Lower and Upper Reliability Bounds for Consecutive- -Out-of- : Systems


Once a comprehensive review of reliability bounds for consecutive- k-out-of- n: F systems with statistically independent parts having the identical failure likelihood q (i.i.d. elements), we have a tendency to introduce new classes of lower and upper bounds. Our approach is totally different from previous ones, and depends on alternating summation and on the monotony of some explicit sequences of real numbers. The starting point is represented by the initial formula given by de Moivre; and, by considering partial sums approximating it, new lower and higher bounds on the reliability of a consecutive- k-out-of- n: F system are established. Simulation results show that each one the lower and higher bounds considered here present terribly similar behaviors, as they all are exponentially closing in on the exact reliability of a consecutive- k-out-of- n: F system. Additionally, the accuracy of the different bounds depends not solely on the particular values of k and n, however conjointly on the particular vary of q (some of the new bounds being the most correct ones over sure ranges).

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