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Recently, there has been a lot of interest in comparative life testing for items under jointly censored schemes for products from multiple production lines. The inverse Weibull distribution (IWD) is commonly used in life testing and reliability theory. In this paper, we address the problem of statistical inference from comparative inverse Weibull distributions under joint samples. An adaptive type-II hybrid progressive censoring scheme (HPCS) is used to save the balance between the ideal test time and the number of observed failures. Under the adaptive type-II HPCS, unknown parameters of the inverse Weibull populations are estimated using both maximum likelihood and Bayesian approaches. Asymptotic confidence intervals are established using the observed Fisher information matrix and bootstrap confidence intervals. We suggest using Markov chain Monte Carlo (MCMC) techniques to compute credible intervals under independent gamma priors. Using Monte Carlo simulations, all theoretical conclusions are tested and contrasted. For illustration purposes, an actual sample from comparative populations is analysed. [ABSTRACT FROM AUTHOR]

The joint censoring technique becomes crucial when the study's aim is to assess the comparative advantages of products concerning their service times. In recent years, there has been a growing interest in progressive censoring as a means to reduce both cost and experiment duration. This article delves into the realm of statistical inference for the three-parameter Burr-XII distribution using a joint progressive Type II censoring approach applied to two separate samples. We explore both maximum likelihood and Bayesian methods for estimating model parameters. Furthermore, we derive approximate confidence intervals based on the observed information matrix and employ four bootstrap methods to obtain confidence intervals. Bayesian estimators are presented for both symmetric and asymmetric loss functions. Since closed-form solutions for Bayesian estimators are unattainable, we resort to the Markov chain Monte Carlo method to compute these estimators and the corresponding credible intervals. To assess the performance of our estimators, we conduct extensive simulation experiments. Finally, to provide a practical illustration, we analyze a real dataset. [ABSTRACT FROM AUTHOR]

In many practical applications, such as the studies of financial and biomedical data, the response variable usually is positive, and the commonly used criteria are based on absolute errors, which is not desirable. Rather, the relative errors are more of concern. We consider statistical inference for a partially linear multiplicative regression model when covariates in the linear part are measured with error. The simulation–extrapolation (SIMEX) estimators of parameters of interest are proposed based on the least product relative error criterion and B-spline approximation, where two kinds of relative errors are both introduced and the symmetry emerges in the loss function. Extensive simulation studies are conducted and the results show that the proposed method can effectively eliminate the bias caused by the measurement errors. Under some mild conditions, the asymptotic normality of the proposed estimator is established. Finally, a real example is analyzed to illustrate the practical use of our proposed method. [ABSTRACT FROM AUTHOR]

This study addresses the issue of estimating the shape parameter of the inverted exponentiated Rayleigh distribution, along with the assessment of reliability and failure rate, by utilizing Type-I progressive hybrid censored data. The study explores the estimators based on maximum likelihood, Bayes, and empirical Bayes methodologies. Additionally, the study focuses on the development of Bayes and empirical Bayes estimators with balanced loss functions. A concrete example based on actual data from the field of medicine is used to illustrate the theoretical insights provided in this study. Monte Carlo simulations are employed to conduct numerical comparisons and evaluate the performance and accuracy of the estimation methods. [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]

Today, the reliability or quality practitioner always aims to shorten testing duration and reduce testing costs without neglecting efficient statistical inference. So, a generalized progressively Type-II hybrid censored mechanism has been developed in which the experimenter prepays for usage of the testing facility for T units of time. This paper investigates the issue of estimating the model parameter, reliability, and hazard rate functions of the Maxwell–Boltzmann distribution in the presence of generalized progressive Type-II hybrid censored data by making use of the likelihood and Bayesian inferential methods. Using an inverse gamma prior distribution, the Bayes estimators of the same unknown parameters with respect to the most commonly squared-error loss are derived. Since the joint likelihood function is produced in complex form, following the Monte-Carlo Markov-chain idea, the Bayes' point estimators as well as the Bayes credible and highest posterior density intervals cannot be derived analytically, but they may be examined numerically. Via the normal approximation of the acquired maximum likelihood and log-maximum-likelihood estimators, the approximate confidence interval bounds of the unknown quantities are derived. Via comprehensive numerical comparisons, with regard to simulated root mean squared-error, mean relative absolute bias, average confidence length, and coverage probability, the actual behavior of the proposed estimation methodologies is examined. To illustrate how the offered methodologies may be used in real circumstances, two different applications, representing the failure time points of aircraft windscreens as well as the daily average wind speed in Cairo during 2009, are explored. Numerical evaluations recommend utilizing a Bayes model via the Metropolis-Hastings technique to produce samples from the posterior distribution to estimate any parameter of the Maxwell–Boltzmann distribution when collecting data from a generalized progressively Type-II hybrid censored mechanism. [ABSTRACT FROM AUTHOR]

Comparative lifetime tests are extremely significant when the experimenters study the reliability of the comparative advantages of two products in competition. Considering joint type-II censoring, we deal with the inference when two product lines conform to two Gumbel type-II distributions. The maximum likelihood estimations of Gumbel type-II population parameters were obtained in the current research. An approximate confidence interval and a simultaneous confidence interval based on a Fisher information matrix were also constructed and compared with two bootstrap confidence intervals. Moreover, to evaluate the influence of the prior information, based on the concept of importance sampling, we calculated the Bayesian estimator together with their posterior risks in the case of gamma and non-informative priors under different loss functions. To compare the performances of the overall parameters' estimator, a Monte Carlo simulation was performed using numerical and graphical methods. Finally, a real data analysis was conducted to verify the accuracy of all the models and methods mentioned. [ABSTRACT FROM AUTHOR]

Generalized progressively Type-II hybrid strategy has been suggested to save both the duration and cost of a life test when the experimenter aims to score a fixed number of failed units. In this paper, using this mechanism, the maximum likelihood and Bayes inferential problems for unknown model parameters, in addition to both reliability, and hazard functions of the inverted exponentiated Rayleigh model, are acquired. Applying the observed Fisher data and delta method, the normality characteristic of the classical estimates is taken into account to derive confidence intervals for unknown parameters and several indice functions. In Bayes' viewpoint, through independent gamma priors against both symmetrical and asymmetrical loss functions, the Bayes estimators of the unknown quantities are developed. Because the Bayes estimators are acquired in complicated forms, a hybrid Monte-Carlo Markov-chain technique is offered to carry out the Bayes estimates as well as to create the related highest posterior density interval estimates. The precise behavior of the suggested estimation approaches is assessed using wide Monte Carlo simulation experiments. Two actual applications based on actual data sets from the mechanical and chemical domains are examined to show how the offered methodologies may be used in real current events. [ABSTRACT FROM AUTHOR]

This manuscript focuses on the statistical inference of the Kavya–Manoharan generalized exponential distribution under the generalized type-I progressive hybrid censoring sample (GTI-PHCS). Different classical approaches of estimation, such as maximum likelihood, the maximum product of spacing, least squares (LS), weighted LS, and percentiles under GTI-PHCS, are investigated. Based on the squared error and linear exponential loss functions, the Bayes estimates for the unknown parameters utilizing separate gamma priors under GTI-PHCS have been derived. Point and interval estimates of unknown parameters are developed. We carry out a simulation using the Monte Carlo algorithm to show the performance of the inferential procedures. Finally, real-world data collection is examined for illustration purposes. [ABSTRACT FROM AUTHOR]

This study addresses the estimation problems of the modified Lindley distribution using a progressive Type-II censoring plan. Using the maximum likelihood and maximum product of spacing and Bayesian estimation methods, the unknown parameter, reliability, and hazard rate functions are estimated. Employing the assumption of the gamma prior and a symmetric loss function, Bayes estimators are investigated when the observed data are obtained using the likelihood and product of spacing functions. Additionally, the approximate confidence intervals using both classical methods and the highest posterior density credible intervals are also discussed. To assess the different estimating strategies, a comprehensive simulation experiment that considers various sample sizes and censoring schemes is implemented. Finally, two actual data sets are examined to verify the utility of the modified Lindley distribution and the usefulness of the suggested estimators. The findings demonstrate that, in order to obtain the necessary estimators, the maximum product of the spacing method is preferred over the maximum likelihood method; whereas, when compared to the conventional techniques, the Bayesian approach using the likelihood and product of spacing functions provides more acceptable estimates. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the statistical analysis of a simple step-stress accelerated competing failure model under progressively Type-II censoring. It is assumed that there is more than one cause of failure, and the lifetime of the experimental units at each stress level follows exponential distribution. The distribution functions under different stress levels are connected through the cumulative exposure model. The maximum likelihood, Bayesian, Expected Bayesian, and Hierarchical Bayesian estimations of the model parameters are derived based on the different loss function. Based on Monte Carlo Simulations. We also get the average length and the coverage probability of the 95% confidence intervals and highest posterior density credible intervals of the parameters. From the numerical studies, it can be seen that the proposed Expected Bayesian estimations and Hierarchical Bayesian estimations have better performance in terms of the average estimates and mean squared errors, respectively. Finally, the methods of statistical inference discussed here are illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

This paper explores statistical inferences when the lifetime of product follows the inverse Nakagami distribution using progressive Type-II censored data. Likelihood-based and maximum product of spacing (MPS)-based methods are considered for estimating the parameters of the model. In addition, approximate confidence intervals are constructed via the asymptotic theory using both likelihood and product spacing functions. Based on traditional likelihood and the product of spacing functions, Bayesian estimates are also considered under a squared error loss function using non-informative priors, and Gibbs sampling based on the MCMC algorithm is proposed to approximate the Bayes estimates, where the highest posterior density credible intervals of the parameters are obtained. Numerical studies are presented to compare the proposed estimators using Monte Carlo simulations. To demonstrate the proposed methodology in a real-life scenario, a well-known data set on agricultural machine elevators with high defect rates is also analyzed for illustration. [ABSTRACT FROM AUTHOR]

This paper investigates the statistical inference of inverse power Lomax distribution parameters under progressive first-failure censored samples. The maximum likelihood estimates (MLEs) and the asymptotic confidence intervals are derived based on the iterative procedure and asymptotic normality theory of MLEs, respectively. Bayesian estimates of the parameters under squared error loss and generalized entropy loss function are obtained using independent gamma priors. For Bayesian computation, Tierney–Kadane's approximation method is used. In addition, the highest posterior credible intervals of the parameters are constructed based on the importance sampling procedure. A Monte Carlo simulation study is carried out to compare the behavior of various estimates developed in this paper. Finally, a real data set is analyzed for illustration purposes. [ABSTRACT FROM AUTHOR]