This paper develops Bayesian analysis for Constant Stress Accelerated Life Test (CSALT) under Type-II censoring scheme. Failure times are assumed to distribute as the three-parameter Generalized Logistic (GL) distribution. The inverse power law model is used to represent the relationship between the stress and the scale parameter of a test unit. Bayes estimates are obtained using Markov Chain Monte Carlo (MCMC) simulation algorithm based on Gibbs sampling. Then, confidence intervals, and predicted values of the scale parameter and the reliability function under usual conditions are obtained. Numerical illustration and an illustrative example are addressed for illustrating the theoretical results. WinBUGS software package is used for implementing Markov Chain Monte Carlo (MCMC) simulation and Gibbs sampling.

The optimal designs and statistical inference of accelerated life tests under type-I are studied for constant stress-accelerated life tests (CSALTs). It is assumed that the lifetime at design stress has generalized logistic distribution. The scale parameter of the lifetime distribution at constant stress levels is assumed to be an inverse power law function of the stress level. The maximum likelihood (ML) estimators of the model parameters, Fisher information matrix, the asymptomatic variance-covariance matrix, the confidence bounds, the predictive value of the scale parameter, and the reliability function under the usual conditions are obtained under type-I censoring. Moreover, the optimal design of the accelerated life tests is studied according to the D-optimality criterion to specify the optimal censoring time. Finally, the numerical studies are introduced to illustrate the proposed procedures.

The distribution of ArcSine will be developed to another new distribution using the Quadratic Rank Transmutation (QRT) method proposed by Shaw and Buckley (2007). The new distribution will be called the Transmuted ArcSine distribution, some of its mathematical characteristics such as variance, expectation, residual function, risk function, moments, moment generating function and characteristic function will be presented. The model parameters will be estimated by the maximum likelihood method. Finally, two real data sets are analyzed to illustrates the usefulness of the TAS distribution.

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In  this  article,  we  generalize  the  Rectangular  distribution  using  the  quadratic  rank  transmutation map studied by Shaw and Buckley (2007) to develop a transmuted Rectangular  distribution.  The  expectation,  variance,  moments,  reliability  function,  hazard  rate  function,  Cumulative Hazard function, the moment generating function, and the characteristic function  of the new distribution are provided. In addition, the model parameters are estimated by the  maximum likelihood method. Finally, an application to generated data sets is illustrated.