Mohammed Al-Haj Ebrahem

Estimating Percentiles of Time-to-Failure Distribution Obtained from a Linear Degradation Model Using Kernel Density Method

In this article, we propose a nonparametric estimator for percentiles of the time-to-failure distribution obtained from a linear degradation model using the kernel density method. The properties of the proposed kernel estimator are investigated and compared with well-known maximum likelihood and ordinary least squares estimators via a simulation technique. The mean squared error and the length of the bootstrap confidence interval are used as the basis criteria of the comparisons. The simulation study shows that the performance of the kernel estimator is acceptable as a general estimator. When the distribution of the data is assumed to be known, the maximum likelihood and ordinary least squares estimators perform better than the kernel estimator, while the kernel estimator is superior when the assumption of our knowledge of the data distribution is violated. A comparison among different estimators is achieved using a real data set.

An optimal sign test for one-sample bivariate location model using an alternative bivariate ranked-set sample

The aim of this paper is to find an optimal alternative bivariate ranked-set sample for one-sample location model bivariate sign test. Our numerical and theoretical results indicated that the optimal designs for the bivariate sign test are the alternative designs with quantifying order statistics with labels {((r+1)/2, (r+1)/2)}, when the set size r is odd and {(r/2+1, r/2), (r/2, r/2+1)} when the set size r is even. The asymptotic distribution and Pitman efficiencies of these designs are derived. A simulation study is conducted to investigate the power of the proposed optimal designs. Illustration using real data with the Bootstrap algorithm for P-value estimation is used.

Designing degradation experiments using a Weibull distribution

Abstract This paper deals with the optimal design of a degradation experiment, where the degradation rate follows a Weibull distribution. By minimizing the mean squared error of the estimated 100pth percentile of the life time distribution such that the total experimental cost does not exceed a certain budget, the optimal combinations of the sample size, the inspection frequency and the termination time are obtained. The proposed method was applied to a real drug potency data.

Optimum simple step-stress plans using reliability estimate

This paper presents optimum simple step-stress plans under the log-logistic cumulative exposure model. The likelihood function of the model parameters is derived, from which the Fisher information matrix and the asymptotic variance of the reliability estimate are obtained. Optimum times of changing stress level are obtained by minimizing the asymptotic variance of the reliability estimate at a specified time under normal operating condition. Confidence intervals and hypotheses tests about the model parameters have also been discussed and illustrated by an example. Copyright Sapienza Universita di Roma 2012SummaryThis paper presents optimum simple step-stress plans under the log-logistic cumulative exposure model. The likelihood function of the model parameters is derived, from which the Fisher information matrix and the asymptotic variance of the reliability estimate are obtained. Optimum times of changing stress level are obtained by minimizing the asymptotic variance of the reliability estimate at a specified time under normal operating condition. Confidence intervals and hypotheses tests about the model parameters have also been discussed and illustrated by an example.