Progressive Type-II Censoring Research Articles

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>

Stress–Strength Reliability Analysis for Different Distributions Using Progressive Type-II Censoring with Binomial Removal

In the statistical literature, one of the most important subjects that is commonly used is stress–strength reliability, which is defined as δ=PW<V, where V and W are the strength and stress random variables, respectively, and δ is reliability parameter. Type-II progressive censoring with binomial removal is used in this study to examine the inference of δ=PW<V for a component with strength V and being subjected to stress W. We suppose that V and W are independent random variables taken from the Burr XII distribution and the Burr III distribution, respectively, with a common shape parameter. The maximum likelihood estimator of δ is derived. The Bayes estimator of δ under the assumption of independent gamma priors is derived. To determine the Bayes estimates for squared error and linear exponential loss functions in the lack of explicit forms, the Metropolis–Hastings method was provided. Utilizing comprehensive simulations and two metrics (average of estimates and root mean squared errors), we compare these estimators. Further, an analysis is performed on two actual data sets based on breakdown times for insulating fluid between electrodes recorded under varying voltages.

Statistical inference for the partial area under ROC curve for the lower truncated proportional hazard rate models based on progressive Type-II censoring

This paper considers inference on the partial area under the receiver operating characteristic curve based on two independent progressively Type-II censored samples from the populations that are belonging to the lower truncated proportional hazard rate models with the same baseline distributions. The maximum likelihood estimator, a generalized pivotal estimator and some Bayes estimators are obtained for three structures of prior distributions. The percentile bootstrap confidence interval, a generalized pivotal confidence interval and some Bayesian credible intervals are also presented. A Monte-Carlo simulation study is used to evaluate the performances of the obtained point estimators and confidence and credible intervals. Finally, a real data set is applied for illustrative purposes.

Estimation of stress-strength reliability for generalized Gompertz distribution under progressive type-II censoring

In this study, the stress-strength reliability, $R=P(Y

Analysis of the Stress–Strength Model Using Uniform Truncated Negative Binomial Distribution under Progressive Type-II Censoring

In this study, we introduce a novel estimation technique for assessing the reliability parameter R=P(Y<X) of the uniform truncated negative binomial distribution (UTNBD) in the context of stress–strength analysis. We base our inferences on the assumption that both the strength (X) and stress (Y) random variables follow a UTNBD with identical first shape and scale parameters. In the presence of a progressive type-II censoring scheme, we employ maximum likelihood, two parametric bootstrap methods, and Bayesian estimation approaches to derive the estimators. Due to the complexity introduced by censoring, the estimators are not available in explicit forms and are instead obtained through numerical approximation techniques. Furthermore, we compute the highest posterior density credible intervals and determine the asymptotic variance-covariance matrix. To assess the performance of our proposed estimators, we conduct a Monte Carlo simulation study and provide a comparative analysis. Finally, we illustrate the practical applicability of our study with an engineering application.

Lindley’s method and MCMC technique for estimating the exponentiated Kies lifetime model parameters and reliability characteristics using adaptive type-II progressive censoring with application

In this paper, statistical inferences for the parameters, reliability, and failure rate functions (as parameters) of the exponentiated Kies distribution are accomplished using maximum likelihood and both Lindley and Markov chain Monte Carlo techniques, under adaptive Type-II progressive censoring. Depending on the Fisher information matrix and the delta method, we find the approximate confidence intervals for the parameters and the reliability and failure rate functions, respectively. Furthermore, the samples generated from Markov chains Monte Carlo are used to generate credible intervals for the parameters, reliability, and failure rates functions. Symmetric and asymmetric loss functions are also used to find Bayes estimators using Markov chain Monte Carlo and Lindley techniques. Comparisons between the two techniques of evaluation for different estimators under different sizes of data sets are conducted. Finally, a real-life example is applied to clarify the results of the used techniques.

Optimal sampling and statistical inferences for Kumaraswamy distribution under progressive Type-II censoring schemes

In this paper, we study non-Bayesian and Bayesian estimation of parameters for the Kumaraswamy distribution based on progressive Type-II censoring. First, the maximum likelihood estimates and maximum product spacings are derived. In addition, we derive the asymptotic distribution of the parameters and the asymptotic confidence intervals. Second, Bayesian estimators under symmetric and asymmetric loss functions (Squared error, linear exponential, and general entropy loss functions) are also obtained. The Lindley approximation and the Markov chain Monte Carlo method are used to derive the Bayesian estimates. Furthermore, we derive the highest posterior density credible intervals of the parameters. We further present an optimal progressive censoring scheme among different competing censoring scheme using three optimality criteria. Simulation studies are conducted to evaluate the performance of the point and interval estimators. Finally, one application of real data sets is provided to illustrate the proposed procedures.

