Interval uneffectiveness distribution for parallel redundant reliability systems with repair

When designing a production system, the performances of a number of alternative system configurations are compared. An important performance measure, to which a lot of attention has been paid in literature, is the system long term uneffectiveness. This is defined as the long run fraction of the system capacity which cannot be used due to failure of the systems components. However, the stationary internal uneffectiveness distribution is a subject to which relatively little attention has been paid. This distribution represents the probability that the system uneffectiveness will not exceed some pre-specified level in a time interval of given length, when the system has reached statistical equilibrium. This performance measure is of great importance in practice, e.g. when some pre-specified production level has to be attained in a given time period in order for sales contracts to be met.