Consecutive -within--out-of-:F System with Nonidentical Components

As a generalisation of consecutive 𝑘-out-of-𝑛:F and 𝑘-out-of-𝑛:F system models, a consecutive 𝑘-within-𝑚-out-of-𝑛:F system consists of 𝑛 linearly ordered components and fails if and only if there are 𝑚 consecutive components which include among them at least 𝑘 failed components. In this paper, we study the survival function of a consecutive 𝑘-within-𝑚-out-of-𝑛:F system consisting of independent but nonidentical components. We obtain exact expressions for the survival function when 2𝑚≥𝑛. A detailed analysis for consecutive 2-within-𝑚-out-of-𝑛:F systems is presented and the asymptotic behaviour of hazard rate of these systems is investigated using mixture representations.

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