Progressive Type-II Censoring Research Articles

Bivariate Length-Biased Exponential Distribution under Progressive Type-II Censoring: Incorporating Random Removal and Applications to Industrial and Computer Science Data

Bivariate Length-Biased Exponential Distribution under Progressive Type-II Censoring: Incorporating Random Removal and Applications to Industrial and Computer Science Data

Estimation and Bayesian Prediction of the Generalized Pareto Distribution in the Context of a Progressive Type-II Censoring Scheme

The generalized Pareto distribution plays a significant role in reliability research. This study concentrates on the statistical inference of the generalized Pareto distribution utilizing progressively Type-II censored data. Estimations are performed using maximum likelihood estimation through the expectation–maximization approach. Confidence intervals are derived using the asymptotic confidence intervals. Bayesian estimations are conducted using the Tierney and Kadane method alongside the Metropolis–Hastings algorithm, and the highest posterior density credible interval estimation is accomplished. Furthermore, Bayesian predictive intervals and future sample estimations are explored. To illustrate these inference techniques, a simulation and practical example are presented for analysis.

Epidemiological modeling of COVID-19 data with Advanced statistical inference based on Type-II progressive censoring

This research proposes the Kavya-Manoharan Unit Exponentiated Half Logistic (KM-UEHL) distribution as a novel tool for epidemiological modeling of COVID-19 data. Specifically designed to analyze data constrained to the unit interval, the KM-UEHL distribution builds upon the unit exponentiated half logistic model, making it suitable for various data from COVID-19. The paper emphasizes the KM-UEHL distribution's adaptability by examining its density and hazard rate functions. Its effectiveness is demonstrated in handling the diverse nature of COVID-19 data through these functions. Key characteristics like moments, quantile functions, stress-strength reliability, and entropy measures are also comprehensively investigated. Furthermore, the KM-UEHL distribution is employed for forecasting future COVID-19 data under a progressive Type-II censoring scheme, which acknowledges the time-dependent nature of data collection during outbreaks. The paper presents various methods for constructing prediction intervals for future-order statistics, including maximum likelihood estimation, Bayesian inference (both point and interval estimates), and upper-order statistics approaches. The Metropolis-Hastings and Gibbs sampling procedures are combined to create the Markov chain Monte Carlo simulations because it is mathematically difficult to acquire closed-form solutions for the posterior density function in the Bayesian framework. The theoretical developments are validated with numerical simulations, and the practical applicability of the KM-UEHL distribution is showcased using real-world COVID-19 datasets.

Bayesian and E-Bayesian Estimation for a Modified Topp Leone–Chen Distribution Based on a Progressive Type-II Censoring Scheme

Bayesian and E-Bayesian Estimation for a Modified Topp Leone–Chen Distribution Based on a Progressive Type-II Censoring Scheme

Optimal life-testing plans for joint progressively Type-II censored Birnbaum-Saunders distributions with compound optimal criteria

ABSTRACT In this paper, we first derive the maximum likelihood estimates (MLEs) of the parameters of Birnbaum-Saunders (BISA) distributions based on the joint progressive Type-II censored (JPC) samples. We also discuss using the EM algorithm to obtain the MLEs of the model parameters. Then, we determine the single-objective-criterion optimal JPC schemes for BISA distributions based on the cost minimization criterion, A -optimality criterion, and D -optimality criterion by the complete search method, variable neighborhood search (VNS) algorithm and modified VNS (MVNS) algorithm. These algorithms are compared in terms of accuracy and computation time. In addition, we determine the compound-criterion optimal JPC schemes based on different optimal criteria and the reasonably efficient compound optimal JPC schemes for two competing statistical models, such as the inverse Gaussian and BISA models. The advantages of using the compound optimal scheme over the single-objective-criterion optimal scheme are demonstrated through a real-life data set on the micro-indentation test about the hardness of polymeric bone cement.

