A two-unit parallel system supported by (n − 2) standbys with general and non-identical lifetimes

This paper examines a functioning policy of a parallel system. We assume availability of n non-identical, non-repairable units for replacement or support. Two units start their operation simultaneously at times , and any one of them is replaced instantaneously upon its failure by one of the ( n − 2) standby units at random starting times Si ( ). Thus, with probability one, the system is functioning with two units up till the failure of the ( n − 1)th unit. Unit lifetimes Ti have a general joint distribution function F( t ). The system has to operate 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. The reliability of the system is evaluated by recursive relations. Independent unit lifetimes are considered as special cases.

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