A limit theorem for the reliability of a consecutive-k-out-of-n system. (English) Zbl 0626.60086
Let a system consist of n linearly ordered i.i.d. components. The system fails if and only if at least k consecutive components fail. It is shown that for a fairly general class of component lifetime distributions, the system’s lifetime converges to a Weibull distribution as n converges to infinity.
An example demonstrates this convergence for component exponential distributions, and \(k=2\).
An example demonstrates this convergence for component exponential distributions, and \(k=2\).
Reviewer: V.Abel
MSC:
| 60K10 | Applications of renewal theory (reliability, demand theory, etc.) |
| 90B25 | Reliability, availability, maintenance, inspection in operations research |
| 62N05 | Reliability and life testing |
