Reliability of linear multistate multiple sliding window systems

This paper proposes a new model that generalizes the linear consecutive k ‐out‐of‐ r ‐from‐ n:F system to multistate case with multiple failure criteria. In this model (named linear multistate multiple sliding window system) the system consists of n linearly ordered multistate elements (MEs). Each ME can have different states: from complete failure up to perfect functioning. A performance rate is associated with each state. Several functions are defined for a set of integer numbers ρ in such a way that for each r ∈ ρ corresponding function f r produces negative values if the combination of performance rates of r consecutive MEs corresponds to the unacceptable state of the system. The system fails if at least one of functions f r for any r consecutive MEs for r ∈ ρ produces a negative value. An algorithm for system reliability evaluation is suggested which is based on an extended universal moment generating function. Examples of system reliability evaluation are presented. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.