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In this paper, the stress–strength reliability $ R_{s,k} $ R s , k of a multicomponent s-out-of-k system for exponentiated Gumbel distribution is considered. An s-out-of-k system means a system with total k components and the system can survive only when atleast s of the total components function properly. The ability of the system to overcome the experiencing stress with its strength is termed as its stress–strengh reliability. The maximum likelihood estimator and Bayes estimator for $ R_{s,k} $ R s , k are obtained. The Bayes estimators are obtained using Markov chain Monte Carlo(MCMC) method under both symmetric and asymmetric loss functions. The loss functions we considered are squared error loss function, LINEX loss function and entropy loss function. The asymptotic, bootstrap and highest posterior density(HPD) confidence intervals for $ R_{s,k} $ R s , k are also obtained. A simulation study is conducted for evaluating the efficiency of the estimators derived in this paper. Real data sets are also considered for illustration. [ABSTRACT FROM AUTHOR]

This paper investigates the E-Bayesian and hierarchical Bayesian estimations of shape parameter and reliability function of Kumaraswamy generalized distribution based on upper record values. The classical estimation method is utilized to deduce the maximum likelihood estimation of unknown parameter and reliability function. Bayesian estimates are derived by using conjugate Gamma prior distributions under quadratic and general entropy loss functions. Furthermore, assuming that hyper-hyperparameters obey three prior distributions, the E-Bayesian estimates of unknown parameters and reliability functions are obtained. The hierarchical Bayesian estimates are obtained by using hierarchical prior distributions. We also explore some characteristics and size relationships of E-Bayesian and hierarchical Bayesian estimations. The performance of E-Bayesian, Hierarchical Bayesian, Bayesian, and maximum likelihood estimations is compared based on the minimum mean square error criterion. Finally, the proposed estimation methods are applied to evaluate the reliability of the specimen under ultrasonic fatigue testing, and the results align with their structures and profiles. [ABSTRACT FROM AUTHOR]

This paper proves that in mixed linear model, the analysis of variance estimation (ANOVAE), the minimum norm quadratic unbiased estimation (MINQUE), the spectral decomposition estimation (SDE) and the restricted maximum likelihood estimation (RMLE) of variance components are the same under some conditions. Based on this result, we construct a linear Bayes estimation (LBE) for the parameter vector consisting of variance components and establish its superiorities. Numerical computations and an illustration show that the LBE is comparable to Lindley's approximation, Tierney and Kadane's approximation and the usual Bayes estimation (UBE) obtained by the MCMC method and easy to use as well. [ABSTRACT FROM AUTHOR]

The linear exponential distribution is a generalization of the exponential and Rayleigh distributions. This distribution is one of the best models to fit data with increasing failure rate (IFR). But it does not provide a reasonable fit for modeling data with decreasing failure rate (DFR) and bathtub shaped failure rate (BTFR). To overcome this drawback, we propose a new record-based transmuted generalized linear exponential (RTGLE) distribution by using the technique of Balakrishnan and He. The family of RTGLE distributions is more flexible to fit the data sets with IFR, DFR, and BTFR, and also generalizes several well-known models as well as some new record-based transmuted models. This paper aims to study the statistical properties of RTGLE distribution, like, the shape of the probability density function and hazard function, quantile function and its applications, moments and its generating function, order and record statistics, Rényi entropy. The maximum likelihood estimators, least squares and weighted least squares estimators, Anderson-Darling estimators, Cramér-von Mises estimators of the unknown parameters are constructed and their biases and mean squared errors are reported via Monte Carlo simulation study. Finally, the real data sets illustrate the goodness of fit and applicability of the proposed distribution; hence, suitable recommendations are forwarded. [ABSTRACT FROM AUTHOR]

This paper deals with statistical inference for lifetime data in presence of imperfect maintenance. For the maintenance model, the Sheu and Griffith model is considered. The lifetime distribution belongs to exponential distribution class. The maximum likelihood estimation procedure of the model parameters is discussed, and confidence intervals are provided using the asymptotic likelihood theory and bootstrap approach. Based on conjugate and discrete priors, Bayesian estimators of the model parameters are developed under symmetric and asymmetric loss functions. The proposed methodologies are applied to simulated data and sensitivity analysis to different parameters and data characteristics is carried out. The effect of model misspecification is also assessed within this class of distributions through a Monte Carlo simulation study. Finally, two datasets are analyzed for demonstrative aims. [ABSTRACT FROM AUTHOR]

