Hybrid Censoring Scheme Research Articles

Fuzzy multicomponent stress-strength reliability in presence of partially accelerated life testing under generalized progressive hybrid censoring scheme subject to inverse Weibull model

It typically takes a lot of time to monitor life-testing experiments on a product or material. Units can be tested under harsher conditions than usual, known as accelerated life tests to shorten the testing period. This study's goal is to investigate the issue of partially accelerated life testing that use generalized progressive hybrid censored samples to estimate the stress-strength reliability in the multicomponent case. Also, the fuzziness of the model is considered that gives more sensitive and accurate analyses about the underlying system. Maximum likelihood estimation method under the inverse Weibull distribution and using the generalized progressively hybrid censoring scheme is introduced to obtain an estimator for the fuzzy multicomponent stress-strength reliability. Also, an asymptotic confidence interval is deduced to examine the reliability of the fuzzy multicomponent stress-strength. Simulation study is conducted using maximum likelihood estimates and confidence intervals for the fuzzy multicomponent stress-strength reliability for different values of the parameters and different schemes. A real data application representing the data for the failure times for a certain software model is introduced to obtain the fuzzy multicomponent stress-strength reliability for different schemes.•The fuzzy multicomponent stress-strength reliability is investigated under partially accelerated life testing and the generalized progressively hybrid censored scheme.•An algorithm is introduced to simulate data for the censoring scheme.•A real data application is presented to obtain the fuzzy multicomponent stress-strength reliability at different schemes.

Exponentiated gamma constant-stress partially accelerated life tests with unified hybrid censored data: Statistical inferences

This study considers one of the partially accelerated life testing models, mainly a constant-stress approach with unified hybrid censored data. The data represents the lifetime of units following the exponentiated gamma distribution (EGD). The estimation techniques for the parameter of EGD and the acceleration factor are discussed, along with the maximum likelihood estimation technique, the Bayesian and E-Bayesian estimation. Utilizing the squared error loss (SEL) and LINEX loss functions, the E-Bayesian and Bayesian estimates are generated. For deriving the estimates of Bayesian and E-Bayesian approaches, we use the MCMC method. Real-world data is also provided for illustration. Furthermore, unified hybrid censoring schemes (HCSs) are examined to determine their effectiveness in the light of the results. In the end, we compare among the proposed methods during their findings. The study's findings demonstrate how well the suggested techniques work when utilizing unified HCS. The study also makes clear how important it is to adopt the CSPALT model, as it yields more failed things in a shorter amount of time than items with typical use situations. In conclusion, it is suggested that this research be used to tasks like industrial product reliability testing.

Comparative Study with Applications for Gompertz Models under Competing Risks and Generalized Hybrid Censoring Schemes

In reliability and survival analysis, the time-to-failure data play an important role in the development of the reliability and life characteristics of the products. In some cases, these kinds of data are modeled using a competing risks model. The problem of conducting comparative life testing under a competing risks model when the units come from different lines of production has recently been addressed. In this paper, we address this problem when the life of the unit is distributed using the Gompertz distribution, noting that the units come from two lines of production and two independent causes of failure are activated. The data are collected under a joint generalized type-II hybrid censoring scheme. Maximum likelihood estimators of the unknown parameters are derived, along with the corresponding asymptotic confidence intervals. We also adopt two bootstrap confidence intervals. Using independent gamma priors, the Bayes estimators relative to squared error loss function are obtained with credible intervals. The properties and quality of estimators are measured by performing a Monte Carlo simulation study. Finally, a real-life data set is analyzed to discuss the applicability of the proposed methods to real phenomena. The optimal plan with respect to comments on the numerical results is discussed in the conclusion.

Analysis of Two Generalized Exponential Populations Under Joint Type-I Progressive Hybrid Censoring Scheme

Analysis of Two Generalized Exponential Populations Under Joint Type-I Progressive Hybrid Censoring Scheme

An Improved Conditional Inference on General Lifetime Model Parameters

It is widely known that the conditional inference is usually efficient as the Bayesian inference based on the non-informative prior. However, it is less efficient than the Bayesian inference based on the informative prior. Therefore, the main objective of this paper is to introduce an improvement to the conditional inference by using the kernel prior distribution. The improved conditional inference has been used for estimating the general lifetime model parameters, based on the generalized progressive hybrid-censoring scheme, and compared with the Bayesian estimates, via the Monte Carlo simulations. The simulation results have been shown that the improved conditional inference is highly efficient and provides better estimates than the Bayesian estimates based on different loss functions. Finally, real data sets have been given to demonstrate the efficiencies of the proposed methods

Estimating the Parameters of an Exponentiated Logistic Distribution under Progressive Hybrid Censoring Scheme

