chapter  10
15 Pages

## Signature Reliability of k-out-of-n Sliding Window System

ByAkshay Kumar, Mangey Ram

The sliding window system (SWS) is a generalized form of k-out-of-n:F system which has n linearly ordered multistate elements. Each window can 234have two states: completely working and totally failed. Application of SWS is found in quality control, service system, manufacturing, radar, and military system. Chiang and Nui [1] discussed the consecutive k-out-of-n:F system in cases when consecutive elements are failed and computed the reliability in lower and upper form. Levitin [2] discussed a linear multistate SWS, which is the generalized form of the consecutive k-out-of-r-from-n:F system, in case of multiple failure and evaluated the reliability of the considered system with the help of universal generating function (UGF). Koucky [3] evaluated the reliability of the k-out-of-n system with failure elements, and concluded that elements not need to be independent and identically distributed (i.i.d.). Levitin [4] considered a linear multistate multiple SWS, which is the generalized form of the linear consecutive k-out-of-r-from-n:F system, in case of multiple failures and computed the system reliability with the help of UGF. Habib et al. [5] discussed the reliability of a linear consecutive k-out-of-r-from-n:G system in case of multistate failure using the total probability theorem. Ram and Singh [6] considered a complex system with common cause failure and where each element could have constant failure rate. They determined the system reliability and cost analysis using the supplementary variable technique. Levitin and Ben-Haim [7] determined the reliability of a consecutive SWS using an algorithm based on the UGF technique; the considered system fails if the sum of the performance rate is lower than the total allocation weight. Levitin and Dai [8] discussed the reliability of linear m-consecutive k-out-of-r-from-n:F systems in case of multiple failure elements. Levitin and Dai [9] considered the k-out-of-n SWS in case of multiple failures and computed the reliability of the proposed system using UGF. Xiang and Levitin [10] generalized the linear multistate SWS which consisted of n linearly multistate windows. They evaluated the reliability of a combined m-consecutive and k-out-of-n SWS using the UGF technique. Ram and Singh [11] discussed the reliability, availability, and cost analysis of two independent repairable subsystems using the supplementary variable technique, Laplace transformation, and Gumbel-Hougaard family copula technique. Ram [12] discussed and reviewed the engineering system and physical science and provided different methods for computing system reliability. Pham [13] discussed the modeling of complex systems both hardware and software and calculated the reliability of the considered system. Negi and Singh [14] studied the non-repairable complex system which had two binary subsystems, namely, weighted A-out-of-G:g and weighted l-out-of-b:g and computed the reliability and sensitivity using UGF. Ram and Davim [15] measured the reliability of multistate systems, optimization of multistate systems, and continuous multistate systems using new computational techniques applied to probabilistic and non-probabilistic safety assessment.