Nahed S. A. Ali

Estimation in Step-Stress Accelerated Life Tests for Power Generalized Weibull Distribution with Progressive Censoring

Based on progressive censoring, step-stress partially accelerated life tests are considered when the lifetime of a product follows power generalized Weibull distribution. The maximum likelihood estimates (MLEs) and Bayes estimates (BEs) are obtained for the distribution parameters and the acceleration factor. In addition, the approximate and bootstrap confidence intervals (CIs) of the estimators are presented. Furthermore, the optimal stress change time for the step-stress partially accelerated life test is determined by minimizing the asymptotic variance of MLEs of the model parameters and the acceleration factor. Simulation results are carried out to study the precision of the MLEs and BEs for the parameters involved.

Optimal Plans of Constant-Stress Accelerated Life Tests for the Lindley Distribution

In this paper, the optimal plans for k-level constant-stress accelerated life test are presented for Lindley failure data under complete sampling. According to the log-linear life-stress relationship, the optimal proportion of test units allocated to each stress level is determined under D- and C-optimality criteria. Moreover, two real data sets are analyzed to illustrate the proposed procedures. Furthermore, the real data sets are used to show that the Lindley distribution can be a better model than one based on the exponential distribution. In addition, numerical examples are used to compare between the D-optimal plan, C-optimal plan, and traditional plan through asymptotic variance of maximum likelihood estimators (MLEs). Finally, some interesting conclusions are obtained.

Residual and Past Entropy for Concomitants of Ordered Random Variables of Morgenstern Family

For a system, which is observed at time t, the residual and past entropies measure the uncertainty about the remaining and the past life of the distribution, respectively. In this paper, we have presented the residual and past entropy of Morgenstern family based on the concomitants of the different types of generalized order statistics (gos) and give the linear transformation of such model. Characterization results for these dynamic entropies for concomitants of ordered random variables have been considered.

On the Properties of the UBAC(2) Class of Life Distributions

This paper provided some properties of a new class of life distributions that are denoted as used better than aged in an increasing concave ordering class (UBAC(2)). This class includes many classes of life distributions like used better than aged (UBA), used better than aged in convex ordering (UBAC), used better than aged in expectation (UBAE) and decreasing mean residual life (DMRL). The considered properties included the moment inequalities, moment generating function behavior, and testing hypotheses about the survival function of this class. The distribution of the proposed statistic was investigated via simulation. We used real data as an application of the proposed test statistic.