RELIABILITY EVALUATION OF LINEAR CONSECUTIVE-WEIGHTED-k-OUT-OF-n:F SYSTEM

Abstract

Reliability evaluation has a vital importance at all stages of processing and controlling modern engineering systems. In most of these modern systems the components have different contributions to the system, which are defined as weights. Among the other weighted systems, a linear consecutive-weighted-k-out-of-n:F system consists of n components, where each component has its own weight and reliability. The system fails if and only if the total weight of the failed consecutive components is at least k. The aim of this paper is to study the reliability of linear consecutive-weighted-k-out-of-n:F system consisting of independent & nonidentical and nonhomogeneous Markov dependent components. Exact formulae are provided for computing the reliability for above mentioned cases. Approximation formulae for the reliability are also presented.

Reliability of linear (n, f, k) systems with weighted components

“…For 4 f = and 3 k = the corresponding probability can be computed as follows. 5 The next result can be proved similarly using (2). …”

“…On the other hand, a weighted-f-out-of -n:F (G) system is equivalent to a * f -out-of-n:F (G) system if for all * 1 1 j f ≤ < − the sum of any j weights is less than k, and for all * f j n ≤ ≤ the sum of any j weights is at least k. Repeating the above arguments for weighted-f-out-of -n:F (G) system we get (5). (4) and (5) hold true.…”

Reliability and failure functions of some weighted systems

“…Wu & Chen [15][16] were the 1 st who studied such a system; they found the minimal cut sets of the system to compute the reliability of the linear and circular system. Chang et al [1] studied only the circular consecutive weight system and introduced a simpler and more efficient algorithm, while Eryilmaz and Tutuncu [7] provided recursive formulas for the reliability of consecutive weighted kout-of-n: F system. Nowadays, in the modern system, the industrials design electronic system under multiple functioning criteria; they combine various system models with each other to produce a more reliable system.…”

Financial view and profitability evaluation on multi-state weighted k-out-of-n:F system reliability

“…Eryilmaz and Yazgi Tutuncu (2009) propose a recursive formula to evaluate the reliability of consecutive weighted kout-of-n:F systems with binary components. Yamamoto et al (2011) used a recursive algorithm to estimate multi-state k-out-of-n:F systems.…”