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On System Reliability of Increasing multi-state linear k-within-(m,s)-of-(m,n):F lattice system
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Department of Mathematics and Statistics Port Said University Port Said, Egypt
Publication date: 2018-03-31
Eksploatacja i Niezawodność – Maintenance and Reliability 2018;20(1):73–82
A “multi-state linear k-within-(m,s)-of-(m,n):F lattice system” (MS L(k,m,s,n:F)) comprises of m×n components, which are ordered in m rows and n columns. The state of system and components may be one of the following states: 0, 1, 2, …, H. The state of MS L(k,m,s,n:F) is less than j whenever there is at least one sub-matrix of the size m×s which contains kl or more components that are in state less than l for all j ≤ l ≤ H. This system is a model for many applications, for example, tele communication, radar detection, oil pipeline, mobile communications, inspection procedures and series of microwave towers systems. In this paper, we propose new bounds of increasing MS L(k,m,s,n:F) reliability using second and third orders of Boole-Bonferroni bounds with i.i.d components. The new bounds are examined by previously published numerical examples for some special cases of increasing MS L(k,m,s,n:F). Also, illustration examples of modelling the system and numerical examples of new bounds are presented. Further, comparisons between the results of second and third orders of Boole-Bonferroni bounds are given.
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