Search Results (31)

A novel unified progressive hybrid censoring is introduced to combine both progressive and hybrid censoring plans to allow flexible test termination either after a prespecified number of failures or at a fixed time. This work develops both frequentist and Bayesian inferential procedures for estimating the parameters, reliability, and hazard rates of the inverted Nadarajah–Haghighi lifespan model when a sample is produced from such a censoring plan. Maximum likelihood estimators are obtained through the Newton–Raphson iterative technique. The delta method, based on the Fisher information matrix, is utilized to build the asymptotic confidence intervals for each unknown quantity. In the Bayesian methodology, Markov chain Monte Carlo techniques with independent gamma priors are implemented to generate posterior summaries and credible intervals, addressing computational intractability through the Metropolis—Hastings algorithm. Extensive Monte Carlo simulations compare the efficiency and utility of frequentist and Bayesian estimates across multiple censoring designs, highlighting the superiority of Bayesian inference using informative prior information. Two real-world applications utilizing rare minerals from gold and diamond durability studies are examined to demonstrate the adaptability of the proposed estimators to the analysis of rare events in precious materials science. By applying four different optimality criteria to multiple competing plans, an analysis of various progressive censoring strategies that yield the best performance is conducted. The proposed censoring framework is effectively applied to real-world datasets involving diamonds and gold, demonstrating its practical utility in modeling the reliability and failure behavior of rare and high-value minerals. Full article

Accelerated life tests are vital in reliability studies, especially as new technologies create highly reliable products to meet market demand and competition. Progressive stress accelerated life test (PSALT) allows continual stress adjustments. For reliability and survival analysis in accelerated life studies, generalized progressive hybrid censoring (GPHC) is very important. The research on GPHC in PSALT models is lacking despite its growing importance. Binomial elimination and generalized progressive hybrid censoring augment PSALT in this investigation. This research examines PSALT under the Generalized Kavya–Manoharan exponential distribution based on the GPHC scheme. Using gamma prior, maximum likelihood, and Bayesian techniques, estimate model parameters. Squared error and entropy loss functions yield Bayesian estimators using informational priors in simulation and non-informative priors in application. Various censoring schemes are calculated using Monte Carlo simulation. The methodology is demonstrated using two real-world accelerated life test data sets. Full article

In this paper, inference under dependent competing risk data is considered with multiple causes of failure. We discuss both classical and Bayesian methods for estimating model parameters under the assumption that data are observed under generalized progressive hybrid censoring. The maximum likelihood estimators of model parameters are obtained when occurrences of latent failure follow a bivariate inverted exponentiated Pareto distribution. The associated existence and uniqueness properties of these estimators are established. The asymptotic interval estimators are also constructed. Further, Bayes estimates and highest posterior density intervals are derived using flexible priors. A Monte Carlo sampling algorithm is proposed for posterior computations. The performance of all proposed methods is evaluated through extensive simulations. Moreover, a real-life example is also presented to illustrate the practical applications of our inferential procedures. Full article

Based on Type-I generalized progressive hybrid censored samples (GPHCSs), the parameter estimate for the unit-half logistic-geometry (UHLG) distribution is investigated in this work. Using maximum likelihood estimation (MLE) and Bayesian estimation, the parameters, reliability, and hazard functions of the UHLG distribution under GPHCSs have been assessed. Likewise, the computation is carried out for the asymptotic confidence intervals (ACIs). Furthermore, two bootstrap CIs, bootstrap-p and bootstrap-t, are mentioned. For symmetric loss functions, like squared error loss (SEL), and asymmetric loss functions, such as linear exponential loss (LL) and general entropy loss (GEL), there are specific Bayesian approximations. The Metropolis–Hastings samplers methodology were used to construct the credible intervals (CRIs). In conclusion, a genuine data set measuring the mortality statistics of a group of male mice with reticulum cell sarcoma is regarded as an application of the methods given. Full article

