The Role of a Group of Modules in the Failure of Systems
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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The importance of a module in a system has been a useful concept in Reliability Theory. Several definitions of this concept are available. One such has been called the role of a module in the failure of a system. It is measured by the probability that the module has failed at the time of the failure of the system. In an earlier paper we studied interesting properties of this measure for a class of second order c-out-of-d systems. In this paper we consider the role of a group of modules. As before this is measured by the probability that at least s modules from this group of modules have failed at the time of the failure of the system, for s 1,2,.... We use the tools of arrangement increasing functions and majorization to study monotonicity properties of this measure in terms of the parameters of the system.
- Statistics and Probability