Search Results (79)

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

This study investigates a novel modification for a modified Weibull distribution called the new modification of modified Weibull distribution. Some distributions related to the NMMWD are given. Some characterization of the NMMWD, including quantiles, Bowley skewness, Moors kurtosis, and moments, are given in closed forms. The hazard rate function of the new distribution takes two distinct shapes, the increasing and the bathtub shapes. Different estimating approaches are investigated utilizing complete data. Three real data sets from the engineering field are analyzed to demonstrate the suggested model’s flexibility in practice. In comparison to certain well-known distributions, the proposed distribution fits the tested data better according to both parametric and non-parametric tests. A simulation study is presented to compare the various estimating approaches using mean square error and average absolute bias. Full article

In recent years, there has been growing interest in discrete probability distributions due to their ability to model the complex behavior of real-world count data. In this paper, a new discrete mixture distribution based on two Weibull components is introduced, constructed using the general discretization approach. Several important statistical properties of the proposed distribution, including the survival function, hazard rate function, alternative hazard rate function, moments, quantile function, and order statistics are derived. It was concluded from the descriptive measures that the discrete mixture of two Weibull distributions transitions from being positively skewed with heavy tails to a more symmetric and light-tailed form. This demonstrates the high flexibility of the discrete mixture of two Weibull distributions in capturing a wide range of shapes as its parameter values vary. Estimation of the parameters is performed via maximum likelihood under Type II censoring scheme. A simulation study assesses the performance of the maximum likelihood estimators. Furthermore, the applicability of the proposed distribution is demonstrated using two real-life datasets. In summary, this paper constructs the discrete mixture of two Weibull distributions, investigates its statistical characteristics, and estimates its parameters, demonstrating its flexibility and practical applicability. These results highlight its potential as a powerful tool for modeling complex discrete data. Full article

This study develops an integrated quality inspection and production optimization framework for an imperfect production system, where system deterioration follows a zero-inflated non-homogeneous Poisson process (ZI-NHPP) characterized by a power-law intensity function. Parameters are estimated from historical data using the Expectation-Maximization (EM) algorithm, with a zero-inflation parameter π modeling scenario where the system remains defect-free. Operating in either an in-control or out-of-control state, the system produces products with Weibull hazard rates, exhibiting higher failure rates in the out-of-control state. The proposed model integrates system status, defect rates, employee efficiency, and market demand to jointly optimize the number of conforming items inspected and the production run length, thereby minimizing total costs—including production, inspection, correction, inventory, and warranty expenses. Numerical analyses, supported by sensitivity studies, validate the effectiveness of this integrated approach in achieving cost-efficient quality control. This framework enhances quality assurance and production management, offering practical insights for manufacturing across diverse industries. Full article

The blade is a core component of the gas turbine, and blade fouling is characterized by highly concealed failure modes in the early stages and significant destructive potential in later stages. To address the lack of intelligence in early warning systems for compressor fouling, this study proposes a data-driven approach combining a digital-twin-based dynamic simulation model with the Weibull Proportional Hazards Model (WPHM) algorithm to enable reliable fault early warning. A modular design methodology was first adopted to construct a digital gas turbine model of the gas–gas combined power system on a dynamic simulation platform. High-fidelity fault simulation data were then generated to represent both healthy and faulty operating conditions. Through data governance and uncertainty quantification, key parameters influencing compressor fouling were identified. The Pearson correlation coefficient was applied to screen the most sensitive indicators, ensuring effective input selection for the prognostic model. Using historical health data from the simulation platform, the WPHM algorithm was trained to learn degradation patterns and establish a baseline failure risk model. This trained WPHM was then deployed to monitor real-time performance trends and provide early warnings for compressor blade fouling. Validation results from multi-unit simulations show that the proposed method achieves a fault warning rate of 95.0%, demonstrating its effectiveness and readiness to meet practical engineering requirements. Full article

This paper introduces the Lambert-Lindley distribution, a two-parameter extension of the Lindley model constructed through the Lambert-F generator. The new distribution retains the non-negative support of the Lindley distribution and provides additional flexibility by incorporating a shape parameter that controls skewness and tail behavior. Structural properties are derived, including the probability density function, cumulative distribution function, quantile function, hazard rate, and moments. Parameter estimation is addressed using the method of moments and maximum likelihood, and a Monte Carlo simulation study carried out to evaluate the performance of the proposed estimators. The practical applicability of the Lambert–Lindley distribution is demonstrated with two real datasets: stress rupture times of Kevlar/epoxy composites and hospital stay durations of breast cancer patients. Comparative analyses using goodness-of-fit tests and information criteria demonstrate that the proposed model can outperform classical alternatives such as the Gamma and Weibull distributions. Consequently, the Lambert–Lindley distribution emerges as a flexible alternative for modeling positive unimodal data in contexts such as material reliability studies and clinical duration analysis. Full article