Inference on exponentiated Rayleigh distribution with constant stress partially accelerated life tests under progressive type-II censoring

This study aims to explore the issues of evaluating the parameters and the accelerating factor based on constant stress for partially accelerating life tests when the potential failure times have an exponentiated Rayleigh distribution. Within the framework of progressive Type-II censoring schemes, we employ the Newton-Raphson algorithm as an iterative methodology to gain the maximum likelihood estimates, accompanied by proof of the existence of these point estimators. We also construct asymptotic confidence intervals for interested parameters and acceleration factors by utilizing the asymptotical characteristics of the maximum likelihood estimators. The Bayesian estimations of unknown parameters are derived by using the independent gamma priors and dependent Gamma-Dirichlet prior on the basis of square error and relatively smooth LINEX loss functions, respectively. Furthermore, we adopt the importance sampling method to compute Bayesian point estimates and the credible intervals with the highest posterior density. To validate the effectiveness of the suggested approaches, a series of simulated experiments are carried out. Lastly, we conduct analyzes on two actual datasets to show the applicability of the suggested techniques.

Data analysis with applications in physics and engineering using XLindley model with improved adaptive Type-II progressively censored samples

Recently, a novel improved adaptive Type-II progressive censoring strategy has been suggested in order to obtain adequate data from trials that require a lengthy amount of time. Considering this scheme, this paper focuses on various classical and Bayesian estimation challenges for parameter and some reliability metrics for the XLindley distribution. Two classical estimation methods are considered from the classical perspective to get the point and interval estimations of the model parameter as well as reliability and hazard rate functions. In addition to the usual approaches, the Bayesian methodology is looked at by leveraging the squared error loss function and the Markov chain Monte Carlo technique. The Bayes point and credible intervals are obtained based on two forms of the posterior distribution. A simulation examination is implemented adopting multiple circumstances to distinguish between the conventional and Bayesian estimations. The simulation results demonstrate that the Bayesian approach using the likelihood function is superior for estimating the model parameter when compared with the other methods. In contrast, when estimating reliability metrics, it is advisable to utilize the Bayesian method with the spacings function. Two real-world data sets are analyzed to integrate the proposed approaches into practice, and the ideal progressive censoring strategy is chosen using some optimality criteria.

Parameter estimation of Chen distribution under improved adaptive type-II progressive censoring

ABSTRACT This study focuses on the estimation of the two unknown parameters of Chen distribution, characterized by a bathtub-shaped hazard rate function, within an improved adaptive type-II progressive censored data framework. Maximum likelihood estimation is proposed for the two parameters, and the establishment of approximate confidence intervals is based on asymptotic normality. Bayesian estimation is also conducted under both symmetric and asymmetric loss functions, utilizing the proposed importance sampling and Metropolis–Hastings algorithm. Lastly, the performance of various estimation methods is evaluated through Monte Carlo simulation experiments, and the proposed estimation approach is illustrated using a real dataset.

The Role of Risk Factors in System Performance: A Comprehensive Study with Adaptive Progressive Type-II Censoring

The quality performance of many vital systems depends on how long the units are performing; hence, research works started focusing on increasing the reliability of systems while taking into consideration that many factors may cause the failures of operating systems. In this study, the combination of a parametric generalized linear failure rate distribution model and an adaptive progressive Type-II censoring scheme for practical purposes is explored. A comprehensive investigation is performed on the risk factors that cause failure and determines which of the factors has a more harmful effect on the units. A lifetime experiment is performed under the condition of an adaptive progressive Type-II censoring scheme to obtain observations as a result of the competing factors of failures. The obtained observations are assumed to follow a three-parameter generalized linear failure rate distribution and are assumed to be competing to cause failure. Two statistical inference methods are employed for estimating this model’s parameters: the frequentist maximum likelihood method and the Bayesian approach. Our model’s validity is demonstrated through extensive simulations and real data applications in the medical and electrical engineering fields.

Statistical analysis of double stress accelerated life testing under adaptive type-Ⅱ progressive censoring

Aiming at the traditional accelerated life test only considering the single stress and single failure cause, the inference method of double stress accelerated competing risks data is studied under the adaptive type-Ⅱ progressively censored and the life of test units follow Weibull distribution. The maximum likelihood estimations and the asymptotic confidence intervals of unknown parameters are obtained by using the Newton-Raphson iteration and asymptotic likelihood theory. A Gibbs sampling combining with Metropolis-Hasting algorithm method is developed to obtain Bayes estimations, and the Monte Carlo method is employed to construct the HPD credible intervals. The simulated results show that the present method has good statistical inference performance, meanwhile the failure sample size and the expected experimentation time have significant effect on the estimations.

