Censored Samples Research Articles

Analysis of Reliability for the Electrical Industries Company in Diyala using Modified Extension Weibull Distribution (An Application and Simulation study)

In this paper defining modified extension Weibull distribution, reliability function and hazerd function, we explain the maximum likelihood method under type one censoring sample. The censored samples play an important role in reliability analysis .In this paper we estimate and derived modified extension Weibull distribution whith three parameters under the censored samples type one by maximum likelihood estimation method depend on Newton-Raphson method. Then we applied simulation procedure using Monte-Carlo technique to estimate reliability function under different samples sizes and various initial values for the parameters for all estimated parameters of modified extension Weibull model by used MATLAB program. Finally we find the probability density function f(t), reliability function R(t),and hazard function h(t) for real data which get it from (Diyala province Company) is one of the formations of the Ministry of Industry and Minerals. Paper type: Research paper

Analysis of Reliability for the Electrical Industries Company in Diyala using Modified Extension Weibull Distribution (An Application and Simulation study)

In this paper defining modified extension Weibull distribution, reliability function and hazerd function, we explain the maximum likelihood method under type one censoring sample. The censored samples play an important role in reliability analysis .In this paper we estimate and derived modified extension Weibull distribution whith three parameters under the censored samples type one by maximum likelihood estimation method depend on Newton-Raphson method. Then we applied simulation procedure using Monte-Carlo technique to estimate reliability function under different samples sizes and various initial values for the parameters for all estimated parameters of modified extension Weibull model by used MATLAB program. Finally we find the probability density function f(t), reliability function R(t),and hazard function h(t) for real data which get it from (Diyala province Company) is one of the formations of the Ministry of Industry and Minerals. Paper type: Research paper

Constant Stress-Partially Accelerated Life Tests of Vtub-Shaped Lifetime Distribution under Progressive Type II Censoring

In lifetime tests, the waiting time for items to fail may be long under usual use conditions, particularly when the products have high reliability. To reduce the cost of testing without sacrificing the quality of the data obtained, the products are exposed to higher stress levels than normal, which quickly causes early failures. Therefore, accelerated life testing is essential since it saves costs and time. This paper considers constant stress-partially accelerated life tests under progressive Type II censored samples. This is realized under the claim that the lifetime of products under usual use conditions follows Vtub-shaped lifetime distribution, which is also known as log-log distribution. The log–log distribution is highly significant and has several real-world applications since it has distinct shapes of its probability density function and hazard rate function. A graphical description of the log–log distribution is exhibited, including plots of the probability density function and hazard rate. The log–log density has different shapes, such as decreasing, unimodal, and approximately symmetric. Several mathematical properties, such as quantiles, probability weighted moments, incomplete moments, moments of residual life, and reversed residual life functions, and entropy of the log–log distribution, are discussed. In addition, the maximum likelihood and maximum product spacing methods are used to obtain the interval and point estimators of the acceleration factor, as well as the model parameters. A simulation study is employed to assess the implementation of the estimation approaches under censoring schemes and different sample sizes. Finally, to demonstrate the viability of the various approaches, two real data sets are investigated.

Bayesian inference for Laplace distribution based on complete and censored samples with illustrations

In this paper, Bayesian estimates are derived for the location and scale parameters of the Laplace distribution based on complete, Type-I, and Type-II censored samples under different prior settings. Subsequently, Bayesian point and interval estimates, as well as the associated statistical inference, are discussed in detail. The developed methods are then applied to two real data sets for illustrative purposes. Moreover, a detailed Monte Carlo simulation study is carried out for evaluating the performance of the inferential methods developed here. Finally, we provide a brief discussion of the established results to demonstrate their practical utility and present some associated problems of further interest. Overall, this study fills an existing gap in the development of Bayesian inferential techniques for the parameters of the two-parameter Laplace distribution, making this research innovative and offering more investigative implications. It showcases the potential for broader methodological applications of Bayesian inference for complex real-world data sets, especially in scenarios involving different forms of censoring. This research provides a critical tool for statistical analysis in different fields such as engineering and finance, where the Laplace distribution is frequently adopted as a fundamental model.

Classical and Bayesian estimation of multicomponent stress–strength reliability with power Lindley distribution under progressive first-failure censored samples

This research article presents a methodology for estimating the multicomponent reliability based on progressively first-failure censored samples, where the underlying distribution of stress and strength is modelled using the power Lindley distribution. The classical and Bayesian estimation methods are utilized for estimating the multicomponent reliability. In the Bayesian estimation, the Markov Chain Monte Carlo approximation method is employed to obtain the posterior mean under a generalized entropy loss function. Various intervals including asymptotic confidence, bootstrap-p confidence, bootstrap-t confidence, Bayesian credible, and highest posterior density credible intervals are computed. A simulation study is conducted to evaluate the performance of the proposed methodology. Also, two different real data applications are presented to illustrate the practicality of the approach.