This paper introduces a novel three-parameter probability model, the unit-Gompertz–Makeham (UGM) distribution, designed for modeling bounded data on the unit interval (0,1). By transforming the classical Gompertz–Makeham distribution, we derive a unit-support distribution that flexibly accommodates a wide range of shapes in both the density and hazard rate functions, including increasing, decreasing, bathtub, and inverted-bathtub forms. The UGM density exhibits rich patterns such as symmetric, unimodal, U-shaped, J-shaped, and uniform-like forms, enhancing its ability to fit real-world bounded data more effectively than many existing models. We provide a thorough mathematical treatment of the UGM distribution, deriving explicit expressions for its quantile function, mode, central and non-central moments, mean residual life, moment-generating function, and order statistics. To facilitate parameter estimation, eight classical techniques, including maximum likelihood, least squares, and Cramér–von Mises methods, are developed and compared via a detailed simulation study assessing their accuracy and robustness under varying sample sizes and parameter settings. The practical relevance and superior performance of the UGM distribution are demonstrated using two real-world engineering datasets, where it outperforms existing bounded models, such as beta, Kumaraswamy, unit-Weibull, unit-gamma, and unit-Birnbaum–Saunders. These results highlight the UGM distribution’s potential as a versatile and powerful tool for modeling bounded data in reliability engineering, quality control, and related fields. Full article

The paper is intended to put forward a modified Weibull-type lifetime model. Modification consists of replacing the shape parameter of the original Weibull model with the shape function. It is self-evidently a novelty among lifetime models. The model in question will further be named the Weibull-sf model. To present the Weibull-sf, we need appropriate background. The background comes from an extensive review performed on 165 Weibull-type lifetime models we found in the source literature. Performing this review, we focused on two properties of the models: modality of failure density functions, as well as shape of the hazard rate functions. It does not matter that these are strongly interrelated, incidentally. The Weibull-sf lifetime model has the valuable property of flexibility. It may have a bathtub-like hazard rate function and bimodal density function. This is exactly what reliability analysts want to have. Foreseeing the huge numerical problems one will face when trying the maximum-likelihood method, we promote the method of the least absolute values that is a “close relative” to the method of least squares. Examples of fitting the Weibull-sf to real data are given. The cumulative failure functions of bimodal models with a bathtub-like hazard rate function and R codes are given. Full article

The exponential distribution is one of the most popular models for fitting lifetime data. This study proposes a novel generalization of the exponential distribution, referred to as the exponentiated generalized Weibull exponential, for the modeling of lifetime data. This new distribution is a member of a family that combines two well-known distribution families: the exponentiated generalized family and the T-X family. It has five parameters, allowing it to fit data that exhibit increasing, decreasing, bathtub, upside-down bathtub, S-shaped, J-shaped and reversed-J hazard rates. Some mathematical and statistical properties of the newly suggested distribution are derived and the estimation of its parameters is studied using the method of maximum likelihood. Different simulation studies have been applied to evaluate the parameter estimation. Four lifetime datasets are analyzed to investigate the superiority of the proposed exponentiated generalized Weibull exponential distribution. A regression model based on the proposed distribution is then developed for both complete and censored samples, and its performance is assessed on two real datasets. The new distribution and its associated regression model are empirically demonstrated to be practically useful. Full article

As part of this study, we design a reliability acceptance sampling plan under the assumption that the lifetime of a product follows the Topp–Leone generated Weibull (TLGW) distribution, a model that exhibits structural symmetry in its hazard rate behavior and distributional form. The fundamental procedures for constructing such a plan are described. We compute and tabulate the minimum sample sizes required for given risk criteria using both binomial and Poisson models for the number of failures. We also provide the operating characteristic (OC) values for the proposed sampling plans, and determine the minimum ratios of true mean life to specified mean life needed to satisfy a given producer’s risk. The role of symmetry in the TLGW distribution is highlighted in its balanced tail properties and shape characteristics, which influence the performance of the acceptance sampling plan. Finally, we illustrate the applicability of the proposed plan with real-world data. Full article

Many scholars are interested in modeling complex data in an effort to create novel probability distributions. This article proposes a novel class of distributions based on the inverse of the exponentiated Weibull hazard rate function. A particular member of this class, the Weibull–Rayleigh distribution (WR), is presented with focus. The WR features diverse probability density functions, including symmetric, right-skewed, left-skewed, and the inverse J-shaped distribution which is flexible in modeling lifetime and systems data. Several significant statistical features of the suggested WR are examined, covering the quantile, moments, characteristic function, probability weighted moment, order statistics, and entropy measures. The model accuracy was verified through Monte Carlo simulations of five different statistical estimation methods. The significance of WR is demonstrated with three real-world data sets, revealing a higher goodness of fit compared to other competing models. Additionally, the change point for the WR model is illustrated using the modified information criterion (MIC) to identify changes in the structures of these data. The MIC and curve analysis captured a potential change point, supporting and proving the effectiveness of WR distribution in describing transitions. Full article

