The Role of a Module in the Failure of a System
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
Pagination or Media Count:
Arrangement increasing and Schur functions play a central role in establishing stochastic inequalities in several areas of statistics and reliability. The role of a module in the failure of a system measures the importance of the module. We define the role to be the probability that this module is among the modules that failed before the failure of the system. A system is called a second order upsilon-out-of-kappa if it is a upsilon-out-of- kappa system based on kappa modules, without common components, and where each module is a alpha i-out-of-n i system. For such systems, we show that the role of a module is an arrangement increasing or Schur function of parameters that describe the system. These results allow us to compare the role of a module under different values of the parameters of the system.
- Statistics and Probability