Search Results (133)

Generalized censoring, combined with a power-based distribution, improves inferential efficiency by capturing more detailed failure-time information in complex testing scenarios. Conventional censoring schemes may discard substantial failure-time information, leading to inefficiencies in parameter estimation and reliability prediction. To address this limitation, we develop a comprehensive inferential framework for the alpha-power Weibull (APW) distribution under a generalized progressive hybrid Type-II censoring scheme, a flexible design that unifies classical, hybrid, and progressive censoring while guaranteeing test completion within preassigned limits. Both maximum likelihood and Bayesian estimation procedures are derived for the model parameters, reliability function, and hazard rate. Associated uncertainty quantification is provided through asymptotic confidence intervals (normal and log-normal approximations) and Bayesian credible intervals obtained via Markov chain Monte Carlo (MCMC) methods with independent gamma priors. In addition, we propose optimal censoring designs based on trace, determinant, and quantile-variance criteria to maximize inferential efficiency at the design stage. Extensive Monte Carlo simulations, assessed using four precision measures, demonstrate that the Bayesian MCMC estimators consistently outperform their frequentist counterparts in terms of bias, mean squared error, robustness, and interval coverage across a wide range of censoring levels and prior settings. Finally, the proposed methodology is validated using real-life datasets from engineering (electronic devices), clinical (organ transplant), and physical (rare metals) studies, demonstrating the APW model’s superior goodness-of-fit, reliability prediction, and inferential stability. Overall, this study demonstrates that combining generalized censoring with the APW distribution substantially enhances inferential efficiency and predictive performance, offering a robust and versatile tool for complex life-testing experiments across multiple scientific domains. Full article

The very flexible Weibull (VF-W) distribution is formulated by expressing its cumulative risk function as a logarithmic composite of auxiliary cumulative risks, making the model particularly well-suited for modeling heterogeneous life behaviors. This model admits a remarkably flexible hazard structure, capable of generating monotone increasing, unimodal (increase-then-decrease), and multi-turning-point shapes, thereby capturing complex failure behaviors far beyond those allowed by the classical Weibull distribution. This paper presents a comprehensive inferential study of the VF-W model through the unified progressive hybrid (UPH) censoring framework for modeling shock-type lifetime data. The UPH scheme integrates the advantages of Type-II, generalized hybrid, and progressive hybrid censoring mechanisms into a unified structure that ensures efficiency and adaptability in reliability testing. Classical inference is developed through maximum likelihood estimation with asymptotic interval construction, while Bayesian inference is performed using independent gamma priors and a Markov iterative algorithm. Extensive Monte Carlo experiments are conducted to evaluate the finite-sample performance of both approaches under various censoring intensities, revealing that the Bayesian MCMC-based estimators and their highest posterior density intervals provide superior precision, coverage, and robustness. The proposed VF-W model using UPH-based strategy is further validated through the analysis of a real shocks dataset, where it demonstrates a comparative performance improvement over existing models. The VF-W model exhibits stable parameter estimation under diverse censoring levels, indicating robustness in incomplete-data scenarios. Furthermore, the model maintains analytical tractability, offering closed-form expressions for key reliability measures, which facilitates practical implementation in different scenarios. The results confirm the VFW model’s strong potential as a unifying and computationally stable tool for reliability modeling, particularly in complex engineering and physical systems operating under stochastic shock environments. Full article

General progressive Type-II censoring is widely applied in life-testing experiments to enhance efficiency by allowing early removal of surviving units, thereby reducing experimental time and cost. This paper develops exact inference and prediction procedures for one- and two-parameter exponential models based on multiple independent general progressively Type-II censored samples. Using the recursive algorithm repeatedly, exact confidence intervals for model parameters and exact prediction intervals for unobserved failure times are constructed. The proposed methods are illustrated with simulated and real (tire wear) data, demonstrating their practical applicability to partially censored reliability experiments. Full article

