Reliability of a k-out-of-n: G System Subjected to Marshall-Olkin Type Shocks Concerning Magnitude

In this paper the reliability of a k-out-of-n: G system under the effect of shocks having the Marshall-Olkin type shock models, is studied. The magnitudes of the shocks are considered. The system contains n components and only functions when at least k of these components function. The system is subjected to (n + 1) shocks coming from (n + 1) different sources. The shock coming from the it h source may destroy the it h component, i = 1, . . . , n, while the shock coming from the (n + 1)t h source may destroy all components simultaneously. A shock is fatal, destroys a component (components), whenever its magnitude exceeds an upper threshold. The system reliability is obtained by considering the arrival time and the magnitude of a shock as a bivariate random variable. It is assumed that the bivariate random variables representing the arrival times and the magnitudes of the shocks are independent with non-identical bivariate distributions. Since the computation of the reliability formula obtained is not easy to handle, an algorithm is introduced for calculating the reliability formula. The reliability of a k-out-of-n: G system subjected to independent and identical shocks is obtained as a special case, as well as the reliabilities of the series and the parallel systems. As an application, the bivariate exponential Gumbel distribution is considered. Also, numerical illustrations are performed to highlight the results obtained

Exact reliability formula for a linear consecutive k-out-of-n: F system and relayed consecutive systems with a change point for any k?n, with stress-strength application.

This paper presents exact formulas for the reliability of linear consecutive k-out-of-n: F, and relayed consecutive k-out-of-n: F systems, having a change point at position c, 1 ? c ? n, for any k?n. A change point at position c, means that the components after this point have reliabilities that are different from those before or at position c. The components are assumed to be independent. Practically, the change in the components reliabilities may be due to change in the stress applied. Assuming a change in stress, exact formulas of the stress-strength reliability of the systems are derived, considering two cases. The first case assumed strength and stress having the same form of distributions, while the second case assumed strength and stress having different forms of distributions. Estimation of the stress-strength reliability for both cases is discussed. Application to both cases are considered with numerical illustration

Stress Strength Reliability of Regular and Relayed Linear Consecutive k Out of n : F Systems with m Change Points

This paper presents a stress strength reliability model of regular and relayed linear consecutive k out of n : F systems with m change points. The components are assumed to be identical and independent. Explicit expressions of the reliabilities are obtained, and hence the stress strength reliability is obtained generally for any distributions of stresses and strengths. As an application, the distribution of the strength is taken to be generalized Lindely, while the stresses are exponential. The reliability estimators are obtained by applying EM algorithm. Finally, a numerical illustration is performed to highlight the theoretical results obtained

Assessing the error in bootstrap estimates with dependent data

ARMA model, block bootstrap statistics, dependent data, jackknife, sample mean, stationary, time series, variance, 62G05,