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Comparative life tests of a life product have received considerable attention in the past few years for measuring the relative merits of a product in competing duration. In this paper, we are adopting the problem of estimation and prediction of Rayleigh lifetime distributions under joint Type-I censoring scheme. The point and interval estimation is formulated with maximum likelihood and the Bayes methods for the unknown parameters. Also, Bayesian approach is applied in viewpoint both point and interval prediction. The results of estimation and prediction are discussed through analysis the set of real data and bulding Monte-Carlo simulation studies. Finally, we built a numerical discussion of the most important results and future recommendations. [ABSTRACT FROM AUTHOR]

This paper discusses inferential approaches for the problem of constant-stress accelerated life testing when the failure data are progressive type-I interval censored. Both frequentist and Bayesian estimations are carried out under the assumption that the log-normal location parameter is nonconstant and follows a log-linear life-stress model. The confidence intervals of unknown parameters are also constructed based on asymptotic theory and Bayesian techniques. An analysis of a real data set is combined with a Monte Carlo simulation to provide a thorough assessment of the proposed methods. [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, classical and Bayesian estimation for the parameters and the reliability function for the generalized logarithmic transformation exponential (GLTE) distribution has been proposed when the life-times are progressively censored. The maximum likelihood estimator of unknown parameters and their corresponding reliability function are obtained under the classical setup. The Bayes estimators are obtained for symmetric (squared error) and asymmetric (LINEX and general entropy) loss functions. This was achieved by considering discrete prior for the scale parameter and conditional gamma prior for the shape parameter. Interval estimation of the unknown parameters and reliability function for classical and Bayesian schemes is also considered. The performances of various derived estimators are recorded using simulation study for different sample sizes and progressive censoring schemes. Finally, the COVID-19 mortality data sets are provided to illustrate the computation of various estimators. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the problem of constant-stress accelerated life test when the failure data are progressive type-I interval censored. Both classical and Bayesian inferential approaches of the distribution parameters and reliability characteristics are discussed. In the classical scenario, the maximum likelihood estimates are approximated using the EM algorithm and the mid-point approximation method. Furthermore, the model's parameters are estimated by method of moments. Next in the Bayesian framework, the point estimates of unknown parameters are obtained using Tierney-Kadane's technique and Markov Chain Monte Carlo (MCMC) method. In addition, both approximate and credible confidence intervals (CIs) of the estimators are constructed. For illustration purpose, a Monte Carlo simulation is conducted to investigate the performance of the proposed estimators and a real data set is analysed. [ABSTRACT FROM AUTHOR]

There are many situations in reliability or medical studies, where items may fail due to one of several causes. Further, censoring is unavoidable in any life testing. In this paper attempts to estimate problem for the competing risks model where the data are adaptive type-II progressive hybrid censored scheme and follow the inverse Weibull distribution. In this regards, we obtain the maximum likelihood estimation of the parameters and the asymptotic confidence intervals for the unknown parameters. Further, Bayes estimates of the parameters which obtained based on squared error and LINEX loss functions under the assumptions of independent gamma priors. For Bayesian estimation, we take advantage of Markov Chain Monte Carlo techniques by applying the Metropolis-Hasting algorithm under the square error and LINEX loss function to derive Bayesian estimators. Finally, two data sets with a Monte Carlo simulation study and a real data set of the electronic applications are analyzed for illustrative purposes. [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]

In this paper, based on an adaptive Type-II progressive censoring scheme, estimation of flexible Weibull extension-Burr XII distribution is discussed. Maximum likelihood estimation and asymptotic confidence intervals of the unknown parameters are obtained. The adaptive Metropolis (AM) method is applied to carry out a Bayesian estimation procedure under symmetric and asymmetric loss functions and calculate the credible intervals. A simulation study is carried out to assess the performance of the estimators. Finally, a real life data set is used for illustration purpose. [ABSTRACT FROM AUTHOR]

Joint Type-I progressive hybrid censoring scheme has been proposed to terminate the life-test experiment at maximum time that the experimenter can afford to continue. This article deals with the problem of estimating the two Weibull population parameters with the same shape parameter under joint Type-I progressively hybrid censoring scheme on the two samples using maximum likelihood and Bayesian inferential approaches. Using Fisher information matrix, the two-sided approximate confidence intervals of the unknown quantities are constructed. Under the assumption of independent gamma priors, the Bayes estimators are developed using squared-error loss function. Since the Bayes estimators cannot be expressed in closed forms, hence, Gibbs within Metropolis-Hastings algorithm is proposed to carry out the Bayes estimates and also to construct the corresponding credible intervals. Moreover, some popular joint censoring plans are generalized and can be obtained as a special cases from our results. Monte Carlo simulations are performed to assess the performance of the proposed estimators. To determine the optimal progressive censoring plan, two different optimality criteria are considered. Finally, to show the applicability of the proposed methods in real phenomenon, a real-life data set is analyzed. [ABSTRACT FROM AUTHOR]

