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Ranked set sampling (RSS) has been proved to be an efficient sampling design for parametric and nonparametric inference. This paper explores inference for a maximum RSS procedure with unequal samples (MRSSU) with multiple dependent failure causes. When the lifetimes of units are characterized by a proposed complementary competing risks model, classical likelihood and Bayesian approaches are discussed for parameters and reliability estimation. Maximum likelihood estimators of model parameters and associated existence and uniqueness are established, and approximate confidence intervals are constructed using asymptotic theory and delta methods. With respect to general flexible priors, Bayesian estimates of interested quantities are also performed and a Monte Carlo sampling algorithm is proposed for complex posterior computation. Additionally, when extra historical information between the competing risks parameters is available, likelihood and Bayesian estimation are also studied under an order restriction case. Different methods are compared based on extensive simulation studies, and another real data example is demonstrated for application propose. [ABSTRACT FROM AUTHOR]

Competing risk analysis of time to failure data is preferred when failure of the unit occurs due to any one of several mutually exclusive causes. Masked data refer to the competing risk data with missing cause of failure. Masking in such data may depend on cause of failure or time to failure of the unit or may be independent of both. In this paper, we discuss competing risk models based on Lindley distribution assuming masking to be symmetric, cause dependent and time dependent. We consider maximum likelihood as well as Bayesian approaches for point and interval estimation of model parameters. We perform extensive simulation study to observe performance of various estimators. Finally, we analyze a real life masked data of cancer patients and select the best masking model for the same. [ABSTRACT FROM AUTHOR]

The ranked set sampling (RSS) is an efficient and flexible sampling method. Based on a modified RSS named minimum ranked set sampling samples (MinRSSU), inference of a dependent competing risks model is proposed in this paper. Then, Marshall–Olkin bivariate distribution model is used to describe the dependence of competing risks. When the competing risks data follow the proportional hazard rate distribution, a dependent competing risks model based on MinRSSU sampling is constructed. In addition, the model parameters and reliability indices were estimated by the classical and Bayesian method. Maximum likelihood estimators and corresponding asymptotic confidence intervals are constructed by using asymptotic theory. In addition, the Bayesian estimator and highest posterior density credible intervals are established under the general prior. Furthermore, according to E-Bayesian theory, the point and interval estimators of model parameters and reliability indices are obtained by a sampling algorithm. Finally, extensive simulation studies and a real-life example are presented for illustrations. [ABSTRACT FROM AUTHOR]

The aim of the paper is to estimate the unknown parameters of weighted exponential distribution based on the competing risks model under progressively Type-II censoring. It is supposed that the latent causes of failures have weighted exponential distributions with different parameters. The maximum likelihood estimations of four unknown parameters are derived and the uniqueness and existence of them are theoretically proved. Moreover, approximate intervals are proposed and constructed with the delta method and Fisher information matrix. Bootstrap methods are also applied to calculate the confidence intervals. Furthermore, Bayes estimates and the corresponding credible intervals under three various loss functions are computed by using the Monte Carlo Markov Chain method. A simulation study is conducted to assess the statistical performance of all the estimators. Ultimately, real data analysis is provided to illustrate all the statistical inferential procedures developed in the paper. [ABSTRACT FROM AUTHOR]

The competing risks model plays an important role in the statistical analysis of engineering, econometric, biological and other fields. A tested product may fail from different causes. Therefore, these failure causes as if competing with each other to bring about the failure of tested products (an experimental unit). Hence, in the statistical literature, this is known as the competing risk problem and it has been studied quite extensively by several researchers when the lifetime of the product is the latent failure time of the first failure cause among all the possible failure causes. In this paper, a competing risks model based on a generalized progressive hybrid type-I (GPH type-I) censoring is considered when the latent lifetime distributions of failure causes are inverse Weibull (IW) distributed and partially observed. We established various estimation methods including Maximum likelihood estimates (MLEs) and Bayes estimates (BEs). MLEs with the corresponding asymptotic confidence intervals are obtained. Bayes estimates of the parameters are obtained based on squared error loss (SEL) function under the assumption of independent gamma priors. Furthermore, we applied Markov Chain Monte Carlo (MCMC) techniques to compute BEs and to calculate the credible intervals. Finally, simulation studies and real data set are used for illustrative purpose. [ABSTRACT FROM AUTHOR]

