1,677 research outputs found
Analysis Of Type-II Progressively Hybrid Censored Competing Risks Data
A Type-II progressively hybrid censoring scheme for competing risks data is introduced, where the experiment terminates at a pre-specified time. The likelihood inference of the unknown parameters is derived under the assumptions that the lifetime distributions of the different causes are independent and exponentially distributed. The maximum likelihood estimators of the unknown parameters are obtained in exact forms. Asymptotic confidence intervals and two bootstrap confidence intervals are also proposed. Bayes estimates and credible intervals of the unknown parameters are obtained under the assumption of gamma priors on the unknown parameters. Different methods have been compared using Monte Carlo simulations. One real data set has been analyzed for illustrative purposes
Analysis of Generalized Inverted Exponential Distribution under Adaptive Type-I Progressive Hybrid Censored Competing Risks Data
The estimation of the unknown parameters of generalized inverted exponential distribution under adaptive type-I progressive hybrid censored scheme (AT-I PHCS) with competing risks data will be discussed. The reason why AT-I PHCS 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 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 of the scale parameters. For Bayesian estimation, we take advantage of Markov Chain Monte Carlo techniques to derive Bayesian estimators and the credible intervals. Finally, two data sets with Monte Carlo simulation study and a real data set are analyzed for illustrative purposes
Confidence intervals for reliability growth models with small sample sizes
Fully Bayesian approaches to analysis can be overly ambitious where there exist realistic limitations on the ability of experts to provide prior distributions for all relevant parameters. This research was motivated by situations where expert judgement exists to support the development of prior distributions describing the number of faults potentially inherent within a design but could not support useful descriptions of the rate at which they would be detected during a reliability-growth test. This paper develops inference properties for a reliability-growth model. The approach assumes a prior distribution for the ultimate number of faults that would be exposed if testing were to continue ad infinitum, but estimates the parameters of the intensity function empirically. A fixed-point iteration procedure to obtain the maximum likelihood estimate is investigated for bias and conditions of existence. The main purpose of this model is to support inference in situations where failure data are few. A procedure for providing statistical confidence intervals is investigated and shown to be suitable for small sample sizes. An application of these techniques is illustrated by an example
Statistical inference for dependent competing risks data under adaptive Type-II progressive hybrid censoring
In this article, we consider statistical inference based on dependent
competing risks data from Marshall-Olkin bivariate Weibull distribution. The
maximum likelihood estimates of the unknown model parameters have been computed
by using the Newton-Raphson method under adaptive Type II progressive hybrid
censoring with partially observed failure causes. The existence and uniqueness
of maximum likelihood estimates are derived. Approximate confidence intervals
have been constructed via the observed Fisher information matrix using the
asymptotic normality property of the maximum likelihood estimates. Bayes
estimates and highest posterior density credible intervals have been calculated
under gamma-Dirichlet prior distribution by using the Markov chain Monte Carlo
technique. Convergence of Markov chain Monte Carlo samples is tested. In
addition, a Monte Carlo simulation is carried out to compare the effectiveness
of the proposed methods. Further, three different optimality criteria have been
taken into account to obtain the most effective censoring plans. Finally, a
real-life data set has been analyzed to illustrate the operability and
applicability of the proposed methods
On competing risk and degradation processes
Lehmann's ideas on concepts of dependence have had a profound effect on
mathematical theory of reliability. The aim of this paper is two-fold. The
first is to show how the notion of a ``hazard potential'' can provide an
explanation for the cause of dependence between life-times. The second is to
propose a general framework under which two currently discussed issues in
reliability and in survival analysis involving interdependent stochastic
processes, can be meaningfully addressed via the notion of a hazard potential.
The first issue pertains to the failure of an item in a dynamic setting under
multiple interdependent risks. The second pertains to assessing an item's life
length in the presence of observable surrogates or markers. Here again the
setting is dynamic and the role of the marker is akin to that of a leading
indicator in multiple time series.Comment: Published at http://dx.doi.org/10.1214/074921706000000473 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
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