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The purpose of this paper is to deal with the Bayesian and non-Bayesian estimation methods of multicomponent stress-strength reliability by assuming the Chen distribution.

The reliability of a multicomponent stress-strength system is obtained by the maximum likelihood (MLE) and Bayesian methods and the results are compared by using MCMC technique for both small and large samples.

The simulation study shows that Bayes estimates based on γ prior with absence of prior information performs little better than the MLE with regard to both biases and mean squared errors. The Bayes credible intervals for reliability are also shorter length with competitive coverage percentages than the condence intervals. Further, the coverage probability is quite close to the nominal value in all sets of parameters when both sample sizes n and m increases.

The lifetime distributions used in reliability analysis as exponential, γ, lognormal and Weibull only exhibit monotonically increasing, decreasing or constant hazard rates. However, in many applications in reliability and survival analysis, the most realistic hazard rate is bathtub-shaped found in the Chen distribution. Therefore, the authors have studied the multicomponent stress-strength reliability under the Chen distribution by comparing the MLE and Bayes estimators.

The step-stress accelerated test is the most appropriate statistical method to obtain information about the reliability of new products faster than would be possible if the product was left to fail in normal use. This paper presents the multiple step-stress accelerated life test using type-II censored data and assuming a cumulative exposure model. The authors propose a Bayesian inference with the lifetimes of test item under gamma distribution. The choice of the loss function is an essential part in the Bayesian estimation problems. Therefore, the Bayesian estimators for the parameters are obtained based on different loss functions and a comparison with the usual maximum likelihood (MLE) approach is carried out. Finally, an example is presented to illustrate the proposed procedure in this paper.

A Bayesian inference is performed and the parameter estimators are obtained under symmetric and asymmetric loss functions. A sensitivity analysis of these Bayes and MLE estimators are presented by Monte Carlo simulation to verify if the Bayesian analysis is performed better.

The authors demonstrated that Bayesian estimators give better results than MLE with respect to MSE and bias. The authors also consider three types of loss functions and they show that the most dominant estimator that had the smallest MSE and bias is the Bayesian under general entropy loss function followed closely by the Linex loss function. In this case, the use of a symmetric loss function as the SELF is inappropriate for the SSALT mainly with small data.

Most of papers proposed in the literature present the estimation of SSALT through the MLE. In this paper, the authors developed a Bayesian analysis for the SSALT and discuss the procedures to obtain the Bayes estimators under symmetric and asymmetric loss functions. The choice of the loss function is an essential part in the Bayesian estimation problems.

The purpose of this paper is to provide a new method to estimate the reliability of series system by using copula functions. This problem is of great interest in industrial and engineering applications.

The authors introduce copula functions and consider a Bayesian analysis for the proposed models with application to the simulated data.

The use of copula functions for modeling the bivariate distribution could be a good alternative to estimate the reliability of a two components series system. From the results of this study, the authors observe that they get accurate Bayesian inferences for the reliability function considering large samples sizes. The Bayesian parametric models proposed also allow the assessment of system reliability for multicomponent systems simultaneously.

Usually, the studies of systems reliability engineering assume independence among the component lifetimes. In the approach the authors consider a dependence structure. Using standard classical inference methods based on asymptotical normality of the maximum likelihood estimators for the parameters the authors could have great computational difficulties and possibly, not accurate inference results, which there is not found in the approach.