Estimation of Marshall–Olkin Extended Generalized Extreme Value Distribution Parameters under Progressive Type-II Censoring by Using a Genetic Algorithm

In this article, we consider the statistical analysis of the parameter estimation of the Marshall–Olkin extended generalized extreme value under liner normalization distribution (MO-GEVL) within the context of progressively type-II censored data. The progressively type-II censored data are considered for three specific distribution patterns: fixed, discrete uniform, and binomial random removal. The challenge lies in the computation of maximum likelihood estimations (MLEs), as there is no straightforward analytical solution. The classical numerical methods are considered inadequate for solving the complex MLE equation system, leading to the necessity of employing artificial intelligence algorithms. This article utilizes the genetic algorithm (GA) to overcome this difficulty. This article considers parameter estimation through both maximum likelihood and Bayesian methods. For the MLE, the confidence intervals of the parameters are calculated using the Fisher information matrix. In the Bayesian estimation, the Lindley approximation is applied, considering LINEX loss functions and square error loss, suitable for both non-informative and informative contexts. The effectiveness and applicability of these proposed methods are demonstrated through numerical simulations and practical real-data examples.

Reliability inference for a family of inverted exponentiated distributions under block progressive Type II censoring

In this article, estimation of survival characteristics is discussed when life tests are performed against different test facilities using block progressive Type-II censoring. Under the assumption that the lifetimes of test units follow a family of inverted exponentiated distributions, estimates are derived under classical and hierarchical Bayesian frameworks when the differences in different test facilities are taken into consideration. Maximum likelihood estimators are obtained and their existence and uniqueness properties are also established. In addition, Bayes estimators are provided under a hierarchical framework, and a hybrid Metropolis-Hastings sampling procedure is proposed for complex posterior computation. The performance of all the proposed approaches is compared via extensive simulation studies and two real-life data are analyzed for illustration. From numerical results we observe that the hierarchical approach provides relatively better estimates for model parameters.

Estimation of stress-strength reliability in s-out-of-k system for new flexible exponential distribution under progressive type-II censoring

This article addresses stress-strength reliability estimation in s-out-of-k systems under progressive type-II censoring. The system consists of components facing common stress, where stress and strength variable follows independent new flexible exponential (NFE) distributions, sharing a common parameter. The estimation procedure is carried out using MLE, Bayesian estimation and uniformly minimum variance unbiased estimation (UMVUE) techniques. MLE is derived for known and unknown common parameters. Bayesian estimates are obtained using Lindley’s approximation and Markov chain Monte Carlo techniques due to the complexity of obtaining the exact Bayesian estimates, when the common parameter is unknown. Moreover, UMVUE is derived when the common parameter is known. The 95% asymptotic confidence interval, highest posterior density credible intervals, and Bayesian credible intervals, are constructed. An extensive simulation study is carried out to compare the performance of various censoring schemes and estimation methods. Finally, two progressively censored real datasets are analyzed for illustration.

Bayesian Inference for Inverse Power Exponentiated Pareto Distribution Using Progressive Type-II Censoring with Application to Flood-Level Data Analysis

Progressive type-II (Prog-II) censoring schemes are gaining traction in estimating the parameters, and reliability characteristics of lifetime distributions. The focus of this paper is to enhance the accuracy and reliability of such estimations for the inverse power exponentiated Pareto (IPEP) distribution, a flexible extension of the exponentiated Pareto distribution suitable for modeling engineering and medical data. We aim to develop novel statistical inference methods applicable under Prog-II censoring, leading to a deeper understanding of failure time behavior, improved decision-making, and enhanced overall model reliability. Our investigation employs both classical and Bayesian approaches. The classical technique involves constructing maximum likelihood estimators of the model parameters and their bootstrap covariance intervals. Using the Gibbs process constructed by the Metropolis–Hasting sampler technique, the Markov chain Monte Carlo method provides Bayesian estimates of the unknown parameters. In addition, an actual data analysis is carried out to examine the estimation process’s performance under this ideal scheme.

Estimation and Optimal Censoring Plan for a New Unit Log-Log Model via Improved Adaptive Progressively Censored Data

To gather enough data from studies that are ongoing for an extended duration, a newly improved adaptive Type-II progressive censoring technique has been offered to get around this difficulty and extend several well-known multi-stage censoring plans. This work, which takes this scheme into account, focuses on some conventional and Bayesian estimation missions for parameter and reliability indicators, where the unit log-log model acts as the base distribution. The point and interval estimations of the various parameters are looked at from a classical standpoint. In addition to the conventional approach, the Bayesian methodology is examined to derive credible intervals beside the Bayesian point by leveraging the squared error loss function and the Markov chain Monte Carlo technique. Under varied settings, a simulation study is carried out to distinguish between the standard and Bayesian estimates. To implement the proposed procedures, two actual data sets are analyzed. Finally, multiple precision standards are considered to pick the optimal progressive censoring scheme.

Reliability estimation for Kumaraswamy distribution under block progressive type-II censoring

In this article, estimates of reliability performance characteristics are discussed when life test is conducted upon various test facilities under block progressive type-II censoring. When the differences in different test facilities are taken into account and lifetime of products follows a distribution with Kumaraswamy hazard function, different estimates are obtained from classical and hierarchical Bayesian frameworks, respectively. The existence and uniqueness of maximum likelihood estimators of model parameters are established, and approximate confidence intervals are obtained as well based on asymptotic theory and delta method. Moreover, associated Bayes estimators are also evaluated using a hybrid Metropolis–Hasting sampling in hierarchical framework. Finally, performances of the proposed approaches are compared via extensive simulation study, and two real data examples are also presented for application viewpoint.

On the study of the recurrence relations and characterizations based on progressive first-failure censoring

<abstract> <p>In this research, the progressive first-failure censored data (PFFC) from the Kumaraswamy modified inverse-Weibull distribution (KMIWD) were used to obtain the recurrence relations and characterizations for single and product moments. The recurrence relationships allow for a rapid and efficient assessment of the means, variances and covariances for any sample size. Additionally, the paper outcomes can be boiled down to the traditional progressive type-II censoring. Also, some special cases are limited to some lifetime distributions as the exponentiated modified inverse Weibull and Kumaraswamy inverse exponential.</p> </abstract>

Reliability analysis for two populations Nadarajah-Haghighi distribution under Joint progressive type-II censoring

<abstract><p>In order to evaluate the competitive advantages and dependability of two products in a competitive environment, comparative lifespan testing becomes essential. We examine the inference problems that occur when two product lines follow the Nadarajah-Haghighighi distribution in the setting of joint type-II censoring. In the present study, we derived the maximum likelihood estimates for the Nadarajah-Haghighi population parameters. Additionally, a Fisher information matrix was constructed based on these maximum likelihood estimations. Furthermore, Bayesian estimators and their corresponding posterior risks were calculated, considering both gamma and non-informative priors under symmetric and asymmetric loss functions. To assess the performance of the overall parameter estimators, we conducted a Monte Carlo simulation using numerical methods. Lastly, a real data analysis was carried out to validate the accuracy of the models and methods discussed.</p></abstract>

Statistical inference for the step-stress model with competing risks from the Kumaraswamy distribution under progressive type-II censoring

In reliability and life analysis, the accelerated life test is frequently used because it can reduce cost and obtain additional reliability and lifetime information. In addition, when a unit fails in a life test, there are often two or more risk factors related to the cause of the failure. In this article, we consider the inference from a step-stress-accelerated life test with competing risks using progressive type-II censored data. Based on the assumption that the parameters affected by stress follow a log-linear model with the stress level, the proportional hazard model with the Kumaraswamy distribution is established. The point estimation of the unknown parameters is derived using maximum likelihood and Bayesian methods. Accordingly, the logarithmic asymptotic confidence and the highest posterior density credible intervals are derived and constructed. Moreover, the algorithm for multi-parameter sampling and simulation technology based on this model is given. Simulation results show that the proposed methods have good performance. In light of the estimates of the parameters, the estimated reliability function under normal conditions can be expressed, and its images under different methods are drawn. Last, a real dataset and a set of simulated data are presented for illustrative purposes.

Bayesian and non-Bayesian analysis for the lifetime performance index based on generalized order statistics from Pareto distribution

<p>Modern businesses depend on efficient management and evaluation of product quality performance to assure that they are on the right track, and process capability analysis is used to gauge business performance in practice. Consequently, the lifetime performance index (LPI) , where is the lower specification limit, is used to gauge a process potential and performance. This paper examines distinct estimators of under Pareto distribution using generalized order statistics (GOS), which is very helpful in a variety of real-world applications. Results for progressive type II censoring (PTIIC) and first-failure censoring are two particular situations. Using symmetric and asymmetric loss functions, the Bayesian estimator was built, then utilized to produce the hypothesis testing technique. A simulation study and real data analysis have been investigated to study the behavior of different estimates for under different schemes, namely PTIIC and the progressive first failure censored scheme.</p>