Computing marginal and joint Birnbaum, and Barlow–Proschan importances in weighted-k-out-of-n:G systems

Reliability Modeling on Consecutive-<inline-formula> <tex-math notation="LaTeX">$k_r $</tex-math> </inline-formula>-out-of-<inline-formula> <tex-math notation="LaTeX">$n_r $</tex-math> </inline-formula>:F Linear Zigzag Structure and Circular Polygon Structure

“…Eryilmaz and Bozbulut [16] reviewed that the JRI of component i and j can be calculated by (2) and used it to study the JRI for weighted-k-out-of-n:G systems. For more research on JRI, one can refer to Eryilmaz [15], Zhu et al [45], Armstrong [4], Hagstrom [22], Hong and Lie [23], Yao et al [39] …”

“…, m − 1) affects the patterns of line r and r + 1. However, when using (6)- (16) to calculate the reliability of line r + 1 with different patterns, we need to ignore the working or failed probability value of component n r because it has been calculated in line r. Therefore, we modify (6)-(16) as (18)- (28), where the superscript of R represents the number of lines; the subscript of R stands for Patterns (a)-(h); the dimension of π 0 , π 1 and U is 1 × |k r + 1|; the dimension of Λ i is |k r + 1| × |k r + 1| …”

Importance of components in k-out-of-n system with components having random weights

“…. , n and k = 1, the system is reduced to weighted-c-out-of-n system, which was introduced in [3] and studied by Higashiyama [4], Chen and Yang [5], Samaniego and Shaked [6] and Eryilmaz and Bozbulut [7]. If k = 1, the system is a weighted-c-out-of-n system with components having random weights.…”

“…Eryilmaz and Bozbulut [7] studied the importance of components in a weighted-c-out-of-n system with respect to Birnbaum marginal and joint reliability importance measures and Barlow-Proschan lifetime importance measure. They used numerical calculations to show that the ranking of the importance of components in a weighted-c-outof-n system depends on the weight of components in addition to their reliabilities or lifetime distributions.…”

Stochastic comparisons of total capacity of weighted-k-out-of-n systems

“…The components 1 importance of weighted-k-out-of-n systems has been studied by Eryilmaz and Bozbulut (2014) and Rahmani et al (2016). 2 Eryilmaz and Sarikaya (2014), because of complexity of the stochastic model, obtained a closed form of survival function 3 of T T w for the case when the components and weights are only of two types.…”