Transient behavior of time-between-failures of complex repairable systems

It is well known for complex repairable systems (with as few as four components), regardless of the time-to-failure (TTF) distribution of each component, that the time-between-failures (TBFs) tends toward the exponential. This is a long-term or steady-state property. Aware of this property, many of those modeling such systems tend to base spares provisioning, maintenance personnel availability and other decisions on an exponential TBFs distribution. Such a policy may suffer serious drawbacks. A non-homogeneous Poisson process (NHPP) accounts for these intervals for some time prior to steady-state. Using computer simulation, the nature of transient TBF behavior is examined. The number of system failures until the exponential TBF assumption is valid is of particular interest. We show, using a number of system configurations and failure and repair distributions, that the transient behavior quickly drives the TBF distribution to the exponential. We feel comfortable with achieving exponential results for the TBF with 30 system failures. This number may be smaller for configurations with more components. However, at this point, we recommend 30 as the systems failure threshold for using the exponential assumption.