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In this paper, studies of competing risks model are considered when the observations are left-truncated and right-censored data. When the failure times of the competing risks are distributed by a generalized inverted exponential model with same scale but different shape parameters with partially observed failure causes, statistical inference for the unknown model parameters is discussed from classical and Bayesian approaches, respectively. Maximum likelihood estimators of the unknown parameters, along with associated existence and uniqueness, are established, and the asymptotic likelihood theory is also used to construct the confidence interval via the observed Fisher information matrix. Moreover, Bayesian estimates and the corresponding highest posterior density credible intervals are also obtained based a flexible Gamma-Beta prior, and a Gibbs sampling technique is constructed to compute associated estimates. Further, under a general practical assumption with order-restriction parameter case, classical and Bayesian estimations are also established under order restriction situations, respectively. Extensive Monte-Carlo simulations are carried out to investigate the performances of our results and two real-life examples are analyzed to show the applicability of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, statistical inference of an inverted exponentiated Rayleigh model is studied when the failure times are obtained under a modified progressive hybrid censoring. The maximum likelihood estimators of the model parameters together with associated existence and uniqueness are established, and approximate confidence intervals are constructed based on asymptotic theory. Alternatively, generalized point and interval estimates for unknown parameters are also constructed based on the proposed pivotal quantities for comparison. In addition, predictive intervals of remaining useful life from the inverted exponentiated Rayleigh distribution are also constructed under classical and generalized inferential approaches, respectively. Finally, extensive simulation studies are carried out to compare the performance of the proposed methods, and two real-life examples are analyzed for illustration. The numerical results indicate that both traditional likelihood and generalized inferential methods work satisfactorily, and that our proposed generalized approach appears much more appealing and are superior to classical results. [ABSTRACT FROM AUTHOR]

An important goal for the producers is to stimulate the purchase intention of consumers so that the profit can be increased. An attractive warranty policy can not only represent the quality of product but also enhance the purchase desire of consumers. A long warranty length usually stands for high quality. However, it is not suitable for the producers to provide an unlimited warranty length. The main purpose of this paper is to establish an approach to determine the optimal warranty length based on one-shot device sample. The one-shot device data are collected under a multiple-level constant-stress accelerated life test. The lifetime distribution at each stress level is assumed to be Rayleigh. A utility function is provided to measure the monetary profit based on a free-replacement warranty policy. The optimization problem is studied under the Bayesian framework. A numerical example is studied for illustrating purpose. Finally, the sensitivity analysis is performed to see the influence of some parameters on the optimal warranty length. [ABSTRACT FROM AUTHOR]

Kinetics of an abiotic method for oxidative pentachlorophenol (PCP) degradation in soil under unsaturated conditions and a neutral pH has been studied. Reagents used were heme as the catalyst and peroxide as the oxidant. Our previous results showed that the heme and peroxide degraded PCP efficiently with two optimum doses of heme and peroxide: one was the optimum point derived from the quadratic model fitting with heme of 0.035 g/2 g soil and peroxide of 0.105 g/2 g soil; the other had lower doses of heme (0.017 g/2 g soil) and peroxide (0.095 g/2 g soil) derived from the calculation of 95% confidence interval of the optimum point. Based on these results, the purpose of this study was to examine the kinetics of soil PCP degradation in terms of the rate and extent of PCP destruction at the optimal dosages determined. The results showed that PCP degradation at both optimal dosages looked similar, which showed about 70% of PCP destruction within the first 2 h of reaction and up to 80% of PCP destruction within 1 day after the heme/peroxide treatment. Use of the radio-labeled [sup.14]C PCP revealed that 17% of the soil PCP was mineralized to carbon dioxide. Moreover a scaled-up experiment with soil pretreated with ethanol was conducted. The results showed about 70% degradation of PCP which agreed well with the results of the laboratory-scale runs. However the addition of ethanol showed little help in PCP oxidation. Finally a pseudofirst- order kinetic model was employed to describe the trend of the PCP degradation over time, and the outcomes were satisfactory. CE Database subject headings: Optimization; Soil treatment; Kinetics; Toxicity; Degradation.

In this article, estimation problems for the Burr X distribution under a progressive-stress accelerated life test with progressive type-II censoring are studied. The stress is assumed to be a linearly increasing function of time. The inverse power law and the cumulative exposure model are considered. The classical and Bayesian estimations for the model parameters are obtained by using maximum likelihood method and Markov chain Monte Carlo technique,respectively. The asymptotic confidence intervals are constructed and highest posterior density intervals are also established. A simulation study is conducted to investigate the performance of the proposed point and interval estimations. Finally, a real data set is analysed for illustration. [ABSTRACT FROM AUTHOR]

In this article, we obtain point and interval estimates of multicomponent stress-strength reliability model of an s-out-of-j system using classical and Bayesian approaches by assuming both stress and strength variables follow a Chen distribution with a common shape parameter which may be known or unknown. The uniformly minimum variance unbiased estimator of reliability is obtained analytically when the common parameter is known. The behavior of proposed reliability estimates is studied using the estimated risks through Monte Carlo simulations and comments are obtained. Finally, a data set is analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper we consider the problems of estimation and prediction when observed data from a lognormal distribution are based on lower record values and lower record values with inter-record times. We compute maximum likelihood estimates and asymptotic confidence intervals for model parameters. We also obtain Bayes estimates and the highest posterior density (HPD) intervals using noninformative and informative priors under square error and LINEX loss functions. Furthermore, for the problem of Bayesian prediction under one-sample and two-sample framework, we obtain predictive estimates and the associated predictive equal-tail and HPD intervals. Finally for illustration purpose a real data set is analyzed and simulation study is conducted to compare the methods of estimation and prediction. [ABSTRACT FROM AUTHOR]

In this article, we study the optimization problem of sample size allocation when the competing risks data are from a progressive type-II censoring in a constant-stress accelerated life test with multiple levels. The failure times of the individual causes are assumed to be statistically independent and exponentially distributed with different parameters. We obtain the estimates of the unknown parameters through a maximum likelihood method, and also derive the Fisher information matrix. We propose three optimization criteria and two search scenarios to obtain the sample size allocation at each stress level. Some numerical results are studied to illustrate the usage of the proposed methods. [ABSTRACT FROM PUBLISHER]