looked at RSSbased Bayesian system reliability estimation for the inverted Topp-Leone distribution.…”

Section: Introductionmentioning

confidence: 99%

Estimation Study of Multicomponent Stress-Strength Reliability Using Advanced Sampling Approach

Hassan

Elshaarawy

Nagy

2024

Gazi University Journal of Science

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In this study, we analyze a multicomponent system with v independent and identical strength components X1, …, Xv and each of these components is exposed to a common random stress Y. The system is considered to be operating only if at least u out of v (1 u  v) strength variables exceeds the random stress. The estimate of system reliability is investigated, assuming strength and stress random variables follow the exponentiated exponential distribution with different shape parameters. The maximum likelihood estimator for system reliability is derived from ranked set sampling (RSS), neoteric RSS (NRSS) and median RSS (MRSS). Some accuracy measurements, such as mean squared errors and efficiencies, are used to examine the behaviour of various estimators. Simulation studies demonstrate that the NRSS scheme's reliability estimates are chosen above those of the RSS and MRSS schemes in the majority of situations. Theoretical research is explained through real data analysis

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Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling

Cited by 14 publications

References 44 publications

A Compound Class of Unit Burr XII Model: Theory, Estimation, Fuzzy, and Application

A Compound Class of Unit Burr XII Model: Theory, Estimation, Fuzzy, and Application

Bayesian Statistical Method Enhance the Decision-Making for Imperfect Preventive Maintenance with a Hybrid Competing Failure Mode

Estimation Study of Multicomponent Stress-Strength Reliability Using Advanced Sampling Approach

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