As the progressive hybrid censoring scheme (PHCS) and exponentiated logistic distribution (ELD) are widely employed in reliability and survival analysis, it is necessary to infer on ELD parameters under PHCS. The maximum product spacings estimator (MPSE) is effective and authors advocated the use of this method as an alternative to maximum likelihood estimator (MLE), and found that MPSE provides better estimates than MLE in various situations. In this paper, we propose the MPSEs for the parameters of the ELD under PHCS. Also, we derive the approximate MPSEs for the parameters of ELD using Talyor series expansion. And we compare the proposed estimators (MPSEs and approximate MPSEs) in the sense of mean squared error (MSE) under PHCS. The progressive hybrid censored data (PHCD) from the ELD are generated for data size = 25, 30, 35, 40, 45 and various PHCS. Using this generated data, the MSEs and biases of MPSE and approximate MPSE are simulated by the Monte Carlo method based on 1,000 times for = 25, 30, 35, 40, 45 and various PHCD. As a result, approximate MPSEs are better than the corresponding MPSEs. Further, a real data set (strength on GPA for single carbon fibers of 10mm in gauge lengths) has been analyzed.

Bayes and Maximum Likelihood Estimation of Uncertainty Measure of the Inverse Weibull Distribution under Generalized Adaptive Progressive Hybrid Censoring

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.

Bayesian Sampling Plan for the Exponential Distribution with Generalized Type-I Hybrid Censoring Scheme

Bayesian Sampling Plan for the Exponential Distribution with Generalized Type-I Hybrid Censoring Scheme

A New Process Performance Index for the Weibull Distribution with a Type-I Hybrid Censoring Scheme

A new life performance index is proposed for evaluating the quality of lifetime products. The maximum likelihood estimation method and the Bayesian approaches using informative and non-informative prior distributions are utilized to infer the parameters of the Weibull distribution and the proposed new life performance index under a Type-I hybrid censoring scheme. Monte Carlo simulation results show that two Bayesian approaches outperform the maximum likelihood estimation method in terms of the measures of relative bias, relative mean square error, and coverage probability for the point and confidence interval estimators, respectively. The Bayesian approach using a non-informative prior distribution is recommended if the knowledge of setting up the hyper-parameters in the informative prior distribution is not available. Two real data sets are provided for illustration.

Statistical Analysis from the Generalized Inverse Lindley Distribution with Adaptive Type-II Progressively Hybrid Censoring Scheme

Statistical Analysis from the Generalized Inverse Lindley Distribution with Adaptive Type-II Progressively Hybrid Censoring Scheme

Inference on adaptive progressively hybrid censoring schemes under partially accelerated life test for OLiHL distribution

AbstractThis article estimates failure times in step‐stress partially accelerated life tests (ALTs) using a new censoring scheme named adaptive Type‐I progressive hybrid censoring scheme (APHCS), where the lifetimes follow odd Lindley Half‐Logistic (OLiHL) distribution. Classical estimation method is used to estimate the parameter of the proposed distribution and the acceleration factor (AF) under progressive hybrid censoring and adaptive progressive hybrid censoring (APHC) schemes. Also, a step‐stress partially ALT is assumed. Furthermore, the Monte Carlo simulation technique is implemented to check the performance of the estimates for biases and mean squared errors.

Multicomponent Stress-Strength Model Based on Generalized Progressive Hybrid Censoring Scheme: A Statistical Analysis.

The statistical inference of the reliability and parameters of the stress–strength model has received great attention in the field of reliability analysis. When following the generalized progressive hybrid censoring (GPHC) scheme, it is important to discuss the point estimate and interval estimate of the reliability of the multicomponent stress–strength (MSS) model, in which the stress and the strength variables are derived from different distributions by assuming that stress follows the Chen distribution and that strength follows the Gompertz distribution. In the present study, the Newton–Raphson method was adopted to derive the maximum likelihood estimation (MLE) of the model parameters, and the corresponding asymptotic distribution was adopted to construct the asymptotic confidence interval (ACI). Subsequently, the exact confidence interval (ECI) of the parameters was calculated. A hybrid Markov chain Monte Carlo (MCMC) method was adopted to determine the approximate Bayesian estimation (BE) of the unknown parameters and the high posterior density credible interval (HPDCI). A simulation study with the actual dataset was conducted for the BEs with squared error loss function (SELF) and the MLEs of the model parameters and reliability, comparing the bias and mean squares errors (MSE). In addition, the three interval estimates were compared in terms of the average interval length (AIL) and coverage probability (CP).

Future Failure Time Prediction Based on a Unified Hybrid Censoring Scheme for the Burr-X Model with Engineering Applications

Industries are constantly seeking ways to avoid corrective maintenance in order to reduce costs. Performing regular scheduled maintenance can help to mitigate this problem, but not necessarily in the most efficient way. In many real life applications, one wants to predict the future failure time of equipment or devices that are expensive, or with long lifetimes, to save costs and/or time. In this paper, statistical prediction was studied using the classical and Bayesian approaches based on a unified hybrid censoring scheme. Two prediction schemes were used: (1) a one-sample prediction scheme that predicted the unobserved future failure times of devices that did not complete the lifetime experiments; and (2) a two-sample prediction scheme to predict the ordered values of a future independent sample based on past data from a certain distribution. We chose to apply the results of the paper to the Burr-X model, due to the importance of this model in many fields, such as engineering, health, agriculture, and biology. Point and interval predictors of unobserved failure times under one- and two-sample prediction schemes were computed based on simulated data sets and two engineering applications. The results demonstrate the ability of predicting the future failure of equipment using a statistical prediction branch based on collected data from an engineering system.

Estimations in a Constant‐Stress Partially Accelerated Life Test for Generalized Rayleigh Distribution under Type‐II Hybrid Censoring Scheme

The constant‐stress partially accelerated life test (CSPALT) model with Type‐II hybrid censoring scheme (Type‐II HCS) is the subject of our research. Units have a lifetime that follows the generalized Rayleigh distribution. Bayesian and E‐Bayesian estimates are derived by applying two of the loss functions, mainly the squared error loss (SEL) and LINEX loss functions. Bayesian and E‐Bayesian estimates are obtained using Markov chain Monte Carlo (MCMC) methods. To prove the applicability and the importance of the subject, a test for real data will be provided. To evaluate the distribution’s effectiveness, we utilized a variety of datasets and proposed several kinds of censoring. Finally, all results are compared in order to determine the effectiveness of the proposed methods. All major findings are concluded in the conclusion section.

Classical and Bayesian Inference under Burr‐X Distribution Based on New Unified Progressive Hybrid Censoring Scheme with Engineering Applications

In this paper, a new unified progressive hybrid censoring scheme (UPHCS) has been constructed. This unified censoring scheme covers eleven famous censoring schemes. The estimation problem of Burr‐X distribution parameters has been studied using the maximum likelihood and Bayes approaches based on the suggested unified progressive hybrid censored samples. Two real data sets have been used as illustrative engineering examples.

Type-I Progressive Hybrid Censoring Scheme: Bayesian Estimation for the Pareto Distribution of the Second Kind

The use of Pareto Distribution of the second kind as a lifetime model is advocated by many authors. For this distribution, we derive maximum likelihood and Bayes estimators of the parameters and reliability function under typeI progressive hybrid censoring scheme. The Bayes estimates are obtained under squared-error, General Entropy (GE) loss function and LINEX loss functions using Lindley's approximation. A simulation study is also done to show the performance of the results

On reliability estimation of Nadarajah–Haghighi distribution under adaptive type‐I progressive hybrid censoring scheme

AbstractIn this paper, the maximum likelihood and Bayesian estimation methods are considered to estimate the unknown parameters, reliability, and hazard rate functions of the Nadarajah–Haghighi (NH) distribution based on adaptive type‐I progressive hybrid censoring (ATIPHC) scheme. The Bayesian estimation is obtained under the assumption of independent gamma priors. The Bayes estimators cannot be obtained in closed form, therefore Lindley's approximation and Markov chain Monte Carlo (MCMC) method are used to solve this problem. The approximate confidence (ACIs) and credible intervals are also considered. To compare the efficiency of the different proposed estimators, a simulation study is considered and the performance of the different estimators are compared using mean square error (MSE) and interval length criterion. Finally, one real data set is analyzed in order to show how these mentioned estimators can be applied in practice. The simulation and real data analysis showed that the Bayes estimates have the smallest MSEs and the BCIs have the smallest lengths compared to their conventional counterparts.

Statistical Inference under Copula Approach of Accelerated Dependent Generalized Inverted Exponential Failure Time with Progressive Hybrid Censoring Scheme

Statistical Inference under Copula Approach of Accelerated Dependent Generalized Inverted Exponential Failure Time with Progressive Hybrid Censoring Scheme

EM Algorithm for Mixture Distributions Model with Type-I Hybrid Censoring Scheme

An expectation–maximization (EM) likelihood estimation procedure is proposed to obtain the maximum likelihood estimates of the parameters in a mixture distributions model based on type-I hybrid censored samples when the mixture proportions are unknown. Three bootstrap methods are applied to construct the confidence intervals of the model parameters. Monte Carlo simulations are conducted to evaluate the performance of the proposed methods. Simulation results show that the proposed methods can perform well to obtain reliable point and interval estimation results. Three examples are used to illustrate the applications of the proposed methods.

Partially Accelerated Model for Analyzing Competing Risks Data from Gompertz Population under Type-I Generalized Hybrid Censoring Scheme

In reliability engineering and lifetime analysis, many units of the product fail with different causes of failure, and some tests require stress higher than normal stress. Also, we need to design the life experiments which present methodology for formulating scientific and engineering problems using statistical models. So, in this paper, we adopted a partially constant stress accelerated life test model to present times to failure in a small period of time for Gompertz life products. Also, considering that, units are failing with the only two independent causes of failure and tested under type-I generalized hybrid censoring scheme the data built. Obtained data are analyzed with two methods of estimations, maximum likelihood and Bayes methods. These two methods are used to construct the point and interval estimators with the help of the MCMC method. The developed results are measured and compared under Monte Carlo studying. Also, a data set is analyzed for illustration purposes. Finally, some comments are presented to describe the numerical results.