RENEWAL THEORETICAL APPROACH TO THE MISSION RELIABILITY OF A REDUNDANT REPAIRABLE SYSTEM WITH TWO DISSIMILAR UNITS

A system consisting of two dissimilar, redundant, repairable units is considered. We shall say that a major breakdown occurs in the system when both units fails. The system fails if one unit under repair is not repaired within a fixed time measured from the instant at which major breakdown occurs, or if the number of major breakdowns during the mission period exceeds a fixed number. As a special case, this number is allowed to be " infinite ". The Laplace transforms of the reliability and the mean time to system failure are derived, and the explicit formulas in the special cases are exhibited. § 1. Model definition. 1. The system consists of two dissimilar redundant units Al and A2. 2. There is only one repair station. When one unit fails, its repair begins at once, and when two units fail simultaneously, unit Ai is sent for repair with a specified constant probability ai, i= 1, 2, where cr1-Fa2=1. Concerning failure and repair we assume the following : 3. When the two units are good, unit-failures occur as three independent Poission processes with failure rates 21, 22 and 212. Events in the process with rate Ai cause failure of unit Ai only, and events in the process with rate 212 cause simultaneous failure of unit Al and A2. 4. When only one unit, Ai is good, failure of the unit is Poisson with rate 2/i 2i. 5. The repair time for each unit, Ai is independently distributed with general probability density function f i(t), but must be well behaved enough for the appropriate analytic operations to be performed. 6. The failure and repair processes for the two units are entirely independent. 7. The repaired unit is considered to be new again. * This research was supported by the Science Research Council under Grant No . 4349/00. ** Sheffield University , Sheffield and Osaka University, Osaka. *** Gifu University , Gifu.