554 research outputs found
Optimal variable acceptance sampling plan for exponential distribution using Bayesian estimate under Type I hybrid censoring
In this study, variable acceptance sampling plans under Type I hybrid
censoring is designed for a lot of independent and identical units with
exponential lifetimes using Bayesian estimate of the parameter .
This approach is new from the conventional methods in acceptance sampling plan
which relay on maximum likelihood estimate and minimising of Bayes risk.
Bayesian estimate is obtained using squared error loss and Linex loss
functions. Optimisation problem is solved for minimising the testing cost under
each methods and optimal values of the plan parameters and are
calculated. The proposed plans are illustrated using various examples and a
real life case study is also conducted. Expected testing cost of the sampling
plan obtained using squared error loss function is much lower than the cost of
existing plans using maximum likelihood estimate
Inference for Step-Stress Partially Accelerated Life Test Model with an Adaptive Type-I Progressively Hybrid Censored Data
Consider estimating data of failure times under step-stress partially accelerated life tests based on adaptive Type-I hybrid censoring. The mathematical model related to the lifetime of the test units is assumed to follow Rayleigh distribution. The point and interval maximum-likelihood estimations are obtained for distribution parameter and tampering coefficient. Also, the work is conducted under a traditional Type-I hybrid censoring plan (scheme). A Monte Carlo simulation algorithm is used to evaluate and compare the performances of the estimators of the tempering coefficient and model parameters under both progressively hybrid censoring plans. The comparison is carried out on the basis of mean squared errors and bias
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 the Sample Information About Parameter and Prediction
The Bayesian measure of sample information about the parameter, known as
Lindley's measure, is widely used in various problems such as developing prior
distributions, models for the likelihood functions and optimal designs. The
predictive information is defined similarly and used for model selection and
optimal designs, though to a lesser extent. The parameter and predictive
information measures are proper utility functions and have been also used in
combination. Yet the relationship between the two measures and the effects of
conditional dependence between the observable quantities on the Bayesian
information measures remain unexplored. We address both issues. The
relationship between the two information measures is explored through the
information provided by the sample about the parameter and prediction jointly.
The role of dependence is explored along with the interplay between the
information measures, prior and sampling design. For the conditionally
independent sequence of observable quantities, decompositions of the joint
information characterize Lindley's measure as the sample information about the
parameter and prediction jointly and the predictive information as part of it.
For the conditionally dependent case, the joint information about parameter and
prediction exceeds Lindley's measure by an amount due to the dependence. More
specific results are shown for the normal linear models and a broad subfamily
of the exponential family. Conditionally independent samples provide relatively
little information for prediction, and the gap between the parameter and
predictive information measures grows rapidly with the sample size.Comment: Published in at http://dx.doi.org/10.1214/10-STS329 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A Multiple Dependent State Repetitive Sampling Plan Based on Performance Index for Lifetime Data with Type II Censoring
In this paper, a multiple dependent state repetitive (MDSR) sampling plan based on the lifetime performance index C-L is proposed for lifetime data with type II censoring when the lifetime of a product follows the exponential distribution or Weibull distribution. The optimal parameters of the proposed plan are determined by minimizing the average sample number while satisfying the producer's risk and consumer's risk at corresponding quality levels. Besides, the performance of the proposed plan is compared with that of the existing lifetime sampling plan in terms of the average sample number and operating characteristic curve. Two illustrative examples are given for the demonstration of the proposed plan.11Ysciescopu
Exponentiated Rayleigh Distribution: A Bayes Study Using MCMC Approach Based on Unified Hybrid Censored Data
This paper aims to estimate the unknown parameters, survival and hazard functions for exponentiated Rayleigh distribution based on unfied hybrid censored data
Planning Step-Stress Life Tests for the Generalized Rayleigh Distribution under Progressive Type-II Censoring with Binomial Removals
In this article, both the parameter estimation and optimal design problems of step-stress partially accelerated life test units whose lifetimes follow the generalized Rayleigh distribution are considered under progressive type-II censoring scheme with binomial removals. The maximum likelihood estimators of the scale and shape parameters as well as the acceleration factor are obtained. The concert of the estimators is assessed. In addition, approximate confidence intervals of the model parameters are constructed and their coverage probabilities are computed. Moreover, optimum test plans are also developed to improve/guarantee the quality of the statistical inference. Finally, simulation studies and a numerical example are provided for illustrative purposes.Рассмотрены параметр оценки и оптимальное проектирование частично ускоренных испытаний на долговечность при ступенчатой нагрузке на основе обобщенного рэлеевского распределения при прогрессивном цензурировании типа II с биномиальными выборками. В качестве фактора ускорения используются максимальные оценки вероятности параметров масштаба и формы, которые согласуются между собой. Построены приближенные доверительные интервалы параметров модели и рассчитаны границы вероятности. Разработаны оптимальные планы испытаний для улучшения статистического анализа. Предложены результаты моделирования и числовой пример.Розглянуто параметр оцінки і оптимальне проектування частково прискорених випробувань на довговічність при ступеневому навантаженні на основі узагальненого релеївського розподілу при прогресивному цензуруванні типу ІІ з біноміальними виборками. Як фактор прискорення використовуються максимальні оцінки імовірності параметрів масштабу і форми, які узгоджуються між собою. Побудовано наближені довірчі інтервали параметрів моделі і розраховано границі імовірності. Розроблено оптимальні плани випробувань із метою покращання статистичного аналізу. Запропоновано результати моделювання і числовий приклад
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