M. M. Mohie El-Din

Moments of order statistics from parabolic and skewed distributions and a characterization of Weibull distribution

In this paper the single and product moments of order statistics from doubly truncated parabolic and skewed distributions have been obtained. Also the Weibull distribution has been characterized through the properties of order statistics.

Two-Sample Bayesian Prediction Intervals of Generalized Order Statistics Based on Multiply Type II Censored Data

In this article, two-sample Bayesian prediction intervals of generalized order statistics (GOS) based on multiply Type II censored data are derived. To illustrate these results, the Pareto, Weibull, and Burr-Type XII distributions are used as examples. Finally, a numerical illustration of the sequential order statistics from the Pareto distribution is presented.

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.

Reliability analysis of a two-unit cold standby system with inspection, replacement, proviso of rest, two types of repair and preparation time

Abstract This paper deals with a two-unit standby system-one operative and the other in cold standby. Single repair facility which acts the inspection, replacement, preparation and repair. We wait the serverman for some maximum time or until the other unit fails. The analysis is carried out on the supposition that all time distributions are general except failure, delivery, replacement and inspection time distributions are exponentials. Stochastic behavior of the system has been studied by the regeneration point technique and several parameters of interest are obtained. Numerical results pertaining to some special cases are also added.

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.

Optimum preventive maintenance for a 2-unit priority-standby system with patience–time for repair

This paper deals with the effect of preventive maintenance (PM) on the reliability measurcs for a 2-unit priority standby system with patience-time for repair. Four types of PM (type (a),(b), (c), and(d)) are considcrcd. Failurc, repair, PM, and replacement time disiributiotls are general whereas delivery time distribution is negative exponential. Regenerative technique in Markov renewal is applied to obtain several reliability characteristics of interest to designers. Finally numerical calculations are given to illustrate the theoretical results

Estimation of the mean and standard deviation of Burr distribution by order statistics

Abstract The product moment of order statistics of Burr distribution (2.1) are obtained in a genral form in terms of n, r, and s for specific values of the parameters of the distribution. The best linear estimates of the mean and standard deviation are obtained as a linear combination of the elements of a complete and censored samples up to size 5.

Estimation of generalized exponential distribution based on an adaptive progressively type-II censored sample

ABSTRACT In this paper, based on an adaptive Type-II progressively censored sample from the generalized exponential distribution, the maximum likelihood and Bayesian estimators are derived for the unknown parameters as well as the reliability and hazard functions. Also, the approximate confidence intervals of the unknown parameters, and the reliability and hazard functions are calculated. Markov chain Monte Carlo method is applied to carry out a Bayesian estimation procedure and in turn calculate the credible intervals. Moreover, results from simulation studies assessing the performance of our proposed method are included. Finally, an illustrative example using real data set is presented for illustrating all the inferential procedures developed here.