In recent years, various forms of progressive hybrid censoring schemes (PHCS) have gained significant traction in survival and reliability analysis studies due to their versatility. However, these PHCS variants are often characterized by complexity stemming from the multitude of parameters involved in their specification. Consequently, the primary objective of this paper is to propose a unified approach termed combined type II progressive hybrid censoring scheme (${\mathrm{ComT}}_2$PHCS) capable of encompassing several existing PHCS variations. Our analysis focuses specifically on the exponential distribution (ExDist). Bayesian inference techniques are employed to estimate the parameters of the ExDist under the ${\mathrm{ComT}}_2$PHCS. Additionally, we conduct fundamental distributional analyses and likelihood inference procedures. We derive the conditional moment-generating function (CondMGF) of maximum likelihood estimator (MLE) for parameters of the ExDist under ${\mathrm{ComT}}_2$PHCS. Further, we use CondMGF for the distribution of MLE for parameters of ExDist under ${\mathrm{ComT}}_2$PHCS. Finally, we provide an illustrative example to elucidate the inference methods derived in this paper. Full article

Generalized progressive hybrid censoring approaches have been developed to reduce test time and cost. This paper investigates the difficulties associated with estimating the unobserved model parameters and the reliability time functions of the Kavya Manoharan Kumaraswamy (KMKu) distribution based on generalized type-II progressive hybrid censoring using classical and Bayesian estimation techniques. The frequentist estimators’ normal approximations are also used to construct the appropriate estimated confidence intervals for the unknown parameter model. Under symmetrical squared error loss, independent gamma conjugate priors are used to produce the Bayesian estimators. The Bayesian estimators and associated highest posterior density intervals cannot be derived analytically since the joint likelihood function is provided in a complicated form. However, they may be evaluated using Monte Carlo Markov chain (MCMC) techniques. Out of all the censoring choices, the best one is selected using four optimality criteria. Full article

A new two-parameter statistical model, obtained by compounding the generalized-exponential and exponential distributions, called the PRC lifetime model, is explored in this paper. This model can be easily linked to other well-known six-lifetime models; namely the exponential, log-logistic, Burr, Pareto and generalized Pareto models. Adaptive progressively hybrid Type-II censored strategy, used to increase the efficiency of statistical inferential results and save the total duration of a test, has become widely used in various sectors such as medicine, biology, engineering, etc. Via maximum likelihood and Bayes inferential methodologies, given the presence of such censored data, the challenge of estimating the unknown parameters and some reliability time features, such as reliability and failure rate functions, of the PRC model is examined. The Markov-Chain Monte Carlo sampler, when the model parameters are assumed to have independent gamma density priors, is utilized to produce the Bayes’ infer under the symmetric (squared-error) loss of all unknown subjects. Asymptotic confidence intervals as well as the highest posterior density intervals of the unknown parameters and the unknown reliability indices are also created. An extensive Monte Carlo simulation is implemented to investigate the accuracy of the acquired point and interval estimators. Four various optimality criteria, to select the best progressive censored design, are used. To demonstrate the applicability and feasibility of the proposed model in a real-world scenario, two data sets from the engineering sector; one based on industrial devices and the other on aircraft windshield, are analyzed. Numerical evaluations showed that the PRC model furnishes a superior fit compared to seven other models in the literature, including: alpha-power exponential, log-logistic, Nadarajah–Haghighi, generalized-exponential, Weibull, gamma and exponential lifetime distributions. The findings demonstrate that, in order to obtain the necessary estimators, the Bayes’ paradigm via Metropolis–Hastings sampler is recommended compared to its competitive likelihood approach. Full article

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. Full article

A new Type-II generalized progressively hybrid censoring strategy, in which the experiment is ensured to stop at a specified time, is explored when the lifetime model of the test subjects follows a two-parameter alpha-power inverted exponential (Alpha-PIE) distribution. Alpha-PIE’s parameters and reliability indices, such as reliability and hazard rate functions, are estimated via maximum likelihood and Bayes estimation methodologies in the presence of the proposed censored data. The estimated confidence intervals of the unknown quantities are created using the normal approximation of the acquired classical estimators. The Bayesian estimators are also produced using independent gamma density priors under symmetrical (squared-error) loss. The Bayes’ estimators and their associated highest posterior density intervals cannot be calculated theoretically since the joint likelihood function is derived in a complicated form, but they can potentially be assessed using Monte Carlo Markov-chain algorithms. We next go through four optimality criteria for identifying the best progressive design. The effectiveness of the suggested estimation procedures is assessed using Monte Carlo comparisons, and certain recommendations are offered. Ultimately, two different applications, one focused on the failure times of electronic tubes and the other on vinyl chloride, are analyzed to illustrate the effectiveness of the proposed techniques that may be employed in real-world scenarios. Full article