In this paper, a dependent competing risks model is considered and investigated by utilizing the copula approach which flexibly constructs dependent relationships between marginal distributions of several competing risk factors, and the closeness of the dependency can be determined by the copula parameters. Samples are collected from the step-stress accelerated life test combined with generalized progressive hybrid censoring, where the test duration is controlled within acceptable limits and a sufficient number of samples are guaranteed. From a classical frequency perspective, the maximum likelihood estimates are derived, then the relevant confidence intervals are provided based on the Fisher information matrix. Furthermore, the bias-corrected accelerated bootstrap method is employed to obtain the interval estimation of parameters. Under the Bayesian framework, Bayesian point estimates and the corresponding credible intervals are also explored, and their results are achieved by Markov Chain Monte Carlo technique. Finally, numerical simulation experiments and real data analysis are developed to more intuitively present the constructed model and the performance of the above-mentioned methods. [ABSTRACT FROM AUTHOR]

Here in this paper, we consider the progressive Type-II censoring Gompertz data under competing risks model with binomial removals. The maximum likelihood estimators of the model parameters involved are obtained by applying numerical methods and the asymptotic variance-covariance matrix of the estimates is also derived. Bayesian estimates based on importance sampling procedure are developed under squared error, LINEX and general entropy loss functions. The confidence intervals using the asymptotic normality and Bayesian approaches are also developed. Finally, a Monte Carlo simulation is conducted to evaluate the performance of the so proposed estimators under all these different estimation methods. [ABSTRACT FROM AUTHOR]

In reliability engineering or medical studies, failure of units or individuals may occurring due to several failure modes which is known by competing risks model. In this paper, we have adopted a competing risks model under consideration that, the failure time has generalized inverted exponential distribution (GIED) and the failure modes are independent and partially observed. Under type-II progressive censoring scheme (type-II PCS), the experiment is designed as a quite popular scheme for collecting data specially, for a highly reliable product. The point estimates of the model parameters are formulated under classical approach (maximum likelihood and bootstrap) and Bayesian approach with respect to the symmetric squared error loss function. Also, the approximate confidence intervals under a large sample theory, bootstrap technique's and Markov chain Monte Carlo method (MCMC) are constructed. The estimators are assessed and compared with building the simulation study. Analysis a set of type-II PCS competing risks mortality data for illustration purpose. [ABSTRACT FROM AUTHOR]

There are many situations in reliability or medical studies, where items may fail due to one of several causes. Further, censoring is unavoidable in any life testing. In this paper attempts to estimate problem for the competing risks model where the data are adaptive type-II progressive hybrid censored scheme and follow the inverse Weibull distribution. In this regards, we obtain the maximum likelihood estimation of the parameters and the asymptotic confidence intervals for the unknown parameters. Further, Bayes estimates of the parameters which obtained based on squared error and LINEX loss functions under the assumptions of independent gamma priors. For Bayesian estimation, we take advantage of Markov Chain Monte Carlo techniques by applying the Metropolis-Hasting algorithm under the square error and LINEX loss function to derive Bayesian estimators. Finally, two data sets with a Monte Carlo simulation study and a real data set of the electronic applications are analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

In real-life experiments, collecting complete data is time-, finance-, and resources-consuming as stated by statisticians and analysts. Their goal was to compromise between the total time of testing, the number of units under scrutiny, and the expenditures paid through a censoring scheme. Comparing failure-censored schemes (Type-Ⅱ and Progressive Type-Ⅱ) to Time-censored schemes (Type-Ⅰ), it's worth noting that the former is time-consuming and is no more suitable to be applied in real-life situations. This is the reason why the Type-Ⅰ adaptive progressive hybrid censoring scheme has exceeded other failure-censored types; Time-censored types enable analysts to accomplish their trials and experiments in a shorter time and with higher efficiency. In this paper, the parameters of the inverse Weibull distribution are estimated under the Type-Ⅰ adaptive progressive hybrid censoring scheme (Type-Ⅰ APHCS) based on competing risks data. The model parameters are estimated using maximum likelihood estimation and Bayesian estimation methods. Further, we examine the asymptotic confidence intervals and bootstrap confidence intervals for the unknown model parameters. Monte Carlo simulations are carried out to compare the performance of the suggested estimation methods under Type-Ⅰ APHCS. Moreover, Markov Chain Monte Carlo by applying Metropolis-Hasting algorithm under the square error of loss function is used to compute Bayes estimates and related to the highest posterior density. Finally, two data sets are studied to illustrate the introduced methods of inference. Based on our results, we can conclude that the Bayesian estimation outperforms the maximum likelihood estimation for estimating the inverse Weibull parameters under Type-Ⅰ APHCS.