Distribution of the lifetime of consecutive k-within-m-out-of-n:F systems |
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Authors: | Iyer S. |
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Affiliation: | Dept. of Stat., Bombay Univ.; |
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Abstract: | The distribution of the lifetime (MTTF) of any consecutive k -within-m-out-of-n:F system, with independent exponentially distributed component lifetimes, is shown to be a convex combination of the distributions (MTTFs) of several convolutions of independent random variables, where each convolution represents a distinct path in the evolution of the system's history, and where in each convolution all but the last random variable is exponential. The last random variable in each convolution is either a zero lifetime or the lifetime of several disjoint consecutive ki within mi-out-of-n:F systems in series with each ki<k, each mi<m, and each ni<n. This enables the calculations to proceed recursively. Calculations are facilitated by the symmetric nature of the convex combination |
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