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. Full article

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. Full article

Generalized progressive hybrid censored procedures are created to reduce test time and expenses. This paper investigates the issue of estimating the model parameters, reliability, and hazard rate functions of the Fréchet (Fr) distribution under generalized Type-II progressive hybrid censoring by making use of the Bayesian estimation and maximum likelihood methods. The appropriate estimated confidence intervals of unknown quantities are likewise built using the frequentist estimators’ normal approximations. The Bayesian estimators are created using independent gamma conjugate priors under the symmetrical squared-error loss. The Bayesian estimators and the associated greatest posterior density intervals cannot be computed analytically since the joint likelihood function is obtained in complex form, but they may be assessed using Monte Carlo Markov chain (MCMC) techniques. Via extensive Monte Carlo simulations, the actual behavior of the proposed estimation methodologies is evaluated. Four optimality criteria are used to choose the best censoring scheme out of all the options. To demonstrate how the suggested approaches may be utilized in real scenarios, two real applications reflecting the thirty successive values of precipitation in Minneapolis–Saint Paul for the month of March as well as the number of vehicle fatalities for thirty-nine counties in South Carolina during 2012 are examined. Full article

The inverse Weibull distribution (IWD) can be applied to a various situations, including applications in reliability and medicine. In a reliability and medicine test, it is generally known that the results of test units may not be recorded. Recently, the generalized adaptive progressive hybrid censoring (GAPHC) scheme was introduced. In this paper, therefore, we consider the classical estimators (maximum likelihood estimator (MLE) and maximum product spacings estimator (MPSE)) and Bayes estimators (BayEsts) of the uncertainty measure of the IWD under GAPHC scheme. We derive the BayEsts of the uncertainty measure based on flexible (symmetrical and asymmetrical) priors. Additionally, we derive the Bayes estimators using the Tierney and Kadane approximation (TiKa) and importance sampling methods. In particular, the importance sampling method is used to obtain the credible interval for the uncertainty measure of the IWD under the GAPHC scheme. To compare the proposed estimators (classical and BayEsts), the Monte Carlo simulation method is conducted. Finally, the real dataset based on GAPHC scheme is analyzed. Full article

Generalized progressive hybrid censored mechanisms have been proposed to reduce the test duration and to save the cost spent on testing. This paper considers the problem of estimating the unknown model parameters and the reliability time functions of the new inverted Nadarajah–Haghighi (NH) distribution under generalized Type-II progressive hybrid censoring using the maximum likelihood and Bayesian estimation approaches. Utilizing the normal approximation of the frequentist estimators, the corresponding approximate confidence intervals of unknown quantities are also constructed. Using independent gamma conjugate priors under the symmetrical squared error loss, the Bayesian estimators are developed. Since the joint likelihood function is obtained in complex form, the Bayesian estimators and their associated highest posterior density intervals cannot be obtained analytically but can be evaluated via Monte Carlo Markov chain techniques. To select the optimum censoring scheme among different censoring plans, five optimality criteria are used. Finally, to explain how the proposed methodologies can be applied in real situations, two applications representing the failure times of electronic devices and deaths from the coronavirus disease 2019 epidemic in the United States of America are analyzed. Full article

This study aims to investigate the estimation problems when the parent distribution of the population under consideration is the Nadarajah–Haghighi distribution in the presence of an adaptive progressive Type-II hybrid censoring scheme. Two approaches are considered in this regard, namely, the maximum likelihood and Bayesian estimation methods. From the classical point of view, the maximum likelihood estimates of the unknown parameters, reliability, and hazard rate functions are obtained as well as the associated approximate confidence intervals. On the other hand, the Bayes estimates are obtained based on symmetric and asymmetric loss functions. The Bayes point estimates and the highest posterior density Bayes credible intervals are computed using the Monte Carlo Markov Chain technique. A comprehensive simulation study is implemented by proposing different scenarios for sample sizes and progressive censoring schemes. Moreover, two applications are considered by analyzing two real data sets. The outcomes of the numerical investigations show that the Bayes estimates using the general entropy loss function are preferred over the other methods. Full article