Linear multistate consecutively-connected systems subject to a constrained number of gaps

• Published in: Reliability engineering & system safety Vol. 133; pp. 246 - 252
• Main Authors: Levitin, Gregory, Xing, Liudong, Dai, Yuanshun
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.01.2015; Elsevier
• Subjects: Applied sciences; Connection element; Constraints; Disengaging; Element reliability importance; Exact sciences and technology; Gap; Joints; Linear multistate consecutively-connected system; Mathematical models; Operational research and scientific management; Operational research. Management science; Optimization; Random numbers; Reliability; Reliability theory. Replacement problems; Sequences; Sequencing; Universal generating function; Connection element; Universal generating function; Reliability; Linear multistate consecutively-connected system; Gap; Element reliability importance; Statistical analysis; Probabilistic approach; Generating function; Dependability; Ordered set; Rupture; Interconnected power system; State space; System reliability; Failures; Modeling; Random number; Mass function; Sequencing
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2014.09.004

Linear multistate consecutively-connected systems (LMCCS) are systems that consist of a set of linearly ordered nodes with some of them containing statistically independent multistate connection elements (MCEs). Each MCE can provide a connection between its host node and a random number of next nodes along the sequence based on a known probability mass function. In traditional LMCCS models, the disconnection of any node causes the failure of the entire system. These models are too strict and thus not appropriate for some real-world applications such as those in sensor detection systems and flow transfer systems, which can tolerate a certain number of disconnected nodes referred to as gaps. In this work, we generalize the traditional LMCCS models by introducing a limited number of allowable gaps. The system fails if the number of gaps exceeds a specified limit. To analyze the reliability of the generalized LMCCS subject to a constrained total number of gaps, a universal generating function based method is first suggested. An optimal element sequencing problem is then solved considering that the system reliability can strongly depend on the sequence of different MCEs along the line. Examples are provided to demonstrate the proposed methodology. •New application motivated model of consecutive system is suggested.•An algorithm for system reliability evaluation is suggested.•Element importance analysis methodology is considered.•Optimal element sequencing problem is formulated and solved.