  This paper proposes a new fuzzy assessing procedure with application in
management decision making. The proposed fuzzy approach build the membership
functions for system characteristics of a standby repairable system. This
method is used to extract a family of conventional crisp intervals from the
fuzzy repairable system for the desired system characteristics. This can be
determined with a set of nonlinear parametric programing using the membership
functions. When system characteristics are governed by the membership
functions, more information is provided for use by management, and because the
redundant system is extended to the fuzzy environment, general repairable
systems are represented more accurately and the analytic results are more
useful for designers and practitioners. Also beside standby, active redundancy
systems are used in many cases so this article has many practical instances.
Different from other studies, our model provides, a good estimated value based
on uncertain environments, a comparison discussion of using fuzzy theory and
conventional method and also a comparison between parallel (active redundancy)
and series system in fuzzy world when we have standby redundancy. When the
membership function intervals cannot be inverted explicitly, system management
or designers can specify the system characteristics of interest, perform
numerical calculations, examine the corresponding {\alpha}-cuts, and use this
information to develop or improve system processes.
