On relevation redundancy to coherent systems at component and system levels

Abstract

Recently, the relevation transformation has received further attention from researchers, and some interesting results have been developed. It is well known that the active redundancy at component level results in a more reliable coherent system than that at system level. However, the lack of study of this problem with relevation redundancy prevents us from fully understanding such a generalization of the active redundancy. In this note we deal with relevation redundancy to coherent systems of homogeneous components. Typically, for a series system of independent components, we have proved that the lifetime of a system with relevation redundancy at component level is larger than that with relevation redundancy at system level in the sense of the usual stochastic order and the likelihood ratio order, respectively. For a coherent system with dependent components, we have developed a sufficient condition in terms of the domination function to the usual stochastic order between the system lifetime with redundancy at component level and that at system level.

Optimal redundancy allocations for series systems under hierarchical dependence structures

“…Since the study on allocation problems of cold standbys involves with convolution of heterogeneous and nonnegative random variables, few results are available in the literature due to the complexity of distribution theory. For relevant studies on allocating the redundancy components in reliability systems with independent components, interested readers may refer to Belzunce et al, 19 Yan et al, 20 Li and Li, 21 and Zhang and Zhang. 22 As discussed by Navarro et al 23 and Navarro and Fernández-Martínez, 24 the independence assumption among components lifetimes is somewhat unrealistic in practical engineering situations.…”

On relevation transform involved with statistical dependence between two component lifetimes

“…Typically, through viewing the relevation as a replacement or repair policy, under which the failed unit is restored to the working condition just previous to the failure with the same age but a different failure rate, Belzunce et al 14 had a discussion on allocating one relevation redundancy to a system component in attempt to improve the system reliability. For coherent systems, Yan et al 15 studied the allocation of relevation of two components to increase the system reliability, Wu et al 16 examined the improvement in reliability due to one relevation allocation, and also Li and Li 17 developed stochastic orders between the lifetime of system with relevation transform at component level and that at system level.…”