Estimation of P(X>Y) with Topp–Leone distribution

We consider the estimation problem of the probability P=P(X>Y) for the standard Topp–Leone distribution. After discussing the maximum likelihood and uniformly minimum variance unbiased estimation procedures for the problem on both complete and left censored samples, we perform a Monte Carlo simulation to compare the estimators based on the mean square error criteria. We also consider the interval estimation of P.     

Reliability estimation in generalized inverted exponential distribution with progressively type II censored sample

In this paper, a generalization of inverted exponential distribution is considered as a lifetime model [A.M. Abouammoh and A.M. Alshingiti, Reliability estimation of generalized inverted exponential distribution, J. Statist. Comput. Simul. 79(11) (2009), pp. 1301–1315]. Its reliability characteristics and important distributional properties are discussed. Maximum likelihood estimation of the two parameters involved along with reliability and failure rate functions are derived. The method of least square estimation of parameters is also studied here. In view of cost and time constraints, type II progressively right censored sampling scheme has been used. For illustration of the performance of the estimates, a Monte Carlo simulation study is carried out. Finally, a real data example is given to show the practical applications of the paper.     

Classical and Bayesian estimation of stress-strength reliability in type II censored Pareto distributions

ABSTRACT

In this paper, the stress-strength reliability, R, is estimated in type II censored samples from Pareto distributions. The classical inference includes obtaining the maximum likelihood estimator, an exact confidence interval, and the confidence intervals based on Wald and signed log-likelihood ratio statistics. Bayesian inference includes obtaining Bayes estimator, equi-tailed credible interval, and highest posterior density (HPD) interval given both informative and non-informative prior distributions. Bayes estimator of R is obtained using four methods: Lindley's approximation, Tierney-Kadane method, Monte Carlo integration, and MCMC. Also, we compare the proposed methods by simulation study and provide a real example to illustrate them.     

Estimation of p(y<x) in the burr case: a comparative study

This paper provides a simulation study which compares three estimators for R = P(Y<X) when Y and X are two independent but not identically distributed Burr random variables. These estimators are the minimum variance unbiased, the maximum likelihood and Bayes estimators. Moreover, the sensitivity of Bayes estimator to the prior parameters is considered.     

Reliability design for a MANET with cluster-head gateway routing protocol

ABSTRACT

A MANET is a self-configuring network connected by wireless links. In order to facilitate communication within the network, a routing protocol is used to control the traffic. One of the prominent routing protocols for MANET is CGSR. Network reliability related problems have resulted in the construction of many algorithms. The UGFT has an enterprise approach to analyze the reliability of the MANET. The emphasis in this paper has been on executing the MANET reliability using UGFT. An efficient algorithm has been proposed to guarantee the reliability of MANET using UGFT with CGSR and is validated with a case study in a military test bed.     

Stochastic comparisons of two-unit repairable systems

Abstract

We consider two models of two-unit repairable systems: cold standby system and warm standby system. We suppose that the lifetimes and repair times of the units are all independent exponentially distributed random variables. Using stochastic orders we compare the lifetimes of systems under different assumptions on the parameters of exponential distributions. We also consider a cold standby system where the lifetimes and repair times of its units are not necessarily exponentially distributed.     

Degradable systems:a survey of multistate system theory

The vast majority of reliability analyses assume that ccmponents and system are in either of two states: functioning or failed. However, in many real life situations we are actually able to distinguish among various 'Ilevels of performance" for both system and components. For such situations, the existing dichotomous model is a gross oversimplification and so models assuming degradable (multistate) systems and components are preferable since they are closer to reality.We present a survey of recent papers which treat the more I sophisticated and more realistic models in which components and systems may assume many states ranging from perfect functioning to complete failure. Our survey updates and complements a previous survey by El-Neweihi and Proschan (1980). Some new results are included.     

Item reliability based on a paucity of item failures

When item reliability is high, lot acceptance sampling is likely to uncover no defective units. Nevertheless, the reliability lower confidence limits are often disappointing. The use of a Bayesian procedure with certain beta priors produces tighter confidence limits. The case where one observed defective is permitted in accepting a lot is also examined. Numerical results for both cases are presented. In addition, the impact of item misclassification is addressed.     

A class of tests for exponentiality against decreasing mean residual life alternatives

A class of tests is proposed for testing Exponentiality against the Decreasing Mean Residual Life (DMRL) class of non-exponential probability distributions. These tests are consistent and asymptotically unbiased against all continuous DMRL alternatives. They are U - statistics and hence asymptotically normally distributed. The asymptotic relative efficiency (ARE) with respect to other tests for DMRL are quite high. Small sample powers are also comparable with small sample powers of the competitors.     

The exponentiated weibull family: some properties and a flood data application

The exponentiated Weibull family, a Weibull extension obtained by adding a second shape parameter, consists of regular distributions with bathtub shaped, unimodal and a broad variety of monotone hazard rates. It can be used for modeling lifetime data from reliability, survival and population studies, various extreme value data, and for constructing isotones of the tests of the composite hypothesis of exponentiality. The structural analysis of the family in this paper includes study of its skewness and kurtosis properties, density shapes and tail character, and the associated extreme value and extreme spacings distributions. Its usefulness in modeling extreme value data is illustrated using the floods of the Floyd River at James, Iowa.