Effects on system availability caused by non-exponential lifetimes

Summary

Reliability calculations normally assume exponential life- and repair times. The reasons are many, the most prominent of them might be mathematical simplicity and that the limiting availability is not dependent on the type of distributions for systems of independent components. This paper will discuss the effects caused by non-exponential distributions. The objective is a classification of systems and situations where the “exponential approximation” is not valid.

In order to avoid unreasonable complexity we consider repairable systems of identical and independent components with given life- and repairtime distributions. It is seen that the transient behaviour of the availability changes considerably with the distribution types. The monotonous form of the decrease to the limiting availability becomes oscillatory in some cases and in other cases it approaches the equilibrium from below. Generally, the time to reach equilibrium is considerably prolonged (a factor of 1000 is not unusual). This “time to relaxation” is taken as an important measure of difference and a simple approximate formula is derived giving an estimate of this “time to relaxation” for any system and life- repairtime distribution.