With the acceleration of urbanization and the increasing demand for aesthetics, cable laying is progressively transitioning into urban dense cable channels. The internal environment of these channels is complex, and arbitrary cable laying poses significant threats to normal cable operation. Therefore, this paper proposes a reliability assessment method for hybrid cable laying configurations in urban dense cable channels based on a modified Weibull distribution. Firstly, a Weibull proportional hazards model is constructed by incorporating channel operational risk factors as covariates. Then, Bayesian inference is employed to update the Weibull parameters by integrating expert experience with cable channel O&M data. Subsequently, we select the parameter distribution and reliability evaluation indicators suitable for the operating environment of the cable channel and analyze the influence of the overcrowding rate of cable laying, the operating temperature of the cable, and the distance between cables in the channel on the reliability of the cable channel. Finally, a case study is conducted on a cable channel in a region of the China Southern Power Grid utilizing its actual O&M data to perform a reliability assessment. The effectiveness of the proposed modified Weibull distribution assessment method is validated through model comparison. Furthermore, this study provides differentiated maintenance strategies for specific cables within the channel and proposes a set of highly applicable O&M guidelines. Full article

This study introduces a novel family of probability distributions, termed the Pi-Power Logistic-G family, constructed through the application of the Pi-power transformation technique. By employing the Weibull distribution as the baseline generator, a new and flexible model, the Pi-Power Logistic Weibull distribution, is formulated. Particular emphasis is given to this specific member of the family, which demonstrates a rich variety of hazard rate shapes, including J-shaped, reverse J-shaped, and monotonic increasing patterns, thereby highlighting its adaptability in modeling diverse types of lifetime data. The paper examines the fundamental properties of this distribution and applies the method of maximum likelihood estimation (MLE) to determine its parameters. A Monte Carlo simulation was performed to assess the performance of the estimation method, demonstrating that both Bias and mean square error decline as the sample size increases. The utility of the proposed distribution is further highlighted through its application to real-world engineering datasets. Using model selection metrics and goodness-of-fit tests, the results demonstrate that the proposed model outperforms existing alternatives. In addition, a Bayesian approach was used to estimate the parameters of both datasets, further extending the model’s applicability. The findings of this study have significant implications for the fields of reliability modeling, survival analysis, and distribution theory, enhancing methodologies and offering valuable theoretical insights. Full article

Background: Prostate cancer (PC) is the second leading cause of cancer-related death in men in the United States. A subset of patients develops non-metastatic, castration-resistant PC (nmCRPC), for which management requires a personalized consideration for appropriate treatment. However, there is no consensus regarding when to switch from androgen deprivation therapy (ADT) to more aggressive treatments like abiraterone or enzalutamide. Methods: We analyzed 5037 nmCRPC patients and employed a Weibull Time to Event Recurrent Neural Network to identify patients who would benefit from switching from ADT to abiraterone/enzalutamide. We evaluated this model using differential treatment benefits measured by the Kaplan–Meier estimation and milestone probabilities. Results: The model achieved an area under the curve of 0.738 (standard deviation (SD): 0.057) for patients treated with abiraterone/enzalutamide and 0.693 (SD: 0.02) for patients exclusively treated with ADT at the 2-year milestone. The model recommended 14% of ADT patients switch to abiraterone/enzalutamide. Analysis showed a statistically significant absolute improvement using model-recommended treatments in progression-free survival (PFS) of 0.24 (95% confidence interval (CI): 0.23–0.24) at the 2-year milestone (PFS rate increasing from 0.50 to 0.74) with a hazard ratio of 0.44 (95% CI: 0.39–0.50). Conclusions: Our model successfully identified nmCRPC patients who would benefit from switching to abiraterone/enzalutamide, demonstrating potential outcome improvements. Full article

This paper explores statistical techniques for estimating unknown lifetime parameters using data from a progressive first-failure censoring scheme. The failure times are modeled with a new Weibull–Pareto distribution. Maximum likelihood estimators are derived for the model parameters, as well as for the survival and hazard rate functions, although these estimators do not have explicit closed-form solutions. The Newton–Raphson algorithm is employed for the numerical computation of these estimates. Confidence intervals for the parameters are approximated based on the asymptotic normality of the maximum likelihood estimators. The Fisher information matrix is calculated using the missing information principle, and the delta technique is applied to approximate confidence intervals for the survival and hazard rate functions. Bayesian estimators are developed under squared error, linear exponential, and general entropy loss functions, assuming independent gamma priors. Markov chain Monte Carlo sampling is used to obtain Bayesian point estimates and the highest posterior density credible intervals for the parameters and reliability measures. Finally, the proposed methods are demonstrated through the analysis of a real dataset. Full article