Scheduling starting times for an active redundant system with non-identical lifetimes

Here we examine an active redundant system with scheduled starting times of the units. We assume availability of n non-identical, non-repairable units for replacement or support. The original unit starts its operation at time s1 = 0 and each one of the (n 1) standbys starts its operation at scheduled time si (i = 2, . . .,n) and works in parallel with those already introduced and not failed before si. The system is up at times si (i = 2, . . .,n), if and only if, there is at least one unit in operation. Thus, the system has the possibility to work with up to n units, in parallel structure. Unit-lifetimes Ti (i = 1, . . .,n) are independent with cdf Fi, respectively. The system has to operate without inspection for a fixed period of time c and it stops functioning when all available units fail before c. The probability that the system is functioning for the required period of time c depends on the distribution of the unit-lifetimes and on the scheduling of the starting times si. The reliability of the system is evaluated via a recursive relation as a function of the starting times si (i = 2, . . .,n). Maximizing with respect to the starting times we get the optimal ones. Analytical results are presented for some special distributions and moderate values of n. 2005 Elsevier Inc. All rights reserved.