When conducting reliability studies, the progressive first-failure censoring (PFFC) method is useful in situations in which the units of the life testing experiment are separated into groups consisting of k units each with the intention of seeing only the first failure in each group. Using progressive first-failure censored samples, the statistical inference for the parameters, reliability, and hazard functions of the extended Rayleigh distribution (ERD) are investigated in this study. The asymptotic normality theory of maximum likelihood estimates (MLEs) is used in order to acquire the maximum likelihood estimates (MLEs) together with the asymptotic confidence intervals (Asym. CIs). Bayesian estimates (BEs) of the parameters and the reliability functions under different loss functions may be produced by using independent gamma informative priors and non-informative priors. The Markov chain Monte Carlo (MCMC) approach is used so that Bayesian computations are performed with ease. In addition, the MCMC method is used in order to create credible intervals (Cred. CIs) for the parameters, which may be used for either informative or non-informative priors. Additionally, computations for the reliability functions are carried out. A Monte Carlo simulation study is carried out in order to provide a comparison of the behaviour of the different estimations that were created for this work. At last, an actual data set is dissected for the purpose of providing an example. [ABSTRACT FROM AUTHOR]

A new life performance index is proposed for evaluating the quality of lifetime products. The maximum likelihood estimation method and the Bayesian approaches using informative and non-informative prior distributions are utilized to infer the parameters of the Weibull distribution and the proposed new life performance index under a Type-I hybrid censoring scheme. Monte Carlo simulation results show that two Bayesian approaches outperform the maximum likelihood estimation method in terms of the measures of relative bias, relative mean square error, and coverage probability for the point and confidence interval estimators, respectively. The Bayesian approach using a non-informative prior distribution is recommended if the knowledge of setting up the hyper-parameters in the informative prior distribution is not available. Two real data sets are provided for illustration. [ABSTRACT FROM AUTHOR]

In this article, the problems of point and interval estimation for the associated parameters, along with reliability function (r(x)) and the hazard rate function (h(x)) of the inverse Gompertz distribution, are considered using a unified hybrid censoring scheme. In the case of point estimation, some classical estimators, such as the maximum likelihood estimator (MLE) and the maximum product spacing estimator (MPSE), are derived. Further, Bayes estimators are considered with respect to a suitable prior for the associated parameters under the balanced loss functions( balanced Linex loss function and balanced general entropy loss function). The asymptotic confidence intervals using the MLEs and MPSEs of the parameters are derived. Furthermore, the equal-tailed and the highest posterior density credible intervals are derived using the posterior samples. The mean squared errors are used to compare the point estimators, whereas the interval estimators are compared through their coverage probability and average lengths. Finally, a real data set is taken for application purposes. [ABSTRACT FROM AUTHOR]

In this article, the problem of reliability inference of multicomponent stress–strength (MSS) from Kumaraswamy-G (Kw-G) family of distributions under progressive first failure censoring is considered. The reliability of MSS is considered when both the stress and strength variables follow Kw-G distributions with different first shape parameters and common second shape parameter. The maximum likelihood (ML) and Bayes estimators of reliability are derived when all the parameters are unknown. Also, the ML, uniformly minimum variance unbiased and Bayes estimators of reliability are derived in case of common shape parameter is known. The Bayesian credible and HPD credible intervals of reliability are developed using Gibbs sampling method. The performance of various estimates developed are discussed by a Monte Carlo simulation study. At last, two real life examples are considered for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new three-parameter distribution called the extended inverse-Gompertz (EIGo) distribution. The implementation of three parameters provides a good reconstruction for some applications. The EIGo distribution can be seen as an extension of the inverted exponential, inverse Gompertz, and generalized inverted exponential distributions. Its failure rate function has an upside-down bathtub shape. Various statistical and reliability properties of the EIGo distribution are discussed. The model parameters are estimated by the maximum-likelihood and Bayesian methods under Type-II censored samples, where the parameters are explained using gamma priors. The performance of the proposed approaches is examined using simulation results. Finally, two real-life engineering data sets are analyzed to illustrate the applicability of the EIGo distribution, showing that it provides better fits than competing inverted models such as inverse-Gompertz, inverse-Weibull, inverse-gamma, generalized inverse-Weibull, exponentiated inverted-Weibull, generalized inverted half-logistic, inverted-Kumaraswamy, inverted Nadarajah–Haghighi, and alpha-power inverse-Weibull distributions. [ABSTRACT FROM AUTHOR]