Repairable consecutive--out-of-: system with fuzzy states

Fuzzy universal generating functions for multi-state system reliability assessment

“…(11) and (12), respectively . The suggested approach is named as the fuzzy universal generating function (FUGF) technique.…”

“…According to (11) and the fuzzy arithmetic operations of the triangular fuzzy numbers [3,7], the subsystem probabilitỹ p i can be obtained as…”

“…., C h is in state t;ĝ ht is the value ofĜ h in state t; and (·) is defined as the product operator of fuzzy numbers by max-min convolution as shown in Eq. (11). After considering all non-leaf nodes, the FUGF representing the PD of the AMNN states can be obtained (U n−n * (z) = T n−n * t=1q n−n * t · zĝ n−n * t ).…”

“…[3] summarized the fuzzy set theory used in system reliability engineering up to the middle of 90th. Further developments of fuzzy set theory applications in the field of reliability engineering are presented in [11,32,37].…”

Fuzzy availability modeling and analysis of biscuit manufacturing plant: a case study

“…Kumar et al (2009) calculated fuzzy reliability and fuzzy availability of the serial process in butter-oil processing plant. Guan and Wu (2006) studied a repairable consecutive-k-out-of-n: F system with fuzzy states. The maintenance of the system is carried out by r repairmen or repair facilities.…”