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.

A new approach to estimate parameters of the two-parameter Weibull distribution

This study proposes a new approach to estimate the parameters of the two-parameter Weibull distribution in the case of complete (uncensored) or doubly Type II censored samples. The proposed estimators have closed forms and can be adapted to Type II right or Type II left censored samples. The new estimators are strongly consistent and the new shape estimator follows asymptotically a normal and the new scale estimator a lognormal distribution. Bias, mean square and efficiency performance of the new estimators are investigated through simulations and compared to some known estimation methods such as maximum likelihood estimation, method of moments, quantile estimation, maximum goodness of fit estimation, L-moments, U-statistics and bias-corrected maximum likelihood. According to the simulations, the newly proposed estimators seem to have good efficiency performance in comparison to the other methods, particularly in small samples. Furthermore, two real data sets are used to illustrate the new estimators.

Statistical inference of comparative generalized inverted exponential populations under joint adaptive progressive type-II censored samples

Design of efficient test plans to assessing product reliability rapidly, is a critical step to obtain product reliability accurately. In this paper, we are adopted the problem of statistical inference of two generalized inverted exponential populations in a competing duration. To save the balance between the optimal test time and the number of failures needing for statistical inference, joint adaptive type-II hybrid progressive censoring scheme is applied. The model parameters are estimated with classical methods (maximum likelihood and bootstrap) for point estimate and the corresponding confidence intervals. Also, Bayes estimators of model parameters are computed under importance sample technique with the corresponding Bayes credible intervals. A real data sets are analyzed for illustrating purposes. The results are compared and assessed through Monte Carlo simulation study.

Statistical inference for a two-parameter Rayleigh distribution under generalized progressive hybrid censoring scheme

The two-parameter Rayleigh distribution, as an extended distribution of the Rayleigh distribution, has been widely applied in reliability analysis. With the introduction of the location parameter, two-parameter Rayleigh distribution becomes more flexible in fitting real-data. In this paper, based on generalized progressively hybrid censored(GPHC) sample from the two-parameter Rayleigh distribution, Classical and Bayesian inferences are discussed. The Newton-Raphson(NR) and Expectation-Maximization(EM) algorithms are used to compute the maximum likelihood estimates(MLEs). As well as the asymptotic confidence interval(ACI) estimation is obtained through the asymptotic distribution theory of maximum likelihood estimation(MLE) and computation of the observed Fisher information matrix. In Bayesian frame, the estimation of unknown parameters and prediction of future observable are taken into consideration. Due to Bayesian estimation is challenging to compute precisely and for the purpose of comparison, the Lindley's approximation, the Tierney-Kadane(TK) approximation and Markov chain Monte Carlo(MCMC) method are employed to obtain Bayesian estimates. Then, combining the MCMC algorithm mentioned in the article, the one- and two- samples Bayesian prediction are obtained. Finally, the simulation results are provided and a real-life data set is used for illustration purpose.

Evaluating the lifetime performance index of omega distribution based on progressive type-II censored samples

Besides achieving high quality products, statistical techniques are applied in many fields associated with health such as medicine, biology and etc. Adhering to the quality performance of an item to the desired level is a very important issue in various fields. Process capability indices play a vital role in evaluating the performance of an item. In this paper, the larger-the-better process capability index for the three-parameter Omega model based on progressive type-II censoring sample is calculated. On the basis of progressive type-II censoring the statistical inference about process capability index is carried out through the maximum likelihood. Also, the confidence interval is proposed and the hypothesis test for estimating the lifetime performance of products. Gibbs within Metropolis–Hasting samplers procedure is used for performing Markov Chain Monte Carlo (MCMC) technique to achieve Bayes estimation for unknown parameters. Simulation study is calculated to show that Omega distribution's performance is more effective. At the end of this paper, there are two real-life applications, one of them is about high-performance liquid chromatography (HPLC) data of blood samples from organ transplant recipients. The other application is about real-life data of ball bearing data. These applications are used to illustrate the importance of Omega distribution in lifetime data analysis.

