UDC 621
FUZZY RELIABILITY
EVALUATION OF TWO-STAGE
FUZZY WEIGHTED-K-OUT-OF-N SYSTEMS HAVING
COMMON COMPONENTS © Shshank
Chaube G.B. Pant University of Agriculture & Technology,
Pantnagar,
Uttarakhand, India S.B. Singh G.B. Pant University of Agriculture & Technology,
Pantnagar,
Uttarakhand, India Abstract. <...> This paper introduces a new
term namely
fuzzy weighted-k-out-of-n
system and studies the
fuzzy reliability of
two-stage fuzzy weighted-k-out-of-n
model having common components following triangular
membership function. <...> Methods are developed to find the
system fuzzy reliability and the
minimal cuts and
minimal paths for two-stage fuzzy weighted-k-out-of-n
systems have been generated. <...> Two types of two-stage fuzzy weighted-k-out-of-n models, the Series Fuzzy Weighted (SFW)-
k-out-of-n model, and the Parallel Fuzzy Weighted (PFW)-
k-out-of-n model, have been applied to evaluate fuzzy reliability in
network applications (
project management, and the shortest
path problems). <...> Keywords:
fuzzy reliability,
minimal cuts,
minimal paths, triangular
fuzzy number, two-stage
fuzzy weighted-k-outof-n model. <...> The foundation for
fuzzy approach is constituted by the fundamental works on
fuzzy set theory of [10]. [7] proposed the theory of
fuzzy reliability in the possibility context, [11], [9] introduced methods for
fuzzy reliability analysis. [8] presented a
fuzzy set based approach to failure rate and
reliability analysis. [2] used triangular
membership function to evaluate
fuzzy reliability. <...> A triangular
fuzzy number A is a
fuzzy number, denoted by A=<a1, a2, a3> and having
membership function where ws 3, …n. . <...> The
k-out-of-n model was first proposed by [1, 9] and [10] gave algorithms to evaluate the reliability of
k-out-of-n system. <...> Weighted-k-out-of-n model is an extension of the
k-out-of-n model firstly introduced by [16]. <...> For a weighted-k-out-of-n: F system, an integral
weight wi >0 is assigned to component i. <...> The system is in functioning state if the
total weight of the failed components is less than a pre-specified value. <...> In earlier studies weight is taken as a crisp
number and then
fuzzy reliability of system is calculated. <...> This study differs from the earlier studies in the sense that here, weight is considered as a fuzzy number and we named the system <...>