Signature reliability of linear multi-state sliding window system

<jats:sec> <jats:title content-type="abstract-subheading">Purpose</jats:title> <jats:p>The purpose of this paper is to deal with a linear multi-state sliding window coherent system which generalizes the consecutive <jats:italic>k</jats:italic>-out-of-<jats:italic>r</jats:italic>-from-<jats:italic>n</jats:italic>:F system in the multi-state case. The system has <jats:italic>n</jats:italic> linearly ordered multi-state elements consisting of <jats:italic>m</jats:italic> parallel independent and identically distributed elements. Every element of the system can have two states: completely working or totally failed. The system fails if the sum of performance rate is lower than the given weight.</jats:p> </jats:sec> <jats:sec> <jats:title content-type="abstract-subheading">Design/methodology/approach</jats:title> <jats:p>The authors proposed to compute the signature, MTTF and Barlow–Proschan index with the help of UGF technique of multi-state SWS which consists of <jats:italic>m</jats:italic> parallel i.i.d. components in each multi-state window.</jats:p> </jats:sec> <jats:sec> <jats:title content-type="abstract-subheading">Findings</jats:title> <jats:p>In the present study, the authors have evaluated the signature reliability, expected lifetime, cost analysis and Barlow–Proschan index.</jats:p> </jats:sec> <jats:sec> <jats:title content-type="abstract-subheading">Originality/value</jats:title> <jats:p>In this study, the authors have studied a linear multi-state sliding window system which consists of <jats:italic>n</jats:italic> ordered multi-state element, and each multi-state element also consists of <jats:italic>m</jats:italic> parallel windows. The focus of the present paper is to evaluate reliability metrices of the considered system with the help of signature from using the universal generating function.</jats:p> </jats:sec>