Inference of reliability model with burr type XII distribution under two sample balanced progressive censored samples

Abstract The balanced joint progressive censoring scheme gives guidelines for researchers in reducing the expense and period of the experiment with modified efficiency. In this paper, the stress-strength reliability model are considered and investigated, in which two independent samples are generated from Burr Type XII distributions under balanced joint progressive censoring scheme. In the classical analysis, the maximum likelihood estimate of the reliability parameter is derived, then the relevant confidence interval is provided based on the Fisher matrix. Under the Bayesian framework, the Lindley’s technique and hybrid Gibbs within Metropolis-Hastings algorithm are applied to acquire the estimates of the parameters, and the corresponding highest posterior density credible interval of the reliability model is also constructed. The reliability inference is realized by numerical simulation, and the validity of the inference method is analyzed based on the splashing data of silicone oil droplets impact (SSODI) under two surfaces wettability conditions.

Inference and other aspects for $ q- $Weibull distribution via generalized order statistics with applications to medical datasets

<abstract><p>This work utilizes generalized order statistics (GOSs) to study the $ q $-Weibull distribution from several statistical perspectives. First, we explain how to obtain the maximum likelihood estimates (MLEs) and utilize Bayesian techniques to estimate the parameters of the model. The Fisher information matrix (FIM) required for asymptotic confidence intervals (CIs) is generated by obtaining explicit expressions. A Monte Carlo simulation study is conducted to compare the performances of these estimates based on type Ⅱ censored samples. Two well-established measures of information are presented, namely extropy and weighted extropy. In this context, the order statistics (OSs) and sequential OSs (SOSs) for these two measures are studied based on this distribution. A bivariate $ q $-Weibull distribution based on the Farlie-Gumbel-Morgenstern (FGM) family and its relevant concomitants are studied. Finally, two concrete instances of medical real data are ultimately provided.</p></abstract>

Inference of stress-strength reliability based on adaptive progressive type-Ⅱ censing from Chen distribution with application to carbon fiber data

<abstract><p>In this paper, we used the maximum likelihood estimation (MLE) and the Bayes methods to perform estimation procedures for the reliability of stress-strength $ R = P(Y < X) $ based on independent adaptive progressive censored samples that were taken from the Chen distribution. An approximate confidence interval of $ R $ was constructed using a variety of classical techniques, such as the normal approximation of the MLE, the normal approximation of the log-transformed MLE, and the percentile bootstrap (Boot-p) procedure. Additionally, the asymptotic distribution theory and delta approach were used to generate the approximate confidence interval. Further, the Bayesian estimation of $ R $ was obtained based on the balanced loss function, which came in two versions here, the symmetric balanced squared error (BSE) loss function and the asymmetric balanced linear exponential (BLINEX) loss function. When estimating $ R $ using the Bayesian approach, all the unknown parameters of the Chen distribution were assumed to be independently distributed and to have informative gamma priors. Additionally, a mixture of Gibbs sampling algorithm and Metropolis-Hastings algorithm was used to compute the Bayes estimate of $ R $ and the associated highest posterior density credible interval. In the end, simulation research was used to assess the general overall performance of the proposed estimators and a real dataset was provided to exemplify the theoretical results.</p></abstract>

Bayesian Estimation of a New Pareto-Type Distribution Based on Mixed Gibbs Sampling Algorithm

In this paper, based on the mixed Gibbs sampling algorithm, a Bayesian estimation procedure is proposed for a new Pareto-type distribution in the case of complete and type II censored samples. Simulation studies show that the proposed method is consistently superior to the maximize likelihood estimation in the context of small samples. Also, an analysis of some real data is provided to test the Bayesian estimation.

The Marshall–Olkin Pareto Type-I Distribution: Properties, Inference under Complete and Censored Samples with Application to Breast Cancer Data

In this paper, we introduce the Marshall–Olkin Pareto type-I (MOPTI) distribution. Structural properties of the MOPTI distribution including the quantile function, mean residual life, and a new theorem for strength-stress measure are introduced. Five methods of estimation for the MOPTI parameters based on complete samples are presented. Furthermore, we explore the estimation of the MOPTI parameters under type-I and type-II censoring. Two Monte Carlo simulation studies are conducted to evaluate the performance of the estimation methods under complete and censored samples. A real-life data set is used to validate the proposed methods.

Reliability Analysis and Its Applications for a Newly Improved Type-II Adaptive Progressive Alpha Power Exponential Censored Sample

Recently, a newly improved Type-II adaptive progressive censoring plan was devised, which can successfully ensure that the test length will not surpass a particular threshold period. In this study, we explore the statistical inference of the alpha power exponential distribution in the context of improved adaptive progressive Type-II censored data. The parameters, reliability, and hazard functions were estimated from both classical and Bayesian viewpoints using this censoring plan. To begin, we applied the maximum likelihood estimation approach to obtain parameter, reliability, and hazard function estimators. Following that, the approximate confidence intervals for the aforementioned metrics were derived, assuming the asymptotic normality traits of the maximum likelihood estimators. Additionally, by employing the Bayesian method via the Markov chain Monte Carlo technique, the point estimators and highest posterior density intervals of various parameters were created based on the symmetric squared error loss. A simulation study that incorporates numerous scenarios was used to assess the effectiveness of various estimation methodologies. The optimal progressive censorship plans are then discussed based on a set of criteria. Finally, three applications from the engineering and medical domains have been offered as examples.

