Bounds for increasing multi-state consecutive k-out-of-r-from-n: F system with equal components probabilities |
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Authors: | Taha Radwan A HabibR Alseedy A Elsherbeny |
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Institution: | Dept. of Mathematics, Faculty of Science, Menofia Uni., Shebin EI Kom, EI Menofia, Egypt |
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Abstract: | The consecutive k-out-of-r-from-n: F system was generalized to multi-state case. This system consists of n linearly ordered components which are at state below j if and only if at least kj components out of any r consecutive are in state below j. In this paper we suggest bounds of increasing multi-state consecutive-k-out-of-r-from-n: F system (k1 ? k2 ? ? ? kM) by applying second order Boole–Bonferroni bounds and applying Hunter–Worsley upper bound. Also numerical results are given. The programs in V.B.6 of the algorithms are available upon request from the authors. |
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Keywords: | Lower bound Upper bound Multi-state consecutive k-out-of-r-from-n: F system Inclusion exclusion formula |
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