Orderings of coherent systems with randomized dependent components

Abstract

Consider a general coherent system with independent or dependent\ud components, and assume that the components are randomly chosen from\ud two different stocks, with the components of the first stock having\ud better reliability than the others. Then here we provide sufficient\ud conditions on the component's lifetimes and on the random numbers of\ud components chosen from the two stocks in order to improve the\ud reliability of the whole system according to different stochastic\ud orders. We also discuss several examples in which such conditions\ud are satisfied and an application to the study the optimal random\ud allocation of components in series and parallel systems. As a\ud novelty, our study includes the case of coherent systems with\ud dependent components by using basic mathematical tools (and copula\ud theory)

Bivariate distributions with conditionals satisfying the proportional generalized odds rate model

“…This is a particular case of the distorted distributions studied in Navarro et al ( , 2014Navarro et al ( , 2015 and in the references therein.…”

Stochastic comparisons of residual lifetimes and inactivity times of coherent systems with dependent identically distributed components

“…Navarro, Pellerey, and Di Crescenzo (2015) studied stochastic comparisons between coherent systems having randomized dependent components. Also Gupta and Kumar (2014) have investigated stochastic comparisons of component and system redundancies with dependent components.…”

Uncertainty theory as a basis for belief reliability

“…Coherent system is the 14 most widely applied system model in reliability theory, which describes the 15 logic of binary monotone systems whose components are all relevant [3,28].…”

“…Gao and Yao [12] Most existing system reliability analysis methods in uncertainty theory are 28 based on structure functions (e.g., see [23] and [30] the minimal cut sets, which is a strong condition and restricts its application.…”

“…23 Currently, the belief reliability of a component or a system can only be e-24 valuated from its definition (i.e., based on design margin, aleotory uncertainty 25 and epistemic uncertainty) [35]. In practice, we often need to calculate the 26 belief reliability of a system based on the structure of the system and the be-27 lief reliabilities of its components (referred to as system reliability analysis in 28 conventional reliability theories [31]). To address this problem, a mathematical 29 theory should be determined as the mathematical foundation of belief reliability, 30 based on which the system belief reliability analysis method can be developed.…”