Estimation of the stress-strength parameter under two-sample balanced progressive censoring scheme

In this paper, we obtain the stress-strength reliability estimation under balanced joint Type-II progressive censoring scheme for independent samples from two different populations. We simultaneously place two independent samples where the experimental units follow Weibull distributions with common shape parameter β and different scale parameters α, λ, respectively. The maximum likelihood estimators of the unknown parameters are derived. Further, the Bayesian inference is considered using Lindley's approximation and Gibbs sampling method. Extensive simulations are performed to see the effectiveness of the proposed estimation methods. Further, we derive the optimal censoring scheme in the Bayesian framework by using the variable neighbourhood search method proposed by [Bhattacharya et al. On optimum life-testing plans under type-ii progressive censoring scheme using variable neighbourhood search algorithm. Test. 2016;25(2):309–330]. Further, some simulation schemes are provided to compare the performances of the estimations under the jointly censored samples versus two separate censored samples.

CenTime: Event-conditional modelling of censoring in survival analysis

Survival analysis is a valuable tool for estimating the time until specific events, such as death or cancer recurrence, based on baseline observations. This is particularly useful in healthcare to prognostically predict clinically important events based on patient data. However, existing approaches often have limitations; some focus only on ranking patients by survivability, neglecting to estimate the actual event time, while others treat the problem as a classification task, ignoring the inherent time-ordered structure of the events. Additionally, the effective utilisation of censored samples−data points where the event time is unknown− is essential for enhancing the model’s predictive accuracy. In this paper, we introduce CenTime, a novel approach to survival analysis that directly estimates the time to event. Our method features an innovative event-conditional censoring mechanism that performs robustly even when uncensored data is scarce. We demonstrate that our approach forms a consistent estimator for the event model parameters, even in the absence of uncensored data. Furthermore, CenTime is easily integrated with deep learning models with no restrictions on batch size or the number of uncensored samples. We compare our approach to standard survival analysis methods, including the Cox proportional-hazard model and DeepHit. Our results indicate that CenTime offers state-of-the-art performance in predicting time-to-death while maintaining comparable ranking performance. Our implementation is publicly available at https://github.com/ahmedhshahin/CenTime.

Estimation of some lifetime parameter of the unit half logistic-geometry distribution under progressively type-II censored data

This research examines the estimation of the parameter for the unit-half logistic-geometry distribution (UHLGD) using progressively type-II right censored samples. The unknown parameter of UHLGD under progressively type II right censoring is estimated using maximum likelihood estimations (MLEs), maximum product space estimators, and Bayesian estimators. The confidence intervals (ACIs) are computed. Additionally, two bootstrap CIs (bootstrap-p and bootstrap-t) are recommended. For symmetric loss functions such as squared error loss (SEL), Bayesian approximations are developed. The Metropolis-Hastings samplers approach is used to get Bayes estimates of unknown parameters and associated credible intervals (CRIs) using the Markov chain Monte Carlo (MCMC) method. A set of real data that measures the tensile strength of polyester fibres is considered an application of the provided techniques.

Bayes Estimation for the Rayleigh–Weibull Distribution Based on Progressive Type-II Censored Samples for Cancer Data in Medicine

The aim of this study is to obtain the Bayes estimators and the maximum likelihood estimators (MLEs) for the unknown parameters of the Rayleigh–Weibull (RW) distribution based on progressive type-II censored samples. The approximate Bayes estimators are calculated using the idea of Lindley, Tierney–Kadane approximations, and also the Markov Chain Monte Carlo (MCMC) method under the squared-error loss function when the Bayes estimators are not handed in explicit forms. In this study, the approximate Bayes estimates are compared with the maximum likelihood estimates in the aspect of the estimated risks (ERs) using Monte Carlo simulation. The asymptotic confidence intervals for the unknown parameters are obtained using the MLEs of parameters. In addition, the coverage probabilities the parametric bootstrap estimates are computed. Real lifetime datasets related to bladder cancer, head and neck cancer, and leukemia are used to illustrate the empirical results belonging to the approximate Bayes estimates, the maximum likelihood estimates, and the parametric bootstrap intervals.