Modern healthcare and engineering both rely on robust reliability models, where handling censored data effectively translates into longer-lasting devices, improved therapies, and safer environments for society. To address this, we develop a novel inferential framework for the ZLindley (ZL) distribution under the improved adaptive progressive Type-II censoring strategy. The proposed approach unifies the flexibility of the ZL model—capable of representing monotonically increasing hazards—with the efficiency of an adaptive censoring strategy that guarantees experiment termination within pre-specified limits. Both classical and Bayesian methodologies are investigated: Maximum likelihood and log-transformed likelihood estimators are derived alongside their asymptotic confidence intervals, while Bayesian estimation is conducted via gamma priors and Markov chain Monte Carlo methods, yielding Bayes point estimates, credible intervals, and highest posterior density regions. Extensive Monte Carlo simulations are employed to evaluate estimator performance in terms of bias, efficiency, coverage probability, and interval length across diverse censoring designs. Results demonstrate the superiority of Bayesian inference, particularly under informative priors, and highlight the robustness of HPD intervals over traditional asymptotic approaches. To emphasize practical utility, the methodology is applied to real-world reliability datasets from clinical trials on leukemia patients and hydrological measurements from River Styx floods, demonstrating the model’s ability to capture heterogeneity, over-dispersion, and increasing risk profiles. The empirical investigations reveal that the ZLindley distribution consistently provides a better fit than well-known competitors—including Lindley, Weibull, and Gamma models—when applied to real-world case studies from clinical leukemia trials and hydrological systems, highlighting its unmatched flexibility, robustness, and predictive utility for practical reliability modeling. Full article

This paper presents a comprehensive reliability analysis framework for the Chris–Jerry (CJ) lifetime distribution under an improved adaptive progressive Type-II censoring plan. The CJ model, recently introduced to capture skewed lifetime behaviors, is studied under a modified censoring structure designed to provide greater flexibility in terminating life-testing experiments. We derive maximum likelihood estimators for the CJ parameters and key reliability measures, including the reliability and hazard rate functions, and construct approximate confidence intervals using the observed Fisher information matrix and the delta method. To address the intractability of the likelihood function, Bayesian estimators are obtained under independent gamma priors and a squared-error loss function. Because the posterior distributions are not available in closed form, we apply the Metropolis–Hastings algorithm to generate Bayesian estimates and two types of credible intervals. A comprehensive simulation study evaluates the performance of the proposed estimation techniques under various censoring scenarios. The framework is further validated through two real-world datasets: one involving rainfall measurements and another concerning mechanical failure times. In both cases, the CJ model combined with the proposed censoring strategy demonstrates superior fit and reliability inference compared to competing models. These findings highlight the value of the CJ distribution, together with advanced censoring methods, for modeling lifetime data in physics and engineering applications. Full article

Life testing of products often requires extended observation periods. To shorten the duration of these tests, products can be subjected to more extreme conditions than those encountered in normal use; an approach known as accelerated life testing (ALT) is considered. This study investigates the estimation of unknown parameters and the acceleration factor for the modified Fréchet-Lomax exponential distribution (MFLED), utilizing Type II progressively first-failure censored (PFFC) samples obtained under the framework of constant-stress partially accelerated life testing (CSPALT). Maximum likelihood (ML) estimation is employed to obtain point estimates for the model parameters and the acceleration factor, while the Fisher information matrix is used to construct asymptotic confidence intervals (ACIs) for these estimates. To improve the precision of inference, two parametric bootstrap methods are also implemented. In the Bayesian context, a method for eliciting prior hyperparameters is proposed, and Bayesian estimates are obtained using the Markov Chain Monte Carlo (MCMC) method. These estimates are evaluated under both symmetric and asymmetric loss functions, and the corresponding credible intervals (CRIs) are computed. A comprehensive simulation study is conducted to compare the performance of ML, bootstrap, and Bayesian estimators in terms of mean squared error and coverage probabilities of confidence intervals. Finally, real-world failure time data of light-emitting diodes (LEDs) are analyzed to demonstrate the applicability and efficiency of the proposed methods in practical reliability studies, highlighting their value in modeling the lifetime behavior of electronic components. Full article

This study focuses on analyzing progressive Type-II right censoring competing risks datasets. The latent causes of failures are assumed to follow independent generalized linear exponential distributions. The maximum likelihood and maximum product of spacing methods are employed to estimate the unknown parameters and survival indices. Furthermore, approximate confidence intervals are derived using the asymptotic normality of the maximum likelihood and the maximum product of spacing estimators. Additionally, bootstrap methods are employed to construct confidence intervals. A comprehensive simulation study is carried out to evaluate the effectiveness of these estimation approaches. Finally, real-world datasets are analyzed to illustrate the practical applicability of the proposed model. Full article

In medical research, random censoring often occurs due to unforeseen subject withdrawals, whereas progressive censoring is intentionally applied to minimize time and resource requirements during experimentation. This work focuses on estimating the parameters of a two-parameter exponential distribution under a progressive Type-II random censoring scheme, which integrates both censoring strategies. The use of symmetric properties in failure and censoring time models, arising from a shared location parameter, facilitates a balanced and robust inferential framework. This symmetry ensures interpretational clarity and enhances the tractability of both frequentist and Bayesian methods. Maximum likelihood estimators (MLEs) are obtained, along with asymptotic confidence intervals. A Bayesian approach is also introduced, utilizing inverse gamma priors, and Gibbs sampling is implemented to derive Bayesian estimates. The effectiveness of the proposed methodologies was assessed through extensive Monte Carlo simulations and demonstrated using an actual dataset. Full article

Accurate modeling of product lifetimes is vital in reliability analysis and engineering to ensure quality and maintain competitiveness. This paper proposes the progressively randomly censored Maxwell distribution, which incorporates both progressive Type-II and random censoring within the Maxwell distribution framework. The model allows for the planned removal of surviving units at specific stages of an experiment, accounting for both deliberate and random censoring events. It is assumed that survival and censoring times each follow a Maxwell distribution, though with distinct parameters. Both frequentist and Bayesian approaches are employed to estimate the model parameters. In the frequentist approach, maximum likelihood estimators and their corresponding confidence intervals are derived. In the Bayesian approach, Bayes estimators are obtained using an inverse gamma prior and evaluated through a Markov Chain Monte Carlo (MCMC) method under the squared error loss function (SELF). A Monte Carlo simulation study evaluates the performance of the proposed estimators. The practical relevance of the methodology is demonstrated using a real data set. Full article

This paper presents a comprehensive statistical analysis of the Gumbel Type-II distribution based on joint progressive Type-II censoring. It derives the maximum likelihood estimators for the distribution parameters and constructs their asymptotic confidence intervals. It investigates Bayesian estimation using non-informative and informative priors under the squared error loss function and the LINEX loss function, applying Markov Chain Monte Carlo methods. A detailed simulation study evaluates the estimators’ performance in terms of average estimates, mean squared errors, and average confidence interval lengths. Results show that Bayesian estimators can outperform maximum likelihood estimators, especially with informative priors. A real data example demonstrates the practical use of the proposed methods. The analysis confirms that the Gumbel Type-II distribution with joint progressive censoring provides a flexible and effective model for lifetime data, enabling more accurate reliability assessment and risk analysis in engineering and survival studies. Full article

This study focuses on estimating the unknown parameters and the reliability function of the inverted-Weibull distribution, using an improved adaptive progressive Type-II censoring scheme under a competing risks model. Both classical and Bayesian estimation approaches are explored to offer a thorough analysis. Under the classical approach, maximum likelihood estimators are obtained for the unknown parameters and the reliability function. Approximate confidence intervals are also constructed to assess the uncertainty in the estimates. From a Bayesian standpoint, symmetric Bayes estimates and highest posterior density credible intervals are computed using Markov Chain Monte Carlo sampling, assuming a symmetric squared error loss function. An extensive simulation study is carried out to assess how well the proposed methods perform under different experimental conditions, showing promising accuracy. To demonstrate the practical use of these methods, a real dataset is analyzed, consisting of the survival times of male mice aged 35 to 42 days after being exposed to 300 roentgens of X-ray radiation. The analysis demonstrated that the inverted Weibull distribution is well-suited for modeling the given dataset. Furthermore, the Bayesian estimation method, considering both point estimates and interval estimates, was found to be more effective than the classical approach in estimating the model parameters as well as the reliability function. Full article

Competing risk models are essential in survival analysis for studying systems with multiple mutually exclusive failure events. This study investigates the application of competing risk models in the presence of progressively Type-II censored data for the Dagum distribution, a flexible distribution suited for modeling data with heavy tails and varying skewness and kurtosis. The methodology includes maximum likelihood estimation of the unknown parameters, with a focus on the special case of a common shape parameter, which allows for a closed-form expression of the relative risks. A hypothesis test is developed to assess the validity of this assumption, and both asymptotic and bootstrap confidence intervals are constructed. The performance of the proposed methods is evaluated through Monte Carlo simulations, and their applicability is demonstrated with a real-world example. Full article

In complex reliability applications, it is common for the failure of an individual or an item to be attributed to multiple causes known as competing risks. This paper explores the estimation of the Hjorth competing risks model based on an adaptive progressive Type II censoring scheme via a binomial removal mechanism. For parameter and reliability metric estimation, both frequentist and Bayesian methodologies are developed. Maximum likelihood estimates for the Hjorth parameters are computed numerically due to their intricate form, while the binomial removal parameter is derived explicitly. Confidence intervals are constructed using asymptotic approximations. Within the Bayesian paradigm, gamma priors are assigned to the Hjorth parameters and a beta prior for the binomial parameter, facilitating posterior analysis. Markov Chain Monte Carlo techniques yield Bayesian estimates and credible intervals for parameters and reliability measures. The performance of the proposed methods is compared using Monte Carlo simulations. Finally, to illustrate the practical applicability of the proposed methodology, two real-world competing risk data sets are analyzed: one representing the breaking strength of jute fibers and the other representing the failure modes of electrical appliances. Full article

This study offers a newly improved Type-II adaptive progressive censoring with data sampled from an inverse XLindley (IXL) distribution for more efficient and adaptive reliability assessments. Through this sampling mechanism, we evaluate the parameters of the IXL distribution, as well as its reliability and hazard rate features. In the context of reliability, to handle flexible and time-constrained testing frameworks in high-reliability environments, we formulate maximum likelihood estimators versus Bayesian estimates derived via Markov chain Monte Carlo techniques under gamma priors, which effectively capture prior knowledge. Two patterns of asymptotic interval estimates are constructed through the normal approximation of the classical estimates and of the log-transformed classical estimates. On the other hand, from the Markovian chains, two patterns of credible interval estimates are also constructed. A robust simulation study is carried out to compare the classical and Bayesian point estimation methods, along with the four interval estimation methods. This study’s practical usefulness is demonstrated by its analysis of a real-world dataset. The results reveal that both conventional and Bayesian inferential methods function accurately, with the Bayesian outcomes surpassing those of the conventional method. Full article

In recent years, there has been an increasing interest in the application of progressive censoring as a means to reduce both cost and experiment duration. In the absence of explanatory variables, the present study employs a statistical inference approach for the inverse Weibull distribution, using a progressive type II censoring strategy with two independent samples. The article expounds on the maximum likelihood estimation method, utilizing the Fisher information matrix to derive approximate confidence intervals. Moreover, interval estimations are computed by the bootstrap method. We explore the application of Bayesian methods for estimating model parameters under both the squared error and LINEX loss functions. The Bayesian estimates and corresponding credible intervals are calculated via Markov chain Monte Carlo (MCMC). Finally, comprehensive simulation studies and real data analysis are carried out to validate the precision of the proposed estimation methods. Full article