Inference and optimal censoring scheme for a competing-risks model with type-II progressive censoring

ABSTRACT For statistical inference of competing risks under type-II progressive censoring, lifetimes are modeled by an inverted exponential Rayleigh distribution, which allows the use of a non-monotonic hazard function. Maximum-likelihood estimators for all parameters exist and are unique. The Newton-Raphson algorithm and maximum stochastic expectation each provide estimates. Confidence intervals result from the Fisher matrix and the asymptotic normality of maximum-likelihood estimators. For small samples, the Bootstrap estimators of the parameters do not need to be asymptotically normal. In addition, the Monte Carlo method with the Metropolis-Hastings algorithm and importance sampling allow for Bayesian estimation, with the associated highest posterior-density intervals. The Bayesian method takes account of prior information, contrary to the frequentist method. The Bootstrap method improves the precision of the estimation, especially in the case of small sample sizes. The estimated range obtained by Bootstrap is between 20% and 60% smaller than that obtained by maximum likelihood. Frequentist and Bayesian estimations using the inverted exponentiated Rayleigh distribution under type-II progressive censoring allow for fitting empirical mouse mortality data and obtaining parameter estimates of this distribution. A quantile-dependent criterion and a quantile-independent criterion are used to determine the optimal censoring and to design the experiment.

A New Asymmetric Modified Topp–Leone Distribution: Classical and Bayesian Estimations under Progressive Type-II Censored Data with Applications

In this article, a new modified asymmetric Topp–Leone distribution is created and developed from a theoretical and inferential point of view. It has the feature of extending the remarkable flexibility of a special one-shape-parameter lifetime distribution, known as the inverse Topp–Leone distribution, to the bounded interval [0, 1]. The probability density function of the proposed truncated distribution has the potential to be unimodal and right-skewed, with different levels of asymmetry. On the other hand, its hazard rate function can be increasingly shaped. Some important statistical properties are examined, including several different measures. In practice, the estimation of the model parameters under progressive type-II censoring is considered. To achieve this aim, the maximum likelihood, maximum product of spacings, and Bayesian approaches are used. The Markov chain Monte Carlo approach is employed to produce the Bayesian estimates under the squared error and linear exponential loss functions. Some simulation studies to evaluate these approaches are discussed. Two applications based on real-world datasets—one on the times of infection, and the second dataset is on trading economics credit rating—are considered. Thanks to its flexible asymmetric features, the new model is preferable to some known comparable models.

Maximum Product Spacings for the Kumaraswamy Distributions Based on Progressive Type-II Censoring Schemes

Maximum Product Spacings for the Kumaraswamy Distributions Based on Progressive Type-II Censoring Schemes

Reliability estimation for bathtub-shaped distribution under block progressive 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 the lifetime of products follows a bathtub-shaped hazard rate distribution, different estimates are obtained from classical and hierarchical Bayesian frameworks, respectively. 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 a real data example is also presented for application viewpoint.

The Process Capability Index of Pareto Model under Progressive Type-II Censoring: Various Bayesian and Bootstrap Algorithms for Asymmetric Data

It is agreed by industry experts that manufacturing processes are evaluated using quantitative indicators of units produced from this process. For example, the Cpy process capability index is usually unknown and therefore estimated based on a sample drawn from the requested process. In this paper, Cpy process capability index estimates were generated using two iterative methods and a Bayesian method of estimation based on stepwise controlled type II data from the Pareto model. In iterative methods, besides the traditional probability-based estimation, there are other competitive methods, known as bootstrap, which are alternative methods to the common probability method, especially in small samples. In the Bayesian method, we have applied the Gibbs sampling procedure with the help of the significant sampling technique. Moreover, the approximate and highest confidence intervals for the posterior intensity of Cpy were also obtained. Massive simulation studies have been performed to evaluate the behavior of Cpy. Ultimately, application to real-life data is seen to demonstrate the proposed methodology and its applicability.

Inference of improved adaptive progressively censored competing risks data for Weibull lifetime models

AbstractRecently, an improved adaptive Type-II progressive censoring scheme is proposed to ensure that the experimental time will not pass a pre-fixed time and ends the test after recording a pre-fixed number of failures. This paper studies the inference of the competing risks model from Weibull distribution under the improved adaptive progressive Type-II censoring. For this goal, we used the latent failure time model with Weibull lifetime distributions with common shape parameters. The point and interval estimation problems of parameters, reliability and hazard rate functions using the maximum likelihood and Bayesian estimation methods are considered. Moreover, making use of the asymptotic normality of classical estimators and delta method, approximate intervals are constructed via the observed Fisher information matrix. Following the assumption of independent gamma priors, the Bayes estimates of the scale parameters have closed expressions, but when the common shape parameter is unknown, the Bayes estimates cannot be formed explicitly. To solve this difficulty, we recommend using Markov chain Monte Carlo routine to compute the Bayes estimates and to construct credible intervals. A comprehensive Monte Carlo simulation is conducted to judge the behavior of the offered methods. Ultimately, analysis of electrodes data from the life-test of high-stress voltage endurance is provided to illustrate all proposed inferential procedures.