S. E. Abu-Youssef

Order statistics from the doubly truncated linear-exponential distribution and its characterizations

In this paper single and product moments of order statistics from the doubly truncated linear-exponential distribution are studied. Some recurrence relations for both single and product moments of order statistics are also derived. Two results for characterizing the linear-exponential distribution through the properties of order statistics are also presented.

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.

An identity for the product moments of order statistics

A general identity for the product moments of successive order statistics is given, which is valid in a class of probability distributions including Weibull, Pareto, exponential and Burr distributions.

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.

Classical and Bayesian inference on progressive-stress accelerated life testing for the extension of the exponential distribution under progressive type-II censoring

In this paper, a progressive-stress accelerated life test under progressive type-II censoring is considered. The cumulative exposure model is assumed when the lifetime of test units follows an extension of the exponential distribution. The maximum likelihood and Bayes estimates of the model parameters are obtained. The approximate and credible confidence intervals of the estimators are derived. Furthermore, a real lifetime data set is analyzed to illustrate the proposed procedures. Finally, the simulation studies are used to compare between 2 different designs of the progressive-stress test (simple and multiple ramp-stress tests).

Testing Exponentiality Against UBAC Using Kernel Methods

In this paper, the problem of testing exponentiality against used better than aged in convex ordering classes of life distributions is investigated. For this property a nonparametric test is presented based on kernel method. The test is presented for complete and right censored data. Furthermore, Pitmans asymptotic relative efficiency (PARE) is discussed to assess the performance of the test with respect to other tests. Selected critical values are tabulated. Some numerical simulations on the power estimates are presented for proposed test. Finally, examples in medical sciences are used as practical applications for the proposed test.