In this paper, we focus on Bayesian estimation of the parameters in the geometric process (GP) in which the first occurrence time of an event is assumed to have Weibull distribution. The Bayesian estimators are derived based on both symmetric (Squared Error) and asymmetric (General Entropy, LINEX) loss functions. Since the Bayesian estimators of unknown parameters cannot be obtained analytically, Lindley's approximation and the Markov Chain Monte Carlo (MCMC) methods are applied to compute the Bayesian estimates. Furthermore, by using the MCMC methods, credible intervals of the parameters are constructed. Maximum likelihood (ML) estimators are also derived for unknown parameters. The confidence intervals of the parameters are obtained based on an asymptotic distribution of ML estimators. Moreover, the performances of the proposed Bayesian estimators are compared with the corresponding ML, modified moment and modified maximum likelihood estimators through an extensive simulation study. Finally, analyses of two different real data sets are presented for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, the longitudinal data analysis is used to interpret the balanced Bühlmann credibility model with correlation risk, and the homogeneous credibility estimator is derived. We obtain the restricted maximum likelihood estimators (RMLE) for the structural parameters involved in the credibility factor and show that they are unbiased. In addition, the linear Bayes method is employed to estimate the structural parameters, and the proposed linear Bayes estimators (LBE) appear to outperform RMLE in terms of the mean squared error matrix (MSEM) criterion. Simulation studies show that the proposed LBE performs well. [ABSTRACT FROM AUTHOR]

In this paper, the Bayesian and non-Bayesian estimation of $$\psi = P(X \gt Y)$$ ψ = P (X > Y) based on the progressively first-failure censored data is considered. The $$X$$ X and $$Y$$ Y are strength and stress random variables and follow the Topp-Leone distributions, respectively. The maximum likelihood and Bayes estimators of $$\psi $$ ψ are derived. The Bayes estimators under generalized entropy loss function are computed using Lindley's approximation and Gibbs sampling methods. Different interval estimates like asymptotic, bootstrap confidence, Bayesian credible, and highest posterior density credible intervals of $$\psi $$ ψ are constructed. Furthermore, a Monte Carlo numerical study is conducted to check the performance of various estimators developed. Finally, an application of algorithm real data is considered for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper a new bivariate lifetime distribution is introduced. Its marginal distribution functions follow two-parameter Chen distribution, which has a bathtub shaped or increasing hazard rate functions. The proposed distribution, which we call a bivariate Chen distribution (BCD), is of Marshall-Olkin type and it is a singular distribution. Several properties of this proposed distribution are discussed. The BCD distribution has four unknown parameters. The maximum likelihood (ML) method and the Bayes techniques are used to estimate the unknown parameters. The maximum likelihood estimators or the Bayes estimators cannot be obtained in closed form. Numerical methods have been used in both cases. A real data set is analyzed using the proposed distribution for illustrative and comparison purposes. An application to dependent competing risks data is discussed, and finally we have extended the BCD to the multivariate case. [ABSTRACT FROM AUTHOR]

The present communication develops the tools for estimation and prediction of the Burr-III distribution under unified progressive hybrid censoring scheme. The maximum likelihood estimates of model parameters are obtained. It is shown that the maximum likelihood estimates exist uniquely. Expectation maximization and stochastic expectation maximization methods are employed to compute the point estimates of unknown parameters. Based on the asymptotic distribution of the maximum likelihood estimators, approximate confidence intervals are proposed. In addition, the bootstrap confidence intervals are constructed. Furthermore, the Bayes estimates are derived with respect to squared error and LINEX loss functions. To compute the approximate Bayes estimates, Metropolis–Hastings algorithm is adopted. The highest posterior density credible intervals are obtained. Further, maximum a posteriori estimates of the model parameters are computed. The Bayesian predictive point, as well as interval estimates, are proposed. A Monte Carlo simulation study is employed in order to evaluate the performance of the proposed statistical procedures. Finally, two real data sets are considered and analysed to illustrate the methodologies established in this paper. [ABSTRACT FROM AUTHOR]

This study focuses on the estimation of the two unknown parameters of Chen distribution, characterized by a bathtub-shaped hazard rate function, within an improved adaptive type-II progressive censored data framework. Maximum likelihood estimation is proposed for the two parameters, and the establishment of approximate confidence intervals is based on asymptotic normality. Bayesian estimation is also conducted under both symmetric and asymmetric loss functions, utilizing the proposed importance sampling and Metropolis–Hastings algorithm. Lastly, the performance of various estimation methods is evaluated through Monte Carlo simulation experiments, and the proposed estimation approach is illustrated using a real dataset. [ABSTRACT FROM AUTHOR]

Inverse Weibull (IW) distribution is widely used due to its non-monotonic hazard function. For the IW distribution, existing research on statistical inference has mostly focused on censored data, but there has been no study on multiply Type-I censoring until now as far as we know. The multiple Type-I censoring, acted as an extended form of Type-I censoring, is frequently encountered in industry and medicine research, which also needs to be paid attention. Thus, this study conducts detailed analyses on the reliability of IW distribution with multiply Type-I censored data, including point estimation and confidence interval (CI) construction. Four methods, including the maximum likelihood estimation (MLE), least square estimation (LSE), and two Bayesian estimations, namely MCMC and Lindley, are adopted in point estimation. Results show that the Lindley method performs best with small mission times, while MLE is optimal for large mission times. Specifically, for the CIs construction, we proposed a pivotal quantity based on LSE to construct the CIs of reliability and compare it with two popular methods, Fisher information matrix (FIM) derivation and MCMC algorithm. Our proposed method shows competitive performance as the MCMC and outperforms FIM. Finally, those estimation methods are applied to an example for illustration. [ABSTRACT FROM AUTHOR]