Inferences for Stress-Strength Reliability Model in the Presence of Partially Accelerated Life Test to Its Strength Variable

EL‐Sagheer, Rashad M.; Tolba, Ahlam H.; Jawa, Taghreed M.; Sayed-Ahmed, Neveen

doi:10.1155/2022/4710536

Cited by 10 publications

(9 citation statements)

References 37 publications

(31 reference statements)

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“…e Markov Chain Monte Carlo (MCMC) method is one of the most important technique in Bayesian paradigm. e MCMC method is the main computational tools which have been broadly used in Bayesian inference [53][54][55][56][57]. In MCMC algorithm, we have summarized the posterior distribution without requiring the given normalized constant.…”

Section: Markov Chain Monte Carlo (Mcmc) Methodmentioning

confidence: 99%

Estimation for Akshaya Failure Model with Competing Risks under Progressive Censoring Scheme with Analyzing of Thymic Lymphoma of Mice Application

Abushal

Kumar²,

Muse³

et al. 2022

Complexity

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In several experiments of survival analysis, the cause of death or failure of any subject may be characterized by more than one cause. Since the cause of failure may be dependent or independent, in this work, we discuss the competing risk lifetime model under progressive type-II censored where the removal follows a binomial distribution. We consider the Akshaya lifetime failure model under independent causes and the number of subjects removed at every failure time when the removal follows the binomial distribution with known parameters. The classical and Bayesian approaches are used to account for the point and interval estimation procedures for parameters and parametric functions. The Bayes estimate is obtained by using the Markov Chain Monte Carlo (MCMC) method under symmetric and asymmetric loss functions. We apply the Metropolis–Hasting algorithm to generate MCMC samples from the posterior density function. A simulated data set is applied to diagnose the performance of the two techniques applied here. The data represented the survival times of mice kept in a conventional germ-free environment, all of which were exposed to a fixed dose of radiation at the age of 5 to 6 weeks, which was used as a practice for the model discussed. There are 3 causes of death. In group 1, we considered thymic lymphoma to be the first cause and other causes to be the second. On the base of mice data, the survival mean time (cumulative incidence function) of mice of the second cause is higher than the first cause.

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Section: Markov Chain Monte Carlo (Mcmc) Methodmentioning

confidence: 99%

Estimation for Akshaya Failure Model with Competing Risks under Progressive Censoring Scheme with Analyzing of Thymic Lymphoma of Mice Application

Abushal

Kumar²,

Muse³

et al. 2022

Complexity

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“…The posterior distribution of the parameters α, β and λ denoted by π * (α, β, λ | data) up to proportionality can be obtained by combining the likelihood function Equation (15) with the prior via Bayes' theorem, and it can be written as…”

Section: Bayesian Estimationmentioning

confidence: 99%

“…For the inverse Rayleigh distribution, inference of a fuzzy reliability model and fuzzy reliability estimation for Frechet distribution by using simulation is presented; see [12,13], respectively. In addition, reliability estimation in Rayleigh distribution based on fuzzy lifetime data has been studied by [14,15], introducing inferences for the stress-strength reliability model's strength variable in the presence of a partially accelerated life test.…”

Section: Introductionmentioning

confidence: 99%

Inference of Reliability Analysis for Type II Half Logistic Weibull Distribution with Application of Bladder Cancer

Mohamed

Tolba

Almetwally

et al. 2022

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The estimation of the unknown parameters of Type II Half Logistic Weibull (TIIHLW) distribution was analyzed in this paper. The maximum likelihood and Bayes methods are used as estimation methods. These estimators are used to estimate the fuzzy reliability function and to choose the best estimator of the fuzzy reliability function by comparing the mean square error (MSE). The simulation’s results showed that fuzziness is better than reality for all sample sizes, and fuzzy reliability at Bayes predicted estimates is better than the maximum likelihood technique. It produces the lowest average MSE until a sample size of n = 50 is obtained. A simulated data set is applied to diagnose the performance of the two techniques applied here. A real data set is used as a practice for the model discussed and developed the maximum likelihood estimate alternative model of TIIHLW as Topp Leone inverted Kumaraswamy, modified Kies inverted Topp–Leone, Kumaraswamy Weibull–Weibull, Marshall–Olkin alpha power inverse Weibull, and odd Weibull inverted Topp–Leone. We conclude that the TIIHLW is the best distribution fit for this data.

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“…Similarly, the estimate of the SSRP for generalised Pareto distribution was described by [4]. Although the El-Sagheer et al [5] discussed the inferences for the SSRP when its strength variable is subjected to a partially accelerated life test. The analyze of the SSRP for the generalised logistic distribution has been investigated by Asgharzadeh et al [6].…”

Section: Introductionmentioning

confidence: 99%

Statistical inference for stress-strength reliability using inverse Lomax lifetime distribution with mechanical engineering applications

et al. 2022

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The inverse Lomax distribution has been extensively used in many disciplines, including stochastic modelling, economics, actuarial sciences, and life testing. It is among the most recognizable lifetime models. The purpose of this research is to look into a new and important aspect of the inverse Lomax distribution: the calculation of the fuzzy stress-strength reliability parameter RF = P(Y < X), as?suming X and Y are random independent variables that follow the inverse Lomax probability distribution. The properties of structural for the proposed reliability model are studied along with the Bayesian estimation methods, maximum product of the spacing and maximum likelihood. Extensive simulation studies are achieved to explore the performance of the various estimates. Subsequently, two sets of real data are considered to highlight the practicability of the model.

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Inferences for Stress-Strength Reliability Model in the Presence of Partially Accelerated Life Test to Its Strength Variable

Cited by 10 publications

References 37 publications

Estimation for Akshaya Failure Model with Competing Risks under Progressive Censoring Scheme with Analyzing of Thymic Lymphoma of Mice Application

Estimation for Akshaya Failure Model with Competing Risks under Progressive Censoring Scheme with Analyzing of Thymic Lymphoma of Mice Application

Inference of Reliability Analysis for Type II Half Logistic Weibull Distribution with Application of Bladder Cancer

Statistical inference for stress-strength reliability using inverse Lomax lifetime distribution